OR at Work

Losing weight fact based

2012-01-04T18:06:00.000+01:00

Made any New Year resolutions this year? What’s your #1 on the list? I bet it is losing weight. In the Netherlands it is the number one resolution for 2012 and I expect in many other countries as well. Research from ING Banking & Insurance indicates that about 80% of the Dutch have made New Year resolutions this year. By equating the fulfillment of a resolution to an economic value ING was even able to calculate that on average the Dutch would give €450 to keep their resolution, resulting in a total economic value of €4.5 billion in the Netherlands alone. Given the economic crisis we are in, a serious amount of money. To stimulate keeping the resolution, maybe the government could introduce a tax in case of failure. This could be a very interesting idea, since not many of us seem to be able to keep our resolutions. To illustrate, 88% will fail to stop smoking, 95% will keep the same weight or even gain weight.

So you want to lose weight, but how much? One way of making that estimate is to use the Body Mass Index. It is a much used number in the medical profession to measure if you’re overweight. It divides your weight in kilograms by the square of your length in meters. So if you’re 1.86 meter tall and weigh 92 kg, a BMI results of 26.6. A BMI score lower than 18.5 kg/m2 implies underweight, above 25 kg/m2 overweight. Interesting to note is that the BMI would put Schwarzenegger (in his Conan years, 1.83 m tall and about 107 kg) in the serious overweight category. I can’t imagine that to be correct. Let’s take an analyst view at this way of assessing overweight.

To calculate the BMI, only height and weight are required. Would that be enough to decide if a person is overweight? It’s important to know that the density of fat is less than that of muscle which in turn has a smaller density than bone. In other words, the less fat you have, and the more your body is made up of muscle and bone (meaning you’re a fit person), the greater the numerator in the BMI formula, and therefore the higher the BMI. So when you start to exercise to lose weight and build up muscle, you will be worse of according to the BMI. This can’t be right, the BMI model must be wrong.

The concept of BMI is the work of a Belgian mathematician, Adolphe Quetelet . He was one of the first to use statistics to draw conclusions about society. He published his "Quetelet Index" in 1832, later known as BMI. Quetelet had no interest in studying overweight when he developed his index. His main interest was to apply probability calculus to human physical characteristics which led him to develop the BMI formula. He found that during normal growth, weight tends to increase in relation to height in meters squared. So for a population as a whole, the BMI is an easy to calculate number that helps study weight issues. There is no rationale or medical evidence that explains why the model is right on indicating whether you are overweight or not. So the BMI was initially developed to measure a societally trend, not as a diagnostic tool to draw conclusions on an individual level. But that is the way in which it is now used, even by doctors. Statistical speaking, that’s rubbish.

So if not the BMI, than what indicator should you use to determine the weight you should lose? You could take a look in the mirror, or ask your partner. But for sure these are not very objective measures. So maybe the best measure is to put on your favorite jeans and feel if they still fit, not to tight. That probably is the best model to use to optimize your weight. Keeping your resolution will also become easier, because buying a complete new wardrobe will probably cost you more than €450.

Optimizing the Human Resource Supply Chain

2011-12-30T20:34:00.000+01:00

Reading the various outlooks for the coming year, I came across the Manpower Employment Outlook for 2012. Interesting statement from the report is that although employers are more inclined to hire new personnel there continues to be uncertainty about the market, so they are reluctant to make the investment in a permanent hire. At the same time employers also have trouble filling vacancies for specialist jobs like technicians, sales people, skilled trade workers and engineers, as indicated by another report from the same agency. This makes balancing the demand and supply of human resources a though job. Overstaffed units will put pressure on the EBIT because of too high cost levels, while understaffed units will suffer from service degradation or loss of revenue. However, when companies link their strategic workforce planning with their business planning the workforce productivity can be optimised which will result in a decrease the total cost of human capital, while maintaining or increasing the overall quality of their workforce and customer service.

Effectively managing demand and supply for human resources requires a structured planning process, starting with a forecast of the demand for human resources as derived from the business planning. Next the supply of resources needs to be forecasted. Since people change jobs, retire, get hired or fired available human capital will change over time, dynamics that need to be taken into account in strategic workforce planning. Matching the forecasted demand and supply for human resources indicates where shortages of overages can be expected. Making a choice on the instruments for adjusting human resource supply a company can than take appropriate action to establish the best possible balance between supply and demand. In this process the HR manager can benefit a lot from the Operations Research models in making these decisions fact based.

When comparing the dynamics of human resource capacity in supply chains with other resources in the supply chain you will see that human resources are different. The dynamics of other resources are mostly restricted to ordering, whereas human resources have a wide variety of characteristics which all influence the availability of human resources over time. To name a few; acquiring new skills, productivity increases due to learning, change of role/function and getting hired or fired. These characteristics will influence the available resource capacity and cause forecasting resource availability to be difficult. Operations Research offers all kinds of methods to incorporate these dynamics, improving the quality of forecasted availability. For example, stochastic loss network models or somewhat simpler the Markov approach as described in my The OR in HR blog entry. The parameters of these models, for example transition probabilities, need to be estimated based on the data in the HR systems and can best used together with subject matter experts to incorporate factors that are not present in the available data. These models than can be used stand alone or for optimisation purposes, like in deciding on the most cost effective capacity deployment.

In long term capacity planning it is decided how to deploy the expected available capacity, which is not straightforward to accomplish. Human resources differ from ‘normal’ resources since they are not consumed in the make process (they deliver a service) and productivity and efficiency depends upon their workload and utilization (Parkinson’s Law and the Student Syndrome in action?). Also human resources can perform more than one skill at a time and doing so across multiple assignments. In the service industry, like in Operations Research consulting and IT services, the process of assigning people to tasks/roles is further complicated by simultaneous allocation of multiple resources and resource sharing over assignments. I know from own experience that making a long term capacity plan for my team is a hard. Assignments simply don’t start when you would want them to start leading to over-utilized or underutilized consultants. Also you want assignments to fit with the capabilities of the consultant and stimulate the development of new capabilities and knowledge. The right assignment for that is not always available. To complicate things even more, both demand and supply for human resources are uncertain. In long-term capacity planning the exact assignment of resources to projects or tasks is not required. What is needed is to verify if there is enough capacity to satisfy demand or master plan. One way to answer that question is by making a rough cut capacity plan, RCCP. Usually this requires formulating and solving a mixed integer linear program. The RCCP will indicate if the master plan can be satisfied (is it do-able?) and what are possible bottlenecks and mitigation actions when the master plan changes, for example due to changes in demand.

Operations Research will improve managing the balance between supply and demand for human resources significantly. It allows for the incorporation of the dynamics of human resources in the decision making, resulting in better quality and fact based decisions. It will support management in making a choice on the instruments for adjusting human resource supply on the longer term optimizing the human resource supply chain.

The incredible balancing act of Unsold and OutOfStock

2011-11-06T16:56:00.002+01:00

Inventory managementis one of the key factors determining the performance of a supply chain. A smallchange of the inventory policy can lead to a dramatic alteration of the supplychain’s efficiency and responsiveness. Traditionally inventory management ischallenging because it directly impacts both cost and service. Uncertain demandand uncertain supply make it necessary to hold inventory at certain places inthe supply chain to provide adequate service to customers. As a consequence,increasing inventories will increase customer service and revenue, but also increasescost. According to the 22^nd annual state of logistics report (pdf), the world is sittingon roughly $8 trillion worth of goods held for sale, and nearly $2 trillion inthe U.S. alone. That's a lot of capital tied up in warehouses. Besides being ahuge capital absorber, inventory also represents a tremendous amount ofenvironmental footprint. If we could permanently reduce the amount of productsitting idle, we'd save money, energy, and material.

Effectiveinventory management is very hard. A recent article in the Financial Times illustrates this. Following theearthquake in Japan, many tech companies started to stockpile critical componentsto avoid shortages later on. However, unexpected low customer demand in US andEurope resulted in tremendous inventory levels. The components for which it wasexpected that there was a risk of shortage are now having the biggest problems interms of oversupply. Deciding on the right level of inventory therefore is an incrediblebalancing act of unsold and out of stock where Operations Research can be yourbalancing pole supporting you in making the trade-off.

Toillustrate, the above figure shows three warehouses and four customers. Thesupply chain manager has to decide how much stock to keep at each of thewarehouses and which customer to serve from which warehouse. Stock keeping costis given for each warehouse. Transportation cost is presented in the tablebelow.

The supplychain manager is uncertain about customer demand but has to decide immediately onthe number of stock keeping units at each warehouse, otherwise the availablefloor space will be leased to another company. He decides to go for the averagedemand. Using his MBA skills he optimises for minimal supply chain cost(warehouse and shipping cost) and decides to have 6215 SKU at warehouse 1 and3000 SKU’s at warehouse 3. Perfect, ….or could he have done a better job?Actual demand will deviate from the average demand (average doesn’t exist, doesit?) leaving the supply chain manager with either unsold stock like in theexamples above or lost sales (on average 431 of either unsold or lost sales given the demand scenarios). Would minimizing forlost sales be a better option? Total supply chain cost will rise for sure,possible also increasing the level of unsold stock. Here Operations Researchcan be of assistance to find a balance. Using the available demand scenario’s(min and max in this case) the average total supply chain cost can bedetermined while varying the level of average lost sales (see graph below). Note that the supply chain cost of the averagedemand is not the same as the average supply chain cost of the demand (the flaw of averages!).

This waythe supply chain manager can make the trade off between supply chain cost and lost sales leading to better quality decisions. He/She can use thisinformation to share with all players in the supply chain, like marketing and sales, production and procurement, building a shared view and plan. OperationsResearch will help find the balance between Unsold and OutofStock and keep it when incorporating deviations from forecasted supply and demand, enabling you to practiceSales and Operations Planning fact based.

Deciding on Lean or Green

2011-10-04T21:29:00.000+02:00

Imagine getting into your car, entering your destination into the satellite navigation system and getting not only the two obvious options for the shortest or fastest route, but also the most sustainable one. What would you think of that? Calculating the shortest or fastest route is easy from an Operations Research perspective, just use Dijkstra’s shortest path algorithm. How about the most sustainable one? Whether a route is sustainable or not depends on many factors; maximising sustainability therefore is different from minimising travel time or distance. There is however a linear relationship between fuel consumption and CO2 emissions. So when fuel consumption can be taken into account, optimising for the most sustainable route would become possible. That is exactly what two of my colleagues at ORTEC, Goos Kant and Patrick Schittekat, did when researching the net effect of focussing on sustainability in logistics.

Fuel consumption is influenced by factors like engine type and aerodynamics of your car, the type of fuel used, traffic density, variance in driving speed, the weather and not to mention your driving habits. Some of these factors can be modelled easily while others, like the weather, are more challenging. Research as reported by UK’s National Atmospheric Emissions Inventory (NAEI) shows that CO2 emission levels can be expressed as a function of vehicle type, fuel type and engine type and of course speed. So when we know these parameters, we are able to calculate emission levels.

In calculating an optimal route, a digital road network is required. Companies like NavTeq and AND provide these maps. A digital road network consists of points and segments connecting these points, representing the road network in the real world. The segments are of different types, representing different road types each with a different speed. Think op motorways, regional roads, local roads and city areas. Given the length of each segment and speed of a vehicle on each of the segment types, the shortest and fastest route can be calculated. An interesting new development is that more and more information is added to digital networks, like the time/day dependent average speed at which these road segments have been travelled, allowing for a better estimation of actual travel time and therefore speed.

Using the formula for CO2 emission levels, the sustainability cost for each segment in the road network can be calculated, using the travel times reported in the digital network segments. Using Dijkstra’s algorithm, the most sustainable route (lowest emission levels) between each point in the network can be calculated and a comparison can be made with the shortest and the fastest routes. Research of my colleagues Goos and Patrick indicate that the greenest route is about 5% slower than the fastest, while the shortest is 35% slower. Also the greenest route is 2% longer than the shortest, while the fastest route is about 6% longer. Comparing on costs (using social cost per ton CO2 as reported by DEFRA and associated cost for vehicle and driver) the greenest route is about 1% more expensive than the fastest, while the shortest is 17% more expensive. So in short taking the green road home is only slightly slower and costs a little bit more than the fastest (time is money after all).

In logistics making the trade off’s between lean or green isn’t common yet but will change in the near future. A example of this trend is the special programme (Sustainable Logistics) in which Dutch companies have committed themselves to achieve a 20% reduction in CO2 emision levels by the end of 2012. Incorporating emission levels in logistic optimisation models will help create insight and guide companies towards more sustainable choices. By the way, focussing on efficiency (cost reduction) will also lead to more sustainable solutions. Driving less kilometres because routes have been optimised by changing the order in which customers are visited or changing the assignment of customers to routes will directly lead to reduced emission levels. So not Green or Lean but Lean & Green!

Distinguishing the Good from the Bad

2011-09-25T19:53:00.000+02:00

In my work toassist companies in improving their decisions making, adding mathematicalrigour and making it fact based, sooner or later my client remarks that nowthat Operations Research is used the quality of decisions must have improved. It’stempting to confirm that, but that would be too single minded. While usingOperations Research will have a positive influence on decision quality, it isonly one of many factors in high quality decision making. In judging thequality of a decision we typically equate decision quality with the attractivenessof the result. Don’t you feel silly whenyou’ve carried around your umbrella all day but there wasn’t a drop of rain toshield you from? What does it say about the quality of the decision you madethat morning? Is good or bad determined by the result? And what does it tellyou about the added value of the decision methodology you used in making thedecision?

When we havea good result we are inclined to conclude that we’ve made a good decision. Likewise, with a bad result, we conclude thatwe’ve made a bad decision. This is definitely not true. Decisions and resultsare two different things. Good resultsare what we desire, whereas good decisions are what we can do to maximise thelikelihood of good results. For decisions that are made at a high frequency(say every day/hour) quality could be measured using statistics, improving consecutivedecisions. The conditions under which operational decisions lead to a result canonly change slightly, given the short time span between the two. But for decisionson the tactic or strategic level it can take months or even years beforeachieving a result, for example in developing a new product. Using statisticsto measure decision quality in that case is unrealistic. Moreover many of thiskind of decisions are of the one-of-a-kind nature. When the time betweendecision and result increases, uncertainty will have a growing impact on thequality of the result. In the future, events can happen that cannot be controlledor foreseen. Such events can cause gooddecisions to have a bad result and vice versa. Therefore, the quality of the result is not a good indicator of decisionquality and the result is irrelevant as a measure of decision quality.

How toassure good decisions then? Key in making a good decision is to have astructured decision making process. A structured decision making process startswith three ingredients:

What do I know (Information) aboutthe business opportunity under consideration and the environment in which itresides?
What are the options (Alternatives) opento me?
What are my preferences (Values) indeciding between the alternatives?

Central ina structured decision making process is the logic or mathematical model. Itallows you to put Information, Alternatives and Values together in a logicallyconsistent way and make a good decision.

Because the inputs of the decision aremade explicit we can establish that a good decision has been made, before theresults of the decision are known. It allows discussion on all the inputs, thereforebuilding a common view and commitment, supporting the implementation of thedecision. Notice that the logic follows from all three factors, Information,Alternatives and Values. So Logic alone is not a guarantee to qualitydecisions. Putting this process to work startswith framing the decision; making sure that purpose and scope of the decisionis discussed and agreed upon. Next is identification of what can change andcan’t be changed in making the decision, creating an explicit or implicit setof alternatives. As Michael Trick blogs, accurate data is essential in achieving high qualitydecisions. Without it, decisions are based on quicksand. It’s the thirdingredient in the decision making process. Final step before preparing a mathematicalmodel is deciding on the valuation principles to be used. A decision is madebecause it will lead to an increase in value within an organisation, like increasein share price, revenue or EBIT. So valuation needs to be explicitly consideredin decision making. With all these ingredientsin place and managed right, good decisions will results.

So nexttime when you return home soaking wet because you left your umbrella at homegiven the weather forecaster was absolutely sure that it was going to be asunny day, go back and review your decision making process that morning. Checkthe information base, the alternatives considered, the values and logic usedbefore you consider yourself a fool. Chances are that it wasn’t a bad decision.The result was bad, but that’s because you can’t trust a weather forecaster. Somethings can’t be changed; it’s your decision to prepare for them or not thatmakes your decision good or bad.

Complexity Defied

2011-08-15T18:01:00.003+02:00

A recent survey of KPMG among senior executives around the globe (Confronting Complexity, 2011) shows that the ability to manage today’s complex business issues is seen as one of the key factors for success. Complexity in business has increased over the past years because of changes in economic, regulatory, political and social environments. Also its causes change as companies move through the business cycle and as economies develop. Increased complexity leads to cost increases and the need for new skills within an organisation. Besides being an important challenge, the senior executives find that increased complexity also creates new opportunities, including gaining a competitive advantage and improving efficiencies. Interesting result from the survey is that technology is a critical issue, both as a cause of complexity and a key solution. New technology changes business models, enables process improvements and opens new markets, but also creates new challenges like how to incorporate it into every day business. Operations Research is one of those new technologies. It requires effort to incorporate it into the decision making DNA of your organisation, but when available it lets you defy complexity.

Operations Research has proved to be the best answer to handle complexity many times. A well known example is the way in which American Airlines used Operations Research to turn the effects of the Airline Deregulation act into an opportunity, changing the way the airline industry operated completely. Comparable to this, the Dutch based Sundio Group reinvented the online travel business with the application of Operations Research. Key for success at Sundio is to offer the best price for flight seats, hotel rooms and package trips. Finding the best price is complex, because Sundio must buy capacity at hotels, resorts and airlines before the can sell it to their customers. Because of the uncertainty in demand and the great amount of products in their portfolio, deciding on the best possible price mix is complex. A dedicated decision support system with optimisation algorithms was build to support Sundio in handling this complexity and turned it into a competitive edge.

Recently Midwest ISO, together with Paragon decision technology, won the Edelman award for their achievements in handling the complexity of the production and transportation of electric power. Midwest is responsible for the delivery of electric power across 14 US states and the Canadian province of Manitoba. In doing so it has to manage over a 1.000 power plants and nearly 60.000 miles of high voltage transportation lines to deliver electric power to 40 million end user customers. According to Midwest, the network is the most complex machine ever created by man. Due to changes in regulation, requiring open access to network transmission lines, Midwest transformed the electric utility industry in the Midwestern United States through the development and implementation of energy and ancillary services markets. Since electric power can’t be stored, Midwest needs to carefully balance supply and demand of electric power each moment in time. Changes in demand must be dealt with immediately by adapting the supply of electric power within the technical capabilities of the whole system. In order to do so Midwest has to solve a dazzling puzzle with millions of decision variables each 5 minutes. With the decision power of Operations Research, made available to decision makers across the Midwest network via the use of AIMMS, Midwest was able to achieve that. As a result Midwest ISO adds significant value to the region through improved reliability and increased efficiencies of the region’s power plants and transmission assets. It has been estimated that Midwest realized a cumulative saving from 2007 through 2010 of at least $2.1 billion.

So in confronting complexity, senior management need not despair. As the KPMG survey concludes, technology is a hot-spot. With the decision power of Operations Research available, senior management has the possibility and capability to improve or even change business models, open up new markets and electrify business performance, defying complexity.

Modelling Magic

2011-06-30T20:26:00.006+02:00

In his third law Arthur C. Clark states that any sufficiently advanced technology is indistinguishable from magic. So, in some cases at least, magic doesn’t derive from an actual mystical or spiritual source; rather, it is technology in disguise. When we would be able to send a car a couple of ages back in time, driving our horseless carriages probably would have created a witch hunt. Not to mention flying an aircraft. Time travelling over shorter distances; our computer networks and phones that can do nearly everything must seem magic for someone living in the late 1960’s. So Arthur C. Clark is probably right. What does it imply for Operations Research? Is it sufficiently advanced technology to be indistinguishable from magic? Initiated only a few decades ago in World War II, Operations Research has enabled us to achieve some remarkable things that to the non-initiated seem to be magic. It has enabled us to solve the unsolvable and step by step it is entering our daily lives becoming an indispensable piece of technology, doing its magic every day.

The simple task of assigning activities to people can become very complex and unsolvable for a human. For small instances it’s a simple puzzle. In case of 2 activities and 2 people there are only 2 possible assignments. Deciding which one is best is therefore easy. But when the size of the instance increases, the number of possible assignments explodes which makes it impossible to find the best possible assignment. In optimising the assignment of 70 activities to 70 people, there are 70! different assignments to be evaluated. Constructing all of the 1.19785717 × 10¹⁰⁰ assignment possibilities would take forever. How to find the best possible one? Here is where Operations Research does its magic. One of the first optimisation techniques developed within Operations Research is the simplex method. It was discovered by George Dantzig in the late 1940’s and it still plays a very central role in Operations Research. With the simplex method the best possible assignment of 70 jobs to 70 people can be found within a few minutes or even seconds. Compared to what a human can do, this for sure is magic.

When we fast forward to our current era, Operations Research applications arise everywhere; in Finance & Accounting, Marketing, Procurement, Production management, Logistics, Personnel management, Government, Sports, etc, etc. It has become a deciding factor for companies to survive or become top players in their market. One of the areas where Operations Research has become a deciding factor is in the airline industry. In 1978 the Airline Deregulation act was signed, its purpose was to remove government control over commercial aviation. As a consequence competition increased with low-cost carriers seizing their opportunity to get a share of the commercial aviation market. The exposure to competition led to heavy losses for a number of carriers, some of them even went bankrupt. To counter low-cost airlines like People Express, several strategies were developed by the main carriers. American Airlines (AA) was the most successful one; using Operations Research they developed a pricing strategy now known as Revenue Management or Yield Management. According to AA it is “the single most important technical development in transportation management”. The essence of Yield Management is to use price to influence customer demand. As a consequence the price for a passenger seat may vary over time. This explains why the price for the same flight may vary between two visits to a booking site, leaving you clueless on the reason why. As if the airline uses a spell to maximise revenue. But because of this magic, we can fly cheap.

Operations Research is entering our daily lives more and more. It is responsible for the fact that we:

have highly reliable electricity and gas supply networks,
can use the internet,
are able to develop reliable public transport schedules,
have attractive soccer match schedules
are able to operate global supply chains,
have satellite navigation,
can manage the risks of pension funds,
have effective cancer treatments
etc

It’s all possible because of Operations Research. It doesn’t matter if you understand why it is possible, just use it. Sit back and enjoy, let it do its magic!

Solving a Mayor’s dilemma; fact based environmental policy development

2011-06-26T20:37:00.008+02:00

This week Rotterdam, one of the major cities of the Netherlands, was on the news. The city’s Court of Audit had analysed the city counsel’s policies on improving the environmental conditions of the inner-city and concluded that things weren’t going great. Rotterdam has set itself emission reduction goals, but with the selected policies it wasn’t going to achieve them according to the Court of Audit. The Court even concluded that the situation was getting worse. Compared to 2009 the number of hot spots on NO₂-emissions in the city has increased from 1 to 5 making the city a less healthy place to be in. The city council however is still convinced that they will achieve the goals set for 2015. Until now however, several countermeasures have been introduced with little or no effect on the air quality in the inner-city. One very drastic way to accomplish emission reductions would be to close down several parts of the inner-city; this would however impact the local economy heavily. Quite a dilemma for Mayor Aboutaleb.

Major part of the air pollution in inner-cities comes from the vehicles doing last mile distribution. Think of the replenishment of shops and stores but also of bars and restaurants. Many of them use a Just-in-time (JIT) based replenishment strategy, increasing the number of vehicle visits while reducing the drop size. JIT minimises the inventory levels in the shop and hence reduces costs. Counter side of it is that the inner cities become congested with vehicles and the emission levels rise. So, reducing the number of vehicles and/or the total distance travelled by those vehicles will lower emission levels and therefore improve air quality. Easy, thing is how to set a reasonable enough level of emission reduction to improve living conditions in the inner-city without harming economic activity and second decide on the necessary measures to achieve it.

It has been the subject of a project that I have been working on in the past months. Objective of the project was to provide decision support to the municipality of cities in deciding on logistical measures to better regulate inner-city logistics and reduce emission levels. One of the objectives of the project was to supply insights on the current sustainability of a city and assist in setting reasonable emission reduction goals. The project resulted in a mathematical model that supports these decisions, fact based. Also the model is capable of evaluating different measures (like a curfew, consolidated transport from city depot, electric vehicles, etc) on congestion and emission reduction effects. That way the most effective measure can be selected before putting it in practice.

Setting a realistic goal is difficult. Cities have different infrastructures and different distribution of shops, bars and restaurants. Taking all this into account would take a lot of modelling effort and detailed information on the route the vehicles take. Information that is not available (yes, even in these data rich times, we sometimes lack the data!). Therefore we decided to use a technique that doesn’t require a lot of detail on the “production” of emissions but would give a good estimate on the “environmental performance”. To achieve this we used Data Envelopment Analysis (DEA). DEA is a technique that is used to calculate and compare the efficiency of decision making units (DMU’s), for example factories, that makes no assumption on the underlying form of the production function. It focuses on the efficiency of the transition of inputs to outputs only. Differences in efficiency tell you how improvements can be achieved. In case of the environmental performance we looked at how vehicle movements and emissions were “produced” by number of deliveries and number of drop-off locations (shops, bars, etc) in the inner-city. The resulting relative environmental performance of the cities in the benchmark tells them how well they are doing compared to other cities and how much the emission levels should be lowered to be as “green” as the most efficient city in the benchmark.

When comparing Rotterdam with Amsterdam, Utrecht, The Hague, Enschede and Tilburg I found that Tilburg is the most environmental efficient city. This is no surprise, Tilburg has been working hard to improve inner-city environment for some years already, with all kinds of initiatives. So in reviewing and perhaps setting new goals for 2015, the city counsel of Rotterdam should have a talk with Tilburg, discussing the measures Tilburg has in place to improve the environmental conditions of the inner-city. Knowing what to aim for, the Mayor of Rotterdam can than make a fact-based trade of between the countermeasures to take to improve the inner-city environment and the economic impact of them. And Mayor Aboutaleb, …..010 is doing better than 020!

Analytics and Operations Research; a practitioner’s view

2011-05-22T18:46:00.014+02:00

The topic whether the O.R. society should embrace (business) analytics is one that will probably go on for a while. It’s THE theme that keeps O.R societies occupied at this moment; all are busy with the question whether they should hook on to analytics since it could boost awareness and interest for O.R. Although the term “Business Analytics” is quite old, it dates back to Frederick Taylor’s time management practice in the late 19th century, it is presented as the latest trend in management and every CEO should start using it. Amazon lists over 1,500 books on the subject, nearly every one of these books has the theme “Start using Analytics in decision making, otherwise you will be doomed to the lower end of the performance ladder and go bust”. In promoting the use of analytics different terms are used which makes it hard to understand what people are really talking about. Terms like business intelligence, business analytics, descriptive analytics, predictive analytics, prescriptive analytics, and so on. From a practitioner’s point of view the discussion on the subject is rather academic, my clients don’t really care whether I use the term Analytics or O.R. in improving their operations or decision making. They just want me to help them solve their problem.

If have been working in O.R. consulting for over 20 years now and have learned something that Plato already knew over 2300 year ago, a good decision is based on knowledge not on numbers. It isn’t the analyses of data (=Analytics?) or building and solving a math models (=O.R.?) that leads to better decisions, it’s the knowledge gained in the process. It starts with understanding the problem and framing it right. This can best be achieved by gathering and analysing relevant data, measuring performance and identifying the applicable business rules. Analytics if you will. This analysis will increase the knowledge about the problem at hand and the environment in which it needs to be solved. Based on the data analysis and the identified business rules, directions for improvement (scenarios) can be identified. By analyzing the scenarios, the impact (consequences) of each of these can be identified, again increasing the knowledge about the problem, but also on how to solve it. The “do’s and dont’s” have come forward at this point. Next step is to use the knowledge about the challenge, the data and the business rules to build and use/solve a math model to find the best possible and achievable solution to the challenge (note: optimality in practice is something different compared to the textbook concept of optimality). With the knowledge gained during each of the above steps, implementing the solution is straight forward, apart from the “normal” potential change management issues. Result of it all is a solution to a practical challenge, and hopefully a satisfied customer.

My clients have never asked me what techniques I use to help solve the challenge they face and I also never tell them. In the past 20 years (See: Does O.R. Sell?) I have never come across a client that hired me because I could analyse data, build a forecast model, build/solve a linear programme or was able to build a simulation model. There is a simple reason for that, they don’t know the difference and they don't need to. Introducing yourself with that you are really good at building a math model, have been in Monte Carlo simulation or Markov chains for years, doesn’t help build your credibility. Talking about O.R. or Analytics doesn’t either. What counts is that you understand or show that you’re able to understand the business of your client, his organisation and the challenge he faces. So discussing whether Analytics and O.R. are the same, part of each other or complementary doesn’t really matter from my point of view. I’ll use the technique that is required to solve my clients challenge, no matter if it’s descriptive, predictive or prescriptive. Whoever thought of the term “Prescriptive Analytics” by the way? It makes O.R. to something that can only be applied when a specialist tells you how and when to use it. “Solve this LP model 3 times a day and your problem is solved?”

I once used just a blank sheet of paper to solve a business challenge, a real back of the napkin situation. One drawing was enough to identify and solve the business issue. The drawing was a simple graph. The shortest path in the graph was the solution to the client’s challenge. Calculations where not required, even my client could see the solution immediately. This shows that O.R. can be down to earth and within reach of everybody. That is also how we should go about in the Analytics vs Operations Research discussion, down to earth and for everybody including clients. I would suggest a small twist and add some special focus on the practical side of it all.

The Risk of being Just in Time

2011-05-16T09:11:00.004+02:00

Most executives don’t realise that optimisation can make companies vulnerable to changes in their environment. They have been taught that efficiency and maximising shareholder value don’t tolerate redundancy. For that reason many manufacturers practice a Just in Time (JIT) stock keeping philosophy for raw materials. Since for most manufacturing operations over 70% of the cost is associated with purchasing of goods and services, keeping stock levels low seems a sensible thing to do. In JIT the focus is on controlling the stock levels of the sourced materials, since finished goods and internal sub-assemblies are within the control of the manufacturer. Unfortunately this is also where the highest risk in the supply chain resides; disruptions in the supply of raw material can cause missed customer shipments or worse shut your customer down.

Buying and shipping of supplies has changed in the past two decades. The locations, at which components are produced, are spread around the world, with technology and low costs as its driving forces. This causes supply chains to become longer and far more complex than in the past, making it hard to asses the risks. An example of such a risk is the bullwhip effect. When supply chains get longer, lead times increase, which in turn amplifies demand fluctuations leading to increased stock levels. Most manufacturing companies have deep knowledge of their primary suppliers; the risks however reside further down the supply chain, at the supplier’s supplier. An example from the electronics industry is the production of silicon wafers, the raw material used to make computer chips which in turn are used in smart phones or tablets. 60% of the world supply in silicon wafers comes from two Japanese companies one of which is the Shin-Etsu Chemical Company. Its main wafer plant in Shirakawa was damaged by the recent earthquake in Japan. Chip makers like Intel, Samsung and Toshiba depend on these wafers for their production of microchips. Typically, they keep stock levels for 4 to 6 weeks of production. So if their supply falls short, Apple and other smart phone/tablet producers might be impacted, just as a tablet war is about to start.

There are many more examples like the silicon wafer example, which can cause shareholder value to degrade when practicing a JIT philosophy. An empirical analysis of share price performance shows that firms facing a disruption in the supply chain experienced share price returns that were 30-40% lower than the industry and general market benchmarks. Showing that being prepared and therefore tolerating some redundancies is a better strategy that will at least preserve shareholder value. But which supplies of raw material to keep in stock and at what level? Not a question that can be solved easy.

First step in making that decision is to understand the dynamics of the supply chain. Since disruptions may have impact not only locally but globally a holistic and system wide approach is required to analyse the risks involved. A structured approach for describing and analysing supply chains therefore is needed to help unravel the supply chain complexity. From personal experience, I find that combining the SCOR method of the Supply Chain Council (SCC) with Operations Research is a good way to achieve that. SCOR is a framework and a methodology that allows companies to create high-level descriptions for supply chain systems. Combined with the power of the mathematical models and optimisation techniques from Operations Research you end up with an understandable and manageable models that can be used to create insights and put fact to beliefs. Second step is to identify the appropriate metrics to measure the supply chain reliability, responsiveness or agility, which allows you to measure supply chain risks and asses and mitigate the risks by evaluating different policies, like which stock levels to keep and where to keep them. In a third step, using techniques like Monte Carlo simulation, stock keeping policies can be evaluated. Last but not least, the model can be used to optimise (not minimise!) the stock levels, while minimising supply chain risks. As a result the best stock keeping locations and levels can be identified.

So, a stock keeping strategy should be a result from a thorough analysis of the full supply chain, focussing on the robustness of the complete chain, taking the risk of disruptions in supply into account. Following what’s common (like JIT) can have high impact on the performance of the supply chain, and destroy instead of create shareholder value. Adding OR to SCOR will enable you to asses risk in a standardized and fact based way, leading to informed choices on which risks should be mitigated and how to mitigate them. This allows you to make a fact based decision on which raw materials to keep on a Just-In-Time or Just-in-Case stock level.

Less is Better; A cure for Dutch healthcare

2011-04-29T13:35:00.010+02:00

This week a wellness centre of the North Star Alliance visited ORTEC headquarters in Gouda. Walking through the wellness centre and listening to the stories on the care offered by North Star to truck drivers, sex workers and local communities along the traffic corridors of sub-Saharan Africa, I realised that we are very fortunate to live in the Western world. Basic healthcare isn’t a top of mind topic for us; it has been arranged very well. Maybe it’s even a bit overdone? Reading the papers seems to confirm that. In nearly every country in Europe rising costs of healthcare is a main topic for the government. Main reasons for ever rising healthcare costs are increase in life expectancy, welfare increase and an increasing number of illnesses that can be cured due to innovation. The Dutch government also attempts to reduce expenditure in healthcare. But much of the political debate is about believes and less about facts.

To illustrate the quality of the Dutch healthcare system, let’s have a look at the accessibility of a hospital bed. A study from 2006 shows that for the European Union, 48% of the inhabitants can reach a hospital within 20 minutes. For the Netherlands this is even 70%, which is far above that EU figure. The travel distance to the closest hospital for a person living in the Netherlands is at most 12 KM for 80% of the population. Average distance travelled is 9.7 kilometres with the maximum distance to a hospital bed close to 50km for people living on the West Frisian Islands. The total number of hospital beds in the Netherlands is 52.714 which results in a hospital bed for every 314 inhabitants, given a total number of inhabitants of 16.5 million (all 2009 figures taken from http://www.dutchhospitaldata.nl/ ). When looking at the distribution of people per hospital bed on hospital level, something interesting comes forward. The number of people per hospital bed varies per hospital from 150 to 1230 with an average of 411! This smells like under and over utilisation of valuable assets, probably due to poorly located hospitals. Room for improvement!

In healthcare, as in any other industry, the implications of poor location decisions or too many or too few locations will result in increased expenses or poor service. If too many locations are deployed, capital costs, staffing costs and inventory carrying cost will be high. If too few locations are used service will degrade. Even if the number of hospitals is optimal, poorly chosen locations will impact service. Poor location decisions in healthcare go beyond cost. If too few hospitals are utilized or if they are poorly located, it will increase mortality and morbidity. So, great care must be taken in making location decisions in healthcare, assuring accessibility. Fortunately Operations Research offers all kinds of models that can assists in making that decision fact based.

To improve the utilisation of the Dutch hospital beds I constructed a math model to look for hospitals that could be closed without degrading the accessibility of hospital beds. So, in the optimised situation still at least 80% of the Dutch travel at most 12 kilometres to a hospital bed. Closing a hospital will reduce the number of available beds and therefore increase utilisation of others. This probably will also increase utilisation of expensive medical equipment like MRI, operating theatres and hospital staff. To make sure that hospitals don’t get overcrowded the model makes sure that utilisation of hospital beds in the optimised situation cannot rise above the maximum utilisation of the current situation. Besides increasing utilisation and productivity, closing hospitals will reduce capital costs and inventory carrying cost. These all together will make healthcare cheaper.

With the model I was able to identify 9 hospitals, out of 93, that could be closed without degrading accessibility. Most of the hospitals that can be closed lie in the west part of the Netherlands, which is not a coincidence. In that region there are many hospitals available which reduces the utilisation of the available beds in that region. Closing them won’t harm the accessibility to a hospital bed because of other hospitals in the vicinity. In the improved setting, still at least 80% of the Dutch need to travel at most 12 kilometres to reach a hospital bed. The spread in utilisation of beds decreases, it runs from 154 to 1181 with an average of 433, which is a 5% improvement. The average distance travelled to reach a hospital bed increases with only 3% to 10.0 kilometres.

So even when maintaining the very high level of accessibility to hospital care there is room for improvement. With the use of Operations Research the debate on healthcare costs can become fact based. Reviewing the current situation based on facts helps getting a clear view on current performance and directs the search for improvements. The optimisation techniques from Operations Research will help find the improvements that reduce cost without degrading our high level of accessibility in Healthcare. Above all they will help improve care in Third World countries.

Da’s logisch (That’s logical )

2011-03-31T12:16:00.003+02:00

Last Tuesday the Dutch national soccer team played against Hungary. As with any match of the national team, it was on television, encapsulated in a programme in which various self pronounced soccer experts discussed and analysed the match and accomplishments of the team. It is fun to listen to the soccer gibberish used by these experts in their comments on the actions of the coach and team performance. They are always able to tell what went wrong and what would have been a better option (as could any other inhabitant of the Netherlands). A famous expert in soccer gibberish is soccer legend Johan Cruijff. He is famous for quotes like “Every disadvantage has its advantage”, “If they have the ball, you can’t win” or “That’s logical". So, being a coach is tough, especially when it concerns the nation soccer team, because the complete nation is watching you. Since much of the decisions in soccer are made through intuition and common sense it might be a good idea to put some numbers to beliefs/convictions and introduce some rigour in the decision making.

The decisions a coach needs to make are complex. Think of scouting for a new team member to fill in an open position and improve the overall quality of the team. Or deciding on the overall composition of the team selection; which players, how many for each position, etc. A decision a coach needs to make often is the line-up for the next match. A simple calculation shows that there are 308.403.583.488.000 possible combinations for the line-up for a soccer game, given 26 players in the team selection. How will a coach be ever able to identify the best possible line up?

Given that a player performance will differ depending on his assignment to a certain position in the field (a goalie is not much good in a forward position), a certain attractiveness score good be given to such an assignment. Identifying the best possible line-up can than be seen as finding the assignment of players to field positions that maximises the total score. Because every position in the field must be filled in and a player can have at most one position in the field the so called maximum-weight bipartite matching problem comes forward. Introducing a source (supply side 11) and sink (demand side 11) and giving the arcs from the source and towards the sink a maximum capacity of 1, this bipartite matching problem can be solved as a transportation problem. It could be easily implemented as an App on the coach’s iPad. The tricky part in this approach is the scoring of the assignment of players to positions. This is where sports analytics come in.

By keeping track of the player performance during matches, the effectiveness of the player can be measured. This score could than be used in the optimisation of the next match line-up. By measuring the number of intercepts, the number of safes, the number of passes, etc all kinds of statistics can be calculated. Using these statistics an overall efficiency score can be calculated, see for example the Match index of SoccerLab. Not only after the match, but in real time as well. The score gives an indication of the players’ ability and effectiveness of the assignment to a position in the field. Companies like ORTEC TSS provide the kind of statistics to calculate this kind of efficiency scores. So instead of listening to the soccer gibberish of the experts, the facts can be used and the actual performance evaluated. The coach could use the statistics together with the line-up model, during the match, to decide on which player the exchange (a much discussed subject in the Netherlands; Bosvelt for Robben EC 2004) and decide on the line up for the next match. With an analytical approach and structural analysis of player performance, deciding on the line-up becomes more fact based leading to more sustainable team results. It doesn’t however offer a guarantee on winning championships, but that’s logical.

Fuel for thought

2011-03-26T16:09:00.009+01:00

With the struggle for a more democratic regime in Libya and other North African countries and the debate on nuclear power given the trouble in Japan, oil prices have risen in the last couple of months to the highest values since august 2008. To illustrate; a barrel of North Sea Brent has gone up from about $80 per barrel in March 2010 to about $110 per barrel today. That’s an increase of nearly 40% in just one year. How does this rapidly increasing oil price effect supply chains and their operations? Should companies just endure this increase in transportation costs, or are there alternatives?

Since the mid-1990’s the focus of many companies has been to lower operations cost, focussing on off-shoring and consolidation of production capacity. As a result many of them set up large plants in countries like China and India because of the low cost of labour and low cost of transporting the finished goods to Europe and the US. Also just-in-time inventory and continuous replenishment strategies emerged, especially in retail (causing inner-city areas to get congested). This was all possible due to low oil prices and therefore low transportation cost. With oil prices rising, things become different. A straightforward analysis of changes in Brent oil price versus changes in diesel price shows that a 10% increase in crude oil price will result in an increase in diesel price of 8.7%. The increase of the past year therefore resulted in 36% diesel price increase, or a € 0.12/km cost increase (assuming 3 km to 1 litre fuel consumption, current diesel price €1.329/litre). Although labour cost is still the highest cost component in transportation, the relative part of cost of fuel has risen drastically.

This increase in transportation cost is significant enough to rethink supply chain strategies especially for makers of products with low profit margins and long product life cycles. Think of consumer packaged goods and chemicals. Higher transportation costs will reduce their profits significantly. So what can they do? Without changing supply chain infrastructure, transportation cost will go down when shipping larger quantities and therefore achieving more economies of scale, but inventory costs will go up. Transportation costs will also decrease when using slower modes of transport; from air to road and from road to rail. This will however increase lead time and inventory. Math modelling can make the trade-off clear and lead to the optimal choice. Using 3^rd party logistics providers will potentially reduce cost, because they have better consolidation possibilities. Last but not least better utilisation of truck capacity using efficient packaging, load and pallet building capabilities will decrease cost. A nice example is the improvement E-Logistics Control (part of Ewals group) was able to achieve. They managed to increase the truck utilisation by 10%.(Dutch) This was not easy, remember playing 3D-Tetris? Special optimisation models and software, like LoadDesigner, is required to get the best possible truck utilisation. It is not only stacking the goods as efficient as possible on the truck, you also have to think about the order in which the goods will be delivered. Otherwise you have to completely rearrange the truck at each stop. It is a combined routing, packing and stacking challenge.

As transportation costs continue to rise optimisation of the supply chain infrastructure might be interesting. Reducing the length of the final leg in the supply chain and consolidation of shipments will reduce transportation cost but will require additional and larger warehouses, which implies more stock, hence higher inventory levels and costs. Deciding on the number of locations to add, requires finding a balance between transportation costs, inventory cost, handling cost and warehouse costs. The best supply chain design can only be found with the use of a supply chain infrastructure optimisation models. Using these models different supply chain designs can be modelled, evaluated and optimised, taking into account not only the costs involved but the impact on lead times and inventory levels as well. So oil price increases are fuel for thought. Supply chain managers have all kinds of options to deal with oil price induced cost increases. Operations Research can assist them, whether a complete supply chain redesign is considered or just better using the available assets.

#LoveSafely

2011-02-20T15:23:00.008+01:00

The #LoveSafely hashtag was introduced on Valentine’s Day by the joined UN programme on HIV/AIDS, UNAIDS, to utilise social media to raise awareness about HIV and AIDS. It was used by over one million tweeters! Mission accomplished? No! Much more needs to be done in the fight against HIV/AIDS. One of the major problems encountered in delivering relief food in Africa is a lack of truck drivers. Number one reason for that is AIDS. The truck drivers represent a whole industry that is fighting to survive and, without them, many businesses within Africa cannot be sustained. Ending the spread of HIV and therefore securing the transport sector in Africa is about education, access to health care, and making sure that we all #LoveSafely. That is what the North Star Alliance (NSA) is aiming at by providing health care services in a number of Roadside Wellness Centres, which are strategically set up across the African continent.

As part of our Optimising the World programme, ORTEC partners with the NSA. Last week I had a talk with Luke Disney, the executive director of NSA. We discussed the challenges NSA has, many of which I belief can be solved with the use of Operations Research. The past years of AIDS prevention have been on scaling up. Primary focus was on getting antiretroviral drugs (ARV) out there, training people and setting up healthcare centres no matter what the cost. This way of providing care will eventually hit a wall, donors and governments will not be able to supply the required funds forever. The recent financial crisis already had its impact on the funds available in support of the fight against AIDS in Africa. As Luke indicated in our talk there is still a lot of ground to cover to reach out to everybody in need of care, but there is only a limited number of people and resources. OR can help to start using the available resources as efficient as possible.

A news item from the Uganda newspaper the Monitor of 2007 shows that the challenges in HIV/AIDS prevention/care are not much different from the supply chain challenges we as OR professionals solve for our customers.

Entebbe — AS thousands of Ugandans die everyday of HIV/Aids and malaria, drugs worth about Shs4 billion are rotting in the National Medical Stores Entebbe. While on their fact finding tour of NMS in Entebbe yesterday, MPs on the Social Services Committee led by James Kubeketerya (Bunya East) were shocked to find eight containers of 2- feet, full of expired drugs yet Ugandans are perishing in hospitals without treatment

Straight forward Inventory management and forecasting the need for ARV drugs could have prevented the available drugs to be wasted and shows that the OR community needs to get involved. The Center for Strategic HIV Operations Research (CSHOR) is one of them. But more is needed, focussing on tactical and operational issues as well.

Together with Luke we decided to start a project to help NSA develop a strategy on how to best extend the wellness centre network in Africa. It is not as straightforward as a normal location problem as you might think, but than again which practical OR challenge is? The wellness centres focus on truck drivers, sex workers and local communities at truck stops and border crossings. At the wellness centres basic healthcare can be offered. For more advanced care people have to be redirected to a nearby hospital. In deciding were to locate the next wellness centre this needs to be taken into account. Also NSA is not the only NGO in Africa. It doesn’t make sense to open a new wellness centre in the vicinity of another centre that offers similar care. Last but not least, since the wellness centre offers care to the local communities, the accessibility of the wellness centre is important as well. Many people travel by foot so it should be close enough for the people to be able to reach it. These are just a few conditions that we know that need to be satisfied; in the project many more will surface.

First step we will take is gathering the relevant data and do a survey to better understand the current situation and develop some basic ideas to develop the network expansion strategy. NSA aims to cover 85% of cross border traffic in sub-Saharan Africa by 2013. I committed myself to support Luke and his team to make that happen. I’ll keep you informed on our progress in a next blog entry. With the support of OR, NSA will be able to offer the required education and safeguard access to healthcare to mobile workers and make sure that we all #LoveSafely.

Does Prime Minister Rutte require an OR/MS counsellor?

2011-01-30T18:22:00.004+01:00

Would the world look a little better if politicians made more use of Operations Research? I think it would. Apart from improving the voting system a little, democracy is mathematically impossible after all, Operations Research will also add value to political decisions. Many of the complex problems a politician has to deal with are the ones we as Operations Researchers like for breakfast!

Fortunately politicians are aware that we are around and know a little of what we can offer. Let me give you an example. In the Netherlands every year on the 3rd Tuesday of September (Prinsjesdag) the Dutch Treasury presents the budget plan for the coming year. Part of the plan is the budget that deals with road construction and maintenance. The height of the budget typically is a political decision (“you need more tarmac to fight traffic jams” is the current political paradigm in the Netherlands. We know they are wrong about that). As with any politically determined budget, it doesn’t cover all that is required to satisfy the ambition levels. So the Ministry of Infrastructure and Environment has to figure out a way to deploy the budget in a way that best satisfies the priorities set in their policy. To support them is this puzzle we at ORTEC constructed a model several years ago that helps them make the trade off. With the model, better insights were available leading to better plans (meeting the budget more closely) with focus on satisfying the ambitions levels from the policy at hand.

But Operations Research can offer more than just a capital budgeting model to help manage the public expenditure. Think of major investments like flood protection systems or aircraft like the Joint Strike Fighter. These decisions are very complex and have a high degree of uncertainty with respect to the costs and benefits involved. For example, the estimated cost per flight for the JSF has risen with 90% since 2002. Ever tried to defend a decision based on that kind of uncertainty? Politicians have to. Use of Operations Research can help here, to show the impact of uncertainty and structure the decision process.

It’s not only investment decisions that are complex; the same applies to the organisation of healthcare, deciding on the location of hospitals and the kind of care to offer there. The growing (and sometimes locally shrinking) population and aging are difficult trends to deal with. How to assure public safety with a possible shortage of policemen? How would you make the society more sustainable, organise country and social security, health insurance and pensions? This list of questions could go on forever. Each of them will benefit from the use Operations Research. With Operations Research these questions are dealt with using facts, not feelings or (political) beliefs. Insight will be gained on the major factors that influence the decisions, improving the overall quality, avoiding big mistakes (like CCS under a densely populated residential area) making the world a little better. So dear Mark, let’s get in touch.

2011, the Year of Math!

2011-01-23T21:10:00.004+01:00

This week Google announced that it will commit itself to support the International Mathematical Olympiad (IMO) for the next 5 years. Google donated one million Euros to help IMO! That’s a large amount of money. With this donation, the IMO will have a jumpstart in organising this global event in the coming years, enabling high school kids from countries around the world to pursue their passion for Mathematics. This year the IMO will be organised in the Netherlands, in Amsterdam to be precise (See https://www.imo2011.nl/ ). A good reason for making 2011 not the year of the rabbit or the bat, but the Year of Math, at least in the Netherlands.

When trying to promote Math my experience is that, as with Operations Research, people are not very keen to support it. In trying to find sponsors to finance the IMO 2011 event, many times I was turned down. Math suffers from the same syndrome as Operations Research, it has great and a positive influence on our daily lives but nobody knows it. Math is, contrary to management and politics, honest, undisputed, straightforward, consistent and creative. It can offer elegant and uncompromising solutions to tough problems. But many people see it otherwise. They think that Math is like Chess, no more than brain training and of no practical use. Maybe they see Math as an art, given the beauty of fractals. When looking back at the Math courses at high school and University, I can understand that (that is something that should improve!) But look around you, there is no escape. Math is everywhere and in a positive way.

While I’m writing this I’m listening to the latest CD from the Killers. Actually, “Change you’re mind” is playing (changed your mind on math yet?). There is no Math in this, besides the digitized version of the song on the CD is there? No, the CD player uses a Math algorithm from Irving Reed and Gustave Solomon to correct for errors due to scratches on the CD surface. Without it, it wouldn’t sound as good as it does now. There are many other examples of Math in daily life. The money system is one of them. Ever wondered why the split of coins (1, 5, 10, 25, 50 and 1 dollar) doesn’t match the split in notes (1, 2, 5, 10, 20, 50 and 100) ? Your satnav is another one, like using a cell phone and surfing the internet, it requires a shortest path algorithm. Taking the train requires a schedule; making a schedule involves Math and even won the Dutch Railways the Edelman award in 2008. Also when you receive a speeding ticket, Math is used to decipher the speed camera image of your licence plate to identify you as the car owner. Computer chip design and data compression (much used to reduce download times of images while surfing the internet) also use Math massively. Magnetic resonance imaging (MRI) is a imaging technique used in radiology to visualize detailed internal bodily structures. Math is used not only to design a MRI scanner; also using the scanner involves Math. Due to the use of Math the accuracy of MRI scanning is very high, up to 0.3 millimetres! Last but not least Business Analytics, whether being it descriptive, predictive or prescriptive, requires data and Math. As does Operations Research.

The above mentioned examples are only a very small set but give a nice impression on the impact of Math. Math is everywhere and if there is no Math around, things go wrong. If the traders of derivatives would have had more mathematical insights in the products they traded, we might have avoided a financial crisis. Math is a modest discipline, but it should get more credit for what it offers. So let me change your mind and start with a modest celebration and announce 2011, the Year of Math. With 2011 being a prime number, no better choice possible!

Happy Holidays thanks to OR

2010-12-21T11:12:00.006+01:00

At this time of the year many of my colleagues and fellow Dutchmen arrange to go ski in France or in Austria (Swiss is too expensive, you know the Dutch) or fly off to some sunny destination to enjoy the December holidays. Personally I like to stay at home and enjoy being with family and friends. It also allows me to write this blog and enter the December Blog Challenge of INFORMS.

How do Holidays and Operations Research relate? Well, a lot I would say. The obvious examples for this time of year are:

Given a (tight) budget which Xmas-presents to buy to maximise joy (Knapsack problem)
The shortest route along all the shops you want to go to for Xmas shopping or all the relatives you want to visit (Travelling salesman). Santa's route actually is that of a travelling salesman.
Getting all the presents you bought into your car (vehicle load optimisation)
Avoid gaining weight during the Xmas holidays, design a healthy Xmas menu (Diet problem)
And many more.

Those who don’t stay at home but book a flight, a train, a hotel room or any other holiday accommodation also come across Operations Research. It is used to determine the fee you have to pay for the flight or hotel room you book. It’s called revenue management or yield management. It explains why the person next to you paid a different fee than you and why prices for hotel rooms and flights fluctuated from day to day. The basic principle of revenue management is rather simple, try to maximise revenue given an uncertain demand. Remember selling lemonade as a child outside your house? You had to decide when to try and sell it, (it didn’t work on a rainy day) decide on a reasonable price and when/how to change the price as the day rolled on. Things are no different in selling flights or hotel rooms. There is however more to revenue management than just determine the right price.

One of my customers is in the travel industry. They offer flights, hotels and holiday accommodations or combinations thereof via the web. It is interesting to see how their planning cycle works and how Operations Research is used to support it. It all starts with having something to sell. Before you can sell, you need to have inventory (How many cans of lemonade to make?). Each year, ahead of the holiday season, it must be decided how many hotel rooms and flight seats are required to fulfil market demands or capture the market potential. This decision can have a lot of impact since, if a too small amount is bought, it is a missed opportunity for increased revenue. However if too much rooms or flights are bought, a lot of the capacity will by left unused leading to uncovered costs. Although deciding on the exact amounts is still a craftsman’s job, a lot can be learned from the past. This is where Operations Research offers a helping hand. Using advanced forecasting methods the capacity managers are able to make good esstimates for the required inventory that is than (together with strategic commercial objectives) input for the sales & booking process.

Given the above, you can imagine that the inventory risk is rather large. Huge amounts of flight seats and hotel rooms need to be bought in advance, which are perishable. If the flight seat, hotel room or accommodation isn’t sold, it expires. Also 95% of the inventory needs to be sold to have a healthy P&L, which leaves not much room to manoeuvre. This is already hard when you are selling just one product. Think about selling 18 million different products! Here is where the Operations Research comes in again. To deal with the complexity and size of the challenge, we developed a specific optimisation model that is incorporated into a revenue management system. The model is used to determine the optimal price for each of the 18 million products. On a daily basis 2-3 million product prices are updated, taking the actual bookings and updated forecasts for future demand into account.

At the introduction of the model, the mindset of the pricing managers was to set prices to sell 100% of the inventory. They achieved high occupation levels, but at the cost of many discounts. With the revenue management model this changed. First they used to model to maximise revenue by making timely price adjustments. Now they are even beyond that, using the model to find new growth opportunities. The revenue management model handles everything so they also can enjoy their holidays as well, thanks to OR. Happy Holidays to you all!

Statistical Reasoning for Dummies

2010-12-08T13:33:00.004+01:00

"Statistical thinking and reasoning is necessary for efficient citizenship as the ability to read and write"

Is this statement to bold? I don’t think so. We are surrounded with statistics, uncertainties and probabilities and need to understand them, use them and make decisions with them. But, as it turns out, statistical reasoning is very difficult given the many mistakes that are made in newspapers, medical decision making, social science, gambling, politics. You name it, it’s everywhere and so are the mistakes. To give you an extreme example, in Innumeracy J.A. Paulos tells a story about a weather forecaster. The weather forecaster reports a 50% change of rain on Saturday, also a 50% chance of rain on Sunday. He concludes that it will rain the weekend for certain. More recently the publication of Stonewall stating that the average coming out age has been dropping was proven to be wrong by Ben Goldacre. The Stonewall survey is seriously flawed and proves the obvious point that people tend to get older when they get older, nothing more and nothing less. See Ben’s Bad Science weblog for more details. Yesterday a big news item on local television was that mother, son and grandson are born on the same date. Statistically it’s not that extraordinary, contrary what the journalist said (“It’s a miracle”). It’s easy to make a long list of these kinds of mistakes (the next Great Operations Research Blog Challenge theme?), but how to resolve this? Maybe some statistical reasoning for dummies could help? Let’s start with an introductory chapter, some basics.

As an Operations Researcher I am used to work with terms like probability, risk, variance, covariance, t-test, and many other statistical “Red” words as Sam Savage calls them is his book The Flaw of Averages. Many times these “Red” words are used to express a probability or risk, leading to many mistakes or confusion. Take for example the story from journalist David Duncan that was in Wired magazine a few years ago. David did a complete gene scan that checked for genetic decease markers in his DNA. Such tests will soon be part of everyday medical care (and insurance acceptance terms?). To his distress David receives the message that he has mutations in his DNA, raising his risk of having a heart attack. Such risks are expressed as the probability that you will have a heart attack is x%, a single event probability. It is similar to the statement that the probability that it will rain tomorrow is 30%. But what does it mean? Will it rain 30% of the time tomorrow, or in 30% of the country? Both inferences are wrong by the way. The problem with single event probabilities expressed in this way is that without a reference to the class of events the probability relates to, you are left in the dark as to how to interpret it. It causes Duncan to worry about having a heart attack, but should he have worries about it? A way around this confusion is to include the reference class to the probability. So, the weather forecaster should state something like that in 3 out of the 10 times he predicted rain for tomorrow, there was at least a trace of rain the next day. Much of the confusion of David could have been resolved if the doctor would have added a reference class, putting things in perspective.

Another classic misunderstanding is the interpretation of a conditional probability, like in interpreting diagnostics tests in medicine. See my earlier blog entry on that. The approach I used to explain the correct way to interpret the test results “translates” the probabilities (stated in percentages) into real numbers, making it easier to understand. Actually it does more or less the same as adding the reference class to the single event probability. It adds context. The last example of a much misunderstood statistic is relative risk. In the Netherlands there was much debate on whether girls should to be vaccinated against cervical cancer caused by the human Papilloma virus (HPV). To express the effectiveness of the vaccination, a relative risk reduction was used. Something like; “This vaccine will reduce the risk of getting cervical cancer from an HPV infection with x%”. This kind of statement is used regularly to express the effectiveness of preventive methods like screening, vaccines or other risk mitigation strategies. Using relative risk reduction as a measure can however be confusing. For example, if the number of women dying of cervical cancer reduces from 4 to 3 per 1000, the relative risk reduction is 25%. A massive risk reduction you would say. However, if you look at the actual reduction of women dying this is only 0,1% (=1/1000). The confusion, again, comes from not expressing the reference data causing many people to think that the relative risk reduction applies to those how take the vaccine, but it actually applies to those how don’t and die (25% less dead).

So first lesson in statistical reasoning is look for the reference and translate probabilities and risks into numbers. For us “professionals”, lest present our results in a smart and easy to understand way and skip using those Red words.

1) I used HG Wells’ statement on statistical reasoning from somewhere in the beginning of last century as a starting point.

Warning, Math Inside!

2010-10-22T20:22:00.009+02:00

Next year the International Mathematical Olympiad (http://www.imo2011.nl/) will be held in the Netherlands. This calls for a celebration of math, but at present mathematical modelling seems to get the blame for all the economical problems we have. To name a few, the models from David X. Li are blamed for causing the credit crunch. The risk assessment models of banks failed; nearly tipping them over if it wasn’t for the government support they received. Also the losses incurred by the pension funds are blamed on mathematical models. In pointing the finger on who’s to blame for al this, many decision makers point to math modelling. It’s far too complicated, they say. It is however invalid to blame math for this; after all it is not the math that makes the decisions. What is to blame is the ignorance with which math models are applied. It’s like buying a state of art electronic device and getting mad at it because it doesn’t work. But if you had read the manual, things get different.

The essence of math modelling is to describe reality in mathematical terms with a specific purpose, like determining the value of an investment portfolio or assessing the risk of a project. A mathematical model always is a simplification of reality. If the model would be as complex and as detailed as reality, it would become as expensive and as difficult to use. Math allows us to focus on the essence of the question at hand and gives us the opportunity to experiment without having to perform tests in real live. No one would think of flying in a new aircraft, without first testing its ability to fly using a math model. After using the model to perform the required analysis, the results are translated back to reality. In both translations (from reality to model and back again) common sense, simplifications, assumptions and approximations are used. The model user and decision maker must be well aware of that.

A well build math model can be a very powerful instrument; you can compare it with a chainsaw. In the hands of a well trained annalist the math model will be an excellent and effective tool. In the hands of an ignorant user it can do a lot of harm, even to the user. A decision maker must know the scope, concepts and dynamics of the models used before adopting its results in decision making. This doesn’t imply that every decision maker should a well trained and skilled mathematical modeller or that the detail and complexity of the model is restricted by the decision makers’ math capabilities. An aircraft pilot for example exactly knows the scope and conditions for using the autopilot of the aircraft, this doesn’t imply that the pilot can build one himself.

Robert Merton states in his Nobel price speech in 1997:

"The mathematics of models can be applied precisely, but the models are not at all precise in their application to the complex real world. Their accuracy as useful approximations to that world varies significantly across time and place. The models should be applied in practice only tentatively, with careful assessment of their limitations in each approximation."

He is absolutely right about it, but it’s forgotten easily. Robert Merton himself failed to keep this in mind and as a result Long Term Capital Management went down in 1998.

As an operations research consultant I use math models all the time. It is tempting to keep the detail of the modelling out of the scope of the decision makers. But my experience is that developing models in close corporation with the decision maker is a far better way. When keeping the decision maker out of the loop, you need to do a lot of explaining after the model has been developed. Many times, when the results from the model are not as expected, it is the math model that gets the blame. However it is the ignorance of the decision maker that is the cause, they didn’t read the manual (or we didn’t explain the model well enough) Therefore developing the model in close corporation with the decision maker is a better way. It leads to better models because scope, assumptions and simplifications are discussed and agreed upon during the development process. This allows the decision maker to learn to use and understand the results of the model while it is being developed. No manual required! It is not only easier; it is also a better way, improving decision quality.

What’s the best option?

2010-09-26T18:02:00.009+02:00

Many of the decisions we make are choices between 2 or more alternatives. When the outcomes of the alternatives are known with certainty, deciding between them is relatively easy. However, since the environment we live in is fraught with uncertainty, things become more difficult. This uncertainty prevents us from making an accurate estimate of the outcome and makes the decision for the best alternative difficult. But uncertainty also offers new opportunities; new information helps to improve our decision and generate more value. In business many of the decisions that need to be made are of that kind. Take for example a manufacturer introducing a new product. It needs to decide on the number of products to make, not knowing how many customers will buy it. Should it first do a test run with the new product? This kind of decision making can benefit a lot from what Operations Research has to offer, it can support companies in answering the question: What’s the best option?

A much used technique in business in finding the best option is the net present value analysis (NPV). By comparing the discounted cash outflows (investments) and discounted cash inflows (revenues) it can be inferred whether the project will add value or not. The trouble with this approach is however that it is incapable to put a value on the uncertainty involved in the decision. To illustrate, assume a company that needs to decide to invest in a new technology that would cost them €650 million to develop and that total (discounted) revenues over the coming 5 years would be €500 million. The NPV of the project (-€150 million) would result in a negative advice to invest in the technology. But is that really the best option? In the above example the company doesn’t know for sure that the expected revenues will be equal €500 million, this depends on the number and price of the products that it will sell after investing the €650 million. The NPV analysis can only capture part of these uncertainties, for example by running a scenario analyses on a range of possible market prices and sales for the product. That way an upper and lower bound of the NPV can be estimated, but it doesn’t help incorporate the variance across the different scenarios into the decision. There is a better way to put a value on the uncertainty by applying a real options approach.

A real option approach uses option valuation techniques to value decisions. In the above example the option was whether or not to invest €650 million to earn €500 million, with much uncertainty about the expected revenues. Real option analysis uses the famous Black & Scholes option valuation model to value this decision, although other models are used as well. The B&S model takes a number of arguments. In a real option valuation the stock price (S) in de B&S model is equal to the estimated present value of the cash inflows (=revenues). The exercise price (X) is equal the present value of the cash outflow (=investments). Uncertainty (σ) is measured by taking the standard deviation of the growth rate of the future cash flows (in our example the volatility in revenue for the new product). The time to expire (t) is the period during which the option can be exercised. Dividends (δ) are the cost incurred to preserve the option. The risk free interest rate (r) is set to the yield of a riskless security (are there any nowadays?) with same maturity as the duration of the option.

Assuming volatility (σ) of 35% standard deviation and a 5 year risk free rate of 2.5% the option value becomes €129 Million, assuming no option preservation cost. That would mean that investing in the new technology really is an opportunity! The difference between the NPV value of the project and the value based on real options approach shows the value of the flexibility the company has because it can wait and invest when uncertainty on product price and sales are resolved, for example by applying market research or running a test with the new product. Note that using the B&S model assumes that revenue (=stock price) follows a lognormal distribution with a constant level of volatility. That may not be the case for the decision at hand. The lognormal distribution also causes the increase in option value when the duration is increased. In practice assuming lognormal returns is probably not valid. There is a way around it (Monte Carlo option valuation for example), I’ll discuss it in a later blog entry.

A real option approach not only offers a better way to value the uncertainty in a decision, it also provides a framework that helps identify and prioritise the key levers management can pull to increase the payoff of the opportunity. In essence all six parameters in de B&S model offer a lever to pull. It allows management to proactively deal with the uncertainty involved in the decision. For example the effect of the entry of competitors with a similar product after 2,5 years (it would cost €56 Million dropping the option value to €73 Million) or the expected increase in revenue from marketing strategies around the product. With real options your able to tell which option is best!

On Beer, Whips and Chaos

2010-08-28T17:58:00.007+02:00

The last couple of months the topic that pops up in many of the conversations I have is forecasting. Last week a beer brewer, this week a mail company was asking about it. Recently the Dutch financial paper had a full page on the value of forecasting for DSM NeoResins. The article (in Dutch) explains why forecasting the demand and the resulting stock impact were crucial for DSM to understand the dynamics of their supply chain and helped to manage the impact of the economic downturn. DSM experienced the classic bullwhip effect, a well known phenomenon in supply chain management, and was looking for ways to tame it.

The bullwhip effect is the amplification of demand fluctuations as one moves up the supply chain from retailer to manufacturer. It can be measured as the variance of the orders divided by the variance of demand. A bullwhip measure larger that one implies that demand fluctuations will be amplified. The bullwhip has three main causes. First there is the supply chain structure itself. The longer the lead time in the supply chain the stronger the bullwhip effect, because a longer lead time will cause more pronounced orders as a reaction to demand increases. Second cause is local optimisation. Since placing an order will involve cost there is an incentive to hold orders back and only place aggregate orders. Last but not least is the lack of information of actual demand. Without actual demand data one has to rely on forecasted demand. When applied without thought, forecasting will aggravated the bullwhip effect, leading to forecasted chaos.

To illustrate the impact of a “nonoptimal” forecasting method picture a simple supply chain, for example the supply chain from the Beer Distribution Game. Each point in time the following sequence of events takes place in each part of the supply chain. Incoming shipments from an upstream decision maker are received and placed in inventory. Next incoming orders from the downstream decision maker are received and are either fulfilled (when stock levels suffice) or backlogged. Last, a new order is placed and passed to the upstream echelon. Inventory is reviewed each time period. In deciding the order quantity we have to estimate future demand. To be able to forecast we need to have a forecast method. The figure below shows the results of a Moving Average (MA) and Exponential Smoothing (ES) method to forecast future demand. Compared to the actual demand one can clearly see that ES forecaster gives better results.

To illustrate the impact of forecasting on stocks and order quantity, assume that it takes 3 periods before an order will be received. This needs to be taken into account when placing an order. The below figure shows actual demand compared with the order quantity based on MA and ES demand forecasts. As can be seen clearly the fluctuation in demand is amplified in the orders, illustrating the bullwhip effect.

The amplification for the ES forecasts is about twice the amplification from the MA demands. So although SE gives better forecasts it amplifies the fluctuations in the demand more than the simple MA forecasting method in this case. Not something you would expect. When comparing net stock with actual demand a similar picture arises.

So, when attempting to forecast be aware of the chaos it can create. Improper forecasting may have a devastating impact on the bull whip effect. As a consequence inventory cost will increase and customer service will be impacted significantly. Best way to start is by selecting a few forecasting methods and order policies and test the accuracy of the forecasts on past periods. Using the mean squared error of the forecasts as a goodness of forecast measure the best forecast method can be selected. One can also use the bullwhip effect measure in selecting the forecast method.

PS: If you would like to have the data from the above examples, just drop me a note.

Operations Research; key factor in competing for the future

2010-07-11T17:36:00.006+02:00

Prahalad’s message in Competing For The Future is clear. Identify, create and then dominate emerging market opportunities before your competitors have the opportunity to exploit them. Applying analytics is suggested to be the best way to achieve that. Many books have been written on how analytics will bring advantages to companies in beating their competition to market dominance. Davenport’s new book Analytics at Work (I wonder where he got the title ;-) ) is another one, it will probably sell big. These books hook up on the global trend that more and more reliable data is becoming available through the use of IT systems. Companies keep track of their business in much more detail, from order to delivery, leading to ever growing piles of data. Mining these mountains of data with computerized analysis, creates new information and insights leading to more fact based decision making. To my opinion these “analytics” books have too much focus on data analysis alone. They focus too little on actually using analytics to learn from past experiences, identify new relationships and push the innovative power of companies to reinvent their business time and time again. Helping them stay ahead of competition. To accomplish that, more is required than just a few data dashboards or regression lines. It’s mathematics or in its applied form Operations Research and the way of thinking that goes with it.

The added value of mathematics is no longer, as the famous mathematician G.H. Hardy in his essay A Mathematician’s Apology, its lack of applications in the outside world. Mathematics has proven to add value over and over again and is not something that came to rise in the past few years with the Analytics trend. Hardy wrote the essay in the same period as Operations Research came into existence at the Bawdsey Research Station in the UK where mathematics were used as a means to analyse and improve the working of the UK's early warning radar system, Chain Home. With Operations Research the limitations of the Chain Home network were exposed and improved allowing for accurate early warning and remedial actions; a turning point in the battle for Britain.

When we look at recent successes in business, we time and time again conclude that the driving power behind these successes is applied mathematics and optimisation. Take Google for example, its key asset is a mathematical algorithm. Another example is Tesco which is the first non American based retailer to be successful in the States. Key in the success is their ability to analyse the buying habits of their customers and to apply this knowledge in targeting customer with specific special offers. Likewise, Albert Hein uses information from buying habits to manage its complete supply chain from sourcing decisions all the way down to managing the stock levels in the shops. These examples show that the gathering of data is not enough to create value from it. Success comes when a company is capable of analysing the acquired data, learns from it, optimises its current operation and ultimately reinvents its business. This can only be achieved when a company makes mathematics and optimisation a core competence. In a recent publication Alexander Rinnooy Kan, chairman of the Social and Economic Council of the Netherlands and well-known mathematician and operations researcher, even goes a little bit further. He signals that not that many (applied) mathematicians are present in the boardrooms of companies in the Netherlands. I expect that to be the case elsewhere. However the ability that applied mathematicians have to structure and solve complex problems could provide the companies the key to competing for the future, he states.

I totally agree. Many companies have invested in IT systems to capture and generate more and more data on their operational processes. These investments lead to vast amounts of data but to their disappointment didn’t improve decision making. The available data, the numerous ways to display and analyse it and the many mistakes that be can made doing this leave the decision makers in the dark. The additional information doesn’t make life easier for them; it creates an ever growing chaos of reports and opinions. It is the capability of applied mathematicians (Operations Researchers or Econometricians which ever term you like better) to create order in this chaos; applying logic and optimisation techniques to guide the decision maker to make the best decision and stay ahead of the competition. Not only should these capabilities be present in the support units of a company, they should be present in the boardroom as well.

Zen and the art of strategic decision making

2010-06-13T12:48:00.006+02:00

Formal models are still rarely used in strategic decision making. In the past few decades a lot of effort has been put into the development of more and more sophisticated models and methods to capture the complexity of decisions boardrooms have to make. Many of the available techniques are well suited for these kinds of questions. Think of Monte Carlo Simulation, game theory or option valuation. When applied correctly these techniques create insight, make decisions fact based and improve the overall quality of the decision. When talking to members of the board on this subject their response many times is that formal models are too complex or not complex enough to support the decisions they need to make. Even if the models could support the members of the board, their feeling is that gathering and validating of the data and analysis with the model would take too much time and is too complex to really support them. They trust their intuition or use analogies instead. It is my experience that it is a misconception; the “way” to go is to combine intuition and formal models into the art of strategic decision making.

The value from using formal models is that they provide a systematic framework that structures the identification of business rules, the gathering of data and most importantly the discussion in the boardroom on the key value drivers of the decision. Which of those drivers can be influenced by the board and which can’t they? How do these drivers influence the decision? To give you an example, government regulations can have an enormous impact on the strategy of a company but they can’t be influenced much. Using a mathematical model can provide insight on the impact of changes of the government policies and supports the development of strategies on each of the possible outcomes. That way the board is prepared for changes and can get things into gear as soon as policies change which gives them a head start over their competitors. There are many other factors that can be treated this way, like competitors, customers or uncertainties in the economy.

The most value is created with formal models when they are build and used interactively in the boardroom. While discussing the structures, business rules and key parameters of the formal model the board members are stimulated to think and discuss about what drives their business. They will touch upon the core strategic issues and find out how much they know about them and what are the blind spots. The collective effort of building the model will stimulate the common understanding of the drivers of the decision to make. Also since all understand the structures, business rules and key parameters that will drive the model and their interaction it will build trust in the model outcomes and ease communication and implementation of the strategic choices later on.

So using formal models is heaven? That would be too easy. Models are not and should not be the deciding factor when making strategic decisions. I have learned some important lessons from using models in boardrooms. One of them is to start managing expectations on the value of using a formal model from day one. One such experience is that the formal model is treated as some kind of black box supplying flawless predictions about the future. Using formal models will not solve the uncertainty involved in boardroom decision making. Making the boardroom members aware of that is an important first step. One other much encountered expectation is that the model is some kind of Delphi oracle, using it will provide all the answers, and this is of course also not true (unfortunately). Even worse perhaps is when the board falls in love with the model and uses it to prove the convictions of the board. Than the model is “tortured” until it provides the answer the board is after.

Strategic decision making requires, like Prisig in his well known book Zen and the Art of Motorcycle Maintenance explains, combining the rational and the irrational. It requires the creativity, intuition and analogies from the board members. With Operations Research the thinking process is structured, rationalizing the decision making process. So, formal modelling and Intuition must coexist in strategic decision making, increasing the overall quality of the decision.

What’s the value of information?

2010-05-13T12:55:00.011+02:00

Every weekday I take my car to either drive to the office or visit a customer. Sometimes I work at home first, especial on Tuesdays or Thursdays. On these weekdays the express ways around the village I live are jammed with traffic, but not always. Of course working at home is great and fits the current way of thinking on how to best mix work and social responsibilities. Working at home allows me take my kids to school, while the internet let’s me stay in touch with my colleagues. However, discussions in front off the whiteboard are still hard using web communications. Nothing beats sitting together in the same room to digest and solve the challenges of a customer. So on a Tuesday with a meeting scheduled at 8:30, what should I do? Take my chances and take my kids to school and hope that I’ll arrive in time at the office? Or should I leave early and drop my kids of at the neighbours? Of course this trade-off depends on what happens if I miss the meeting in the office and how many times I asked my neighbours to take my kids to school already. Can some analytics support me in this?

What helps is to structure this decision and pinpoint the uncertainties. The decision I need to make is whether to take the kids to school or leave home early. If I take the kids to school I enjoy the 40 minutes in the car in which we can talk on all kinds of things. When, in that case, there are traffic jams I will be late in the office. Let’s assume that there is 60% chance of a traffic jam causing me to be late by 60 minutes. I need to catch up that time which will cost me an additional 60 minutes. The other option is to leave home early. I won’t enjoy the 40 minutes in the car with the kids and in addition to that, I will have to take my and the neighbours’ kids to soccer practice next Saturday which will cost me 50 minutes in total. When there is a traffic jam I will make the meeting on time, because I left home early. We’ll have an effective meeting saving me 60 minutes that day. When there is no traffic jam however I’ll be much too early at the office and will have to wait for 30 minutes for the guard to open the doors, costing me 80 minutes in total. Based on the assumed 60% chance of a traffic jam the best option is to take the kids to school. The value of the decision is 4 minutes.

Since I do not travel to the office on all Tuesdays, the 60% chance of a traffic jam is just a guess. One way to be certain about it is to do some research on the internet and find out about the frequency of traffic jams on the express ways. Since time is scarce, how much time would I be willing to invest in that? In decision analysis this is called the Expected Value of Perfect Information (EVPI). It is easy to calculate. In this case there is a 60% change of a traffic jam causing me to leave home early. It will cost me 50 minutes next Saturday but 60 minutes of efficiency gain today, net 10 minutes. There is 40% change that I can take my kids to school and enjoy the 40 minutes in the car with them. So in case of perfect information the value of my decision is 60%*10 + 40%*40 or 22 minutes. The EVPI therefore is 22-4 or 18 minutes. So when I am able to find the correct chance of a traffic jam in less than 18 minutes I can improve the value of my decision.

But you know the internet, “you never know what you’re gonna get”. Let’s assume that the internet fails you 25% of the time in predicting a traffic jam. This works in two ways. It could indicate that there is a traffic jam but there isn’t any, or it indicates that there is no traffic jam but there is one. The expected value of the decision to leave home early or not now becomes 5.5 resulting in an expected value of imperfect information (EVIPI) to be equal to 1.5 (5.5-4) minutes. Note that using the internet only improves the value of your decision when it’s ability to estimate a traffic jam or not rises above 72%.

The EVPI en EVIPI measures are not only useful in everyday decisions; they can be used in any business decision. By computing the value (perfect or not) on each uncertainty in a business decision, a trade off can be made on the cost of gathering additional information and the impact it will have on the total value of the decision. It is a perfect guide to decide on how to best use our scarce resources like time and improve the overall value of the decision.

Risk Analysis Placebo’s

2010-04-11T14:35:00.008+02:00

Carbon Capture and Storage (CCS) has much attention in the Netherlands. It is thought of as one of the ways to meet the climate targets. It’s the Dutch government’s intention to strive for a 100% sustainable energy system. For the Dutch government, CCS offers a solution for the period of transition from fossil fuels to sustainable sources of energy. The government wants to start a CCS pilot project in Barendrecht in which CO2 is stored in an empty gas field. A mandatory risk assessment for the Barendrecht project claims CCS to be safe. Risks of a sudden blow-out of concentrated CO2 would be minimal, with the chance of a mortal accident of less than 1 in a million years. I took a closer look at risk analysis method that was applied and found that is incomplete and unfounded. The calculated risks are underestimated leading to a false belief that it is save to commence with the project. The flaws I found do not only apply to the risk assessment of the Barendrecht project but to many risk assessments of storage or transport of dangerous goods. These risk assessments are therefore Risk Analysis Placebo’s.

The flaws I found are numerous. One of the most important flaws concerns the validation of data used in estimating probabilities like failure rates. In assessing risks it is required to know the failure rates of for example pipelines, compressors, etc. In the Netherlands these parameters are prescribed by law. It is known that these standards are not verified often enough. Also knowledge from accidents is not used to update them. This already is bad practice from a risk management perspective. For the risk assessment of CCS it is even worse. The failure rates for the CO2 pipelines were derived from failure rates of other installations; they were not verified at all. Since CCS is a new technology this is quite questionable. Would you launch a space shuttle for the first time, using the model of a sputnik for test runs?

Another important flaw I found concerns the model used. Besides the standardized parameters, the model to be used for a risk assessment is also prescribed by law in the Netherlands. I’m still wondering why a one size fits all approach would be sufficient in risk assessments. The prescribed model simulates the cloud of the dangerous gas or substance after release under different circumstances. Given this estimated cloud the concentration of the substance can be calculated at different distances from the source. Risk is then calculated at each location by multiplying the estimated number of casualties with the probability of the event. The prescribed model has several flaws. First of all it is not capable of dealing with buildings. It assumes that the area for which the risks are assessed is completely flat. Also it is not capable to deal with wind speeds lower that 1,5m/s. In case of CO2 no wind is the most dangerous scenario as the Monchengladbach incident in 2008 has shown. To my opinion the most important shortcoming is that for many parameters in the model an average estimate is used (see also What’s wrong with average). To name a few, an average is used for failure rates, population density, pressure in the pipeline, amount of substance released, wind speed, temperature and diameter of the leakage. As Sam Savage explains very well, using an average can be a great mistake. Since the model for the mandatory risk assessment for sure is not linear the strong form of the Flaw of Averages (=Jensen’s Inequality) applies. In such a case no average input (=point estimate) must be used but a simulation must be run using the complete probability distribution of each of the parameters to get the true average output of the model and therefore the correct risk measures.

The above flaws in the risk assessment method require change as soon as possible. More sound risk assessment methods are needed, the current one feeds risk analysis placebo’s to the public and the decision makers. The current by law standardized risk assessments in the Netherlands have little value for estimating risks, let alone developing sound risk mitigation strategies. Risk analysis goes beyond plugging a few numbers into a model. It requires thorough knowledge of the situation being assessed, tested and validated models and validated data. Work of experts, not only in engineering in risk analyses as well!

For Dutch readers: A news item for television was made out of my analysis, see Netwerk.

On Her Majesty’s safety

2010-03-28T17:54:00.006+02:00

Last year the Dutch were shocked by the events during the annual celebration of the Queens birthday on April 30th. During the celebration in Apeldoorn which was visited by the Queen and her family, a car ploughed into a crowd killing five people, wounding 12. The 38-year-old driver was targeting the royal family, his attempt failed. In the months after the event it was investigated why this attack wasn’t detected by the extensive risk assessments of the various security agencies involved and why the risk mitigation strategies where not effective enough to either prohibit the attack or at least safeguard the Queen, her family and the people taken part in the celebrations. To my opinion one of the reasons is the method used to do the risk assessments. While reviewing the reports on the risk analysis and the identified risk mitigations of the event I came across an old friend (or is it fo?), the well known risk matrix. The method is used a lot, but this doesn’t imply that it is an effective risk analysis method, let a lone a sound basis for developing risk mitigation strategies. Here is why.

A risk matrix is a table that has several categories of probability and impact. Each cell of the matrix is associated with a recommended risk mitigation strategy. The matrix calculates risk as the product of probability and impact. Note that risk is not a measured but a derived attribute (Risk=Probability*Impact). The cells in the matrix are coloured to indicate the severity of the risks. Red for the highest risks, green of blue for the lowest risks. The matrix offers an easy to use and straightforward way to organise pre-listed scenarios in terms of risk. Its use has spread through many areas of applied risk management consulting and practice. It has even become part of national and international standards. Also it used at the Dutch Ministry of the Interior that is responsible for the Queen’s safety and at the National Coordinator for Counterterrorism which is responsible for policy development and coordinating anti-terrorist security measures. Using a risk matrix doesn’t require any training to explain or apply it. It looks nice with its intuitive colouring. Some people really make an effort in developing wonderful colourings to impress, but this cannot hide what’s wrong with risk matrices as recent research by Tony Cox proves.

In short there are four major shortcomings. First of al the risk matrix uses ordinal scales, for example the probability of a scenario is Extreme, High, Medium, Low or Negligible. The consequence of using ordinal scales is that the scenario’s can only be arranged in either increasing or decreasing order of probability or impact. It is impossible to say that a scenario is twice the probability of another scenario, how than can one decide on the risk of the scenario and decide on the right mitigation strategy? Compare this with the ratings of restaurant or movies. Using the star rating you can decide which restaurant to go to, where dinner at a 4 star restaurant is surly better that at a 1 star restaurant. 4 meals in a 1 star restaurant won’t make up for a dinner in a 4 star restaurant however; these ratings cannot be added or multiplied.

Second shortcoming is the low accuracy of the scales. When 4 categories of probability are used each category takes 25% of the total scale, this means that scenario’s with probability of 51% are in the same category as scenario’s with probability 74%. Quite a loss of detail, while risk management is about details! Third and very serious shortcoming is the assumption that scenarios are independent. Consequence is that in case of correlated scenarios the joined risk of the scenarios is ignored. When the scenario “Attack on the Queen’s bus” was combined with the scenario “Car ploughing into a crowd, breaking the barriers” maybe the April 30th attack could have been prohibited. Finally the risk matrix results in an inconsistent ordering of risks. Scenarios with an equal risk profile are placed into different cells of the matrix leading to different risk mitigations. Very serious shortcoming I would say. To explain see the figure. In the risk matrix curves are shown which connect all possible scenarios with equal risk. As you will see, the curves run through different coloured cells which should not happen, leading to inconsistent ordering of risks and therefore different risk mitigation for the same risks.

A doctor takes the Hippocratic Oath promising to not hurt his patient while applying treatment. The same should apply for risk analysis methods. Be sure that the method applied is effective and really reduces risk (prove it!). Given the above shortcomings it will be clear that risk matrixes will introduce risk instead of reducing it. Be well aware of that next time when you encounter one. I would suggest switching to another risk analysis method, one that is consistent and fact based.

What’s wrong with Average?

2010-02-27T17:07:00.007+01:00

“I'm average looking and I'm average inside. I'm an average lover and I live in an average place. You wouldn't know me if you met me face to face. I'm just your average guy.”

These few lines taken from a song by Lou Reed are about being average. We use averages all the time. To name a few, your IQ-score, the batting average of your favourite baseball player, the average time to complete a project. When creating next year’s business plan the expected future revenue is used, the expected budget requirements also. In a cross dock the average productivity of the floor workers is used to estimate the processing times to unload or load the trucks. Plans based on averages however are below projection, behind schedule and beyond budget. That is because of Jensen’s inequality. When using averages for input of the plans or models, we expect to get the average outcome. That holds in only a few cases in practice. The numbers that we average are actually random numbers, for example the duration of unloading a truck. In plans we do not use all possible outcomes of the random variable but use the average for simplicity instead, not realizing that we are possibly making a big mistake. Sam Savage calls it The Flaw of Averages. One of the examples he uses to explain the flaw is the drunk on the highway. The state of the drunk at his average position is alive, but the average state of the drunk is dead.

More and more companies and government agencies are aware of the value that analytics can bring them. With the availability of Excel doing your own bit of analytics is easy. I agree, Excel is helpful, but like any other tool in inexperienced hands, things can go wrong easily, especially when averages come to play. It is also an area where I come across the flaw of averages a lot. To give you an example, picture a cross dock operation. Trucks will arrive at a certain moment in time. The trucks will be unloaded; the material in the truck will be processed (like sorting or repacking) and loaded on trucks again leaving towards the next destination. The question that the cross dock manager has is how many floor workers he needs to process all the goods passing thru in such a way that all trucks can leave on time again. He start’s up Excel and puts in the scheduled arrival and departure times of the trucks. That was the easy part, although he knows that the trucks from the north arrive on average 10 minutes late. Next question to answer is how much time is required to offload or load a truck. Actually there are two questions; first the volume on the truck is required, next to it the number of items a floor worker can take out, sort and put into the next truck per hour. The cross dock manager does some fact finding and comes up with an average volume per truck and an average productivity for the floor workers. Using the averages he calculates the amount of floor workers required, easy.

After a few weeks the cross dock manager is not that satisfied. His customers complain that the trucks are leaving to late half the time, suggesting that that there are not enough floor workers. The manager has no clue on what is wrong. When he goes out to verify the numbers he used to calculate the number of floor workers, he finds the same averages on volume and productivity. Surely he has become a victim of the flaw of averages. To see why, for simplicity assume that all the trucks arrive at the same time and leave at the same time. Also assume a sort window (the time between trucks arriving and departing) of 1 hour. Also assume that the volume in the trucks is fixed at 100 items. What is left is the productivity of the workers. Assume that a worker can on average unload, sort and load 10 items per hour. Then, on average, 50 workers are required to process the freight of 5 trucks.

Now think of this, the floor workers productivity is on average 50, but not all floor workers will have that productivity all the time. Some will work faster, others slower, due to many reasons. When a floor worker has a lower productivity he will need more time to process the items from the truck and therefore the truck will leave behind schedule. A small Monte Carlo experiment shows the impact of a 10% variation of productivity.

As you can see, the required number of floor workers runs from 40 up to 75. The average number required workers is still 50, but the variation in productivity results in shortages nearly half the time, resulting in unsatisfied customers (and the manager’s headache). To help him a little assuring that in 95% of time he has enough floor workers, he should hire 60 workers. I left out the actual arrival times of the trucks and the actual number of items on the trucks, these will complicate the analysis, but with the use of Monte Carlo analysis these dynamics can be modelled with ease. So instead of using just an average, use all the information you have. This will lead to better plans, and fewer headaches.

Nothing wrong with being an average floor worker, but plans based on average assumptions are wrong on average!

Risky Business

2010-01-31T17:13:00.007+01:00

No, this is not yet another review of Tom Cruise’s breakthrough movie. It is about how decision makers in governments and business make their decisions, especially when the dynamics of the challenge they are facing is misunderstood. Understanding the dynamics of a system requires mastery of concepts like stocks, flows, delays, nonlinearities, feedback loops and uncertainty. Lack of understanding these concepts causes decision makers to make the wrong decisions. With the use of simple and easy to grasp models an analytical consultant can help government and business to make better decisions supporting them to get better understanding of real world challenges.

The concept of stocks and flows is often misunderstood, leading to hard to resolve problems in controlling the performance of supply chains. An example of such lack of control is the bullwhip effect which describes the magnification of fluctuating demand in a supply chain. A very simple example already shows how complex and counterintuitive flows and stocks can get. Let’s take a simple inventory model, in this case a bathtub with water. In the example the bathtub is first filled with water at a varying rate starting from 100 litres/minute reduced to 0 and than up again (see illustration). Next, the bathtub is emptied using the same flow rate profile. Question is how much water will be in the bathtub overtime? Can you draw the picture? What will be the maximum water in the tub? Sent me your answers, I am curious on what you can come up with. Many people draw a picture mimicking the saw tooth profile of the flow rates and use it to estimate the size of the bathtub to contain all the water. As a result they will underestimate it. In practice this would mean that for example the required stock space will be estimated to small or the wrong counter measures are taken to reduce for example carbon emissions to meet certain maximum levels.

The importance of understanding the dynamics of a decision even becomes more important when uncertainty is introduced. To return to our example, assume the rate at which water enters the bathtub now is uncertain and the above figure depict the average rate at which water enters or leaves the bathtub. For simplicity assume that the actual rate is 10 litres/minute higher or lower than average with a 50% change. Now try to estimate what the water level at the end of the time period. What is the chance that it will be less than 100 litres? What will be the change of the bath to overrun if the maximum capacity of the bath is 510 litres and the starting level 100 litres?

In business and government many times average rates are used to cover this kind of challenges. Using that same approach, the average total amount of water flowing into the bath will be 400 litres. With a starting level of a 100 litres the bath will never overrun, so the probability of overruns is 0. Using the same kind of reasoning the water level at the end of the experiment will on average be 100 litres. I have encountered this kind of reasoning a lot and it is wrong, very wrong. The correct answer requires some more work that just adding up averages, but it happens all the time. Together with misunderstanding the dynamics of the system this leads to very poor decisions.

The answer is to apply a mathematical model; in this case a simple model can show you what will happen to the water level in the bath tub. Using a small Monte Carlo model helps you include the uncertainty on the actual rate at which the water enters or leaves the bath tub. The MC model creates insight into the influence of the uncertainty on the flow rates and also warns you about the spread of the water level. The model will tell you that the chance of overrun is arround 25% and that the change of less than 100 litres is arround 50%. Did you guess that upfront? A mathematical model or more general an analytical approach therefore gives you the opportunity to make better decision like buying a bigger bath or a tap that you can control better, otherwise even managing the water level in your bath becomes risky business.

Mexican flu vaccine campaign; a false positive?

2009-12-30T17:29:00.007+01:00

Great news this week, the Mexican flu epidemic is officially over in the Netherlands. In July of this year, the first cases of Mexican flu were reported. At that time the World Health Organisation (WHO) already had signalled that the danger of a flu pandemic was growing and every country was advised to take appropriate counter measures. One in every 3 persons would get infected if no counter measures were taken. In the Netherlands this lead to the “Grip op Griep” campaign informing people on how to reduce the chances of getting infected. With silly posters people were told how to sneeze and to disinfect their hands, reducing the chance of infection. Also people having symptoms of the Mexican flu were tested and if required vaccinated. Later on this was turned into a countrywide vaccination campaign for the elderly and the young. In the Netherlands, until this week, 51 people have died, 2168 people were hospitalized and 4 million people have been vaccinated. The vaccination alone costs around 300 million euros. When comparing the numbers of infected with the previous years, (see http://influenzanet.com/) you can question whether it was all worth the fuzz. You will see that the number of infections from Mexican flu is highly overestimated. Also the cost effectiveness of the campaign is questionable. Can’t this be improved with a little more analytical approach?

One of the things that could be improved is the level of understanding doctors have on risks and probability. A test by Deborah Bennett on the ability of doctors to interpret test results shows this. In the test a doctor is asked to estimate the probability that a patient will have a disease, given a positive test result. The doctor knows that the disease will strike once in every thousand people. Also the test used presents a rate of 5% false positives. People are tested at random, regardless of whether they are suspected of having the disease. What is the probability of the patient having the disease? Most doctors will say 95%, but this is highly overestimated. What did you think?

To get the correct answer use the fact that out of every thousand people who receive the test, one will have the disease and 999 will not. Anyone who actually has the disease gets a positive result, so no false negatives (this is complicated enough for the doctor, but if you like the challenge assume a detection efficiency of 80%). One out of every thousand tests is a true positive. The remaining 999 tests should have negative results, but 49.95 of these tests will also give positive result (the 5% false positive rate). So in summary we have 50.95 positive results in every 1000, but only one of these is a true positive. So one in every 50.95 positive tests identifies a person who actually has the disease, or 2%! Believe it or not, we just applied the Bayes theorem!

P(Ill given Positive) = P(Positive given Ill) * P(Ill)/P(Positive) = 100%*0.1%/5.1% = 2%. Note the dramatic effect on cost if the test results are interpreted the wrong way. It will lead to unnecessary treatment of 50 people in every 1000. 51 times more budget is spent than required, assuming that the 50 false positive patients do not exhibit negative effects as a result of their treatment that require further medical. With this in mind, you can question whether the decision to vaccinate 4 million people is a good one. Recent research from the Groningen University (See Robin de Vries) shows that the current models to estimate cost and effectiveness of preventive vaccination by the Dutch government need improvement. I am convinced that more and better applied analytics will help.

Note : Back to the Bayes Theorem. Just a few days ago a terrorist tried to blow up a plane flying from Amsterdam to Detroit. Questions were raised on the effectiveness of the intelligence agencies trying to identify terrorists. Surly this attack was a false negative in terms of testing. It is interesting to figure out what should be the effectiveness (low false negative rate) of a test applied to identify a terrorist with a high level of reliability, certainly in relation to the level of false positives this test might generate.

Your buying habits revealed!

2009-11-27T14:47:00.005+01:00

You probably do not even think about it when you pay at the checkout counter of your local retailer, but retailers have been collecting massive amounts of data on your shopping for several years now. Ahold alone has registered 32 billion ticket lines over the past 7 years; every week 80 million ticket lines are added to that. That mountain of data has been collecting dust over the past few years. Mathematical modelling, statistical techniques and computer power have given the retailer the tools to mine for gold. But are they making the most of it?

Recently I was invited by the VARA, a Dutch broadcasting company, to explain how retailers use our shopping data. While at the future store of Metro in Germany I was interviewed on the subject. The interview was part of the “Weet wat je koopt” programme. The programme’s objective is to scientifically explain the background of certain products, like night vision glasses or Mexican flu vaccines. A perfect setting to explain how mathematics support retailers and show some of the stuff Stephen Baker has written about in practice. You can see the result on “Uitzending gemist”

Retailing really is paradise for Operations research professionals. With the data from consumer transactions, point of sales scanners, customer loyalty cards, website click through streams, RFID tags and smart carts (that register the way you walk through the store) quality data is absolutely no issue. That data allows us to help retailers to find the most efficient replenishment strategy, sourcing, and optimise on stock levels in both the store and at the distribution centre. But there is more. Assortment planning for example was previously an area where no optimisation methods were applied. It was seen as an art or craftsmanship from the store manager to find the best set of products for the store. From actual sales data, a store manager can learn from the buying habits of the customers to find the best assortment, making it a more fact based decision.

What is next? Well think about the actual lay out of the shelves. Don’t you ever wonder why certain products are displayed on eye level? You bet that it will influence the sales. Research has shown we buy more products on eye level than other. Knowing this, the retailer has to be smart on how to display his products, making sure that products with the highest margin are on eye level. Extending this a bit, knowing how customers move through the store can increase the effectiveness of product display even more. In the future store this was even extended a bit. With the “Einkaufsassistent” (an application on your cell phone) it is possible to direct you to the exact location of a product on your shopping list.

With all the knowledge on our buying habits, the retailer can try to tailor his offering to our preferences. In the old days the grocer around the corner already did this, like the milkman. With the massive stores, we have become unknowns to the store manager. Using the knowledge from our buying habits they can build up that knowledge again. Not that they want to know us personally, they are only interested in our buying habits. With that knowledge they can target us with special offers (like Tesco does in the US) or surprise us with an text message on our cell phone when we enter the store stating whether we forgot the peanut butter on the shopping list.

Go GREEN!

2009-10-25T16:23:00.002+01:00

Last week I had a presentation at the ORTEC user conference, together with one of my friends form the Antwerp University, Patrick Schittekat. Also Walther Ploos van Amstel was there with a nice speech on the diminishing elasticity in logistics. Our subject was on how to be green from an environmental perspective but still be competitive. We state that instead of waiting for the governments to come up with measures to reduce emissions, companies should re-think their supply chain now. That way companies can turn going green from a liability into an asset and are well prepared for the future. This doesn’t have to be a jump into the dark when it is fact based and with analytical support.

The speech we held was a result from the corporation between the Antwerp University and ORTEC as part of the Optimising the World initiative of ORTEC. We started this initiative this year and it contains 4 main themes; Humanity, Environment, Education and Sports. I already explained the Humanity programme in one of my earlier blog entries; see for example the entry on the Uganda flood response. In Education we try to stimulate students to choose mathematics, applied mathematics, econometrics and so on. For example by sponsoring the International Math Olympiad, this is held in Amsterdam in 2011.

Back to our speech, you can find the slides on LinkedIn by the way. Our story starts in Portugal, where Patrick had his holidays. During one of his trips he ended up in an orchard full of orange trees. He is quite surprised to hear that this is probably the only way to eat real Portuguese oranges in Portugal. The oranges in the stores in Portugal are from Turkey! Can you imagine that? It’s cheaper to grow oranges in Turkey and transport them all the way to Portugal than to grow them in Portugal in the first place. This is not very optimal from a green perspective. This will probably change when emission taxes are introduced, as will be the case at the Copenhagen conference later this year. This tax will influence all the logistics in any supply chain. The decision that any company must make is to either endure this tax or start acting now. Many times going green means increasing costs; one has to invest in new technology to have lower emissions. But that is not always the case. During our speech Patrick and I gave several examples in which environmental friendly changes and cost savings go hand in hand.

A straightforward example is the optimisation of the logistics operation, minimizing number of deployed vehicles and kilometres driven. Since a truck on average emits 0.9 kg C02 per kilometre, every saved kilometre leads to a greener operation. But more is possible, for example by changing the modalities used. In one of the projects I was involved in, the supply chain for an electronics company required restructuring. Many of the products they sold were produced in China. Transportation of the products was therefore something to think about. The products can be shipped to Europe by sea or air. Air is expensive and fast and not very green per kg transported. Sea is cheap, has low emission per kg transported but is a bit slow. Transporting products by sea takes a couple of weeks, while using air the products could be at the shops in 2-3 days. The price of the products sold can fluctuate a lot; a long lead time can therefore mean a substantial loss of revenue. How than make the trade-off between sea and air?

What we did is build a supply chain model (using the AIMMS solution) in which we were able to optimise and evaluate different kind of set ups for the complete supply chain, focussing on service (is the product on time at the point of sale), cost (air is expensive!) and CO2 emission (what is the environmental burden of the scenario). The model enabled us to create insight into the dynamics of the supply chain, supporting the management in making their trade-off between air and sea and the environment. In the end the best set up was a combination of the two modalities. In acting this way, the company is well prepared when the CO2 emission taxes are introduced, and ahead of competition. They made going green there asset, not a liability.

What about Risk?

2009-09-26T17:09:00.005+02:00

One of the hot topics in the Dutch news these weeks is the financial disaster the construction of a metro line in Amsterdam is causing. A quantative based risk assessment would have lead to better estimation of the financial risks upfront and better risk mitigation strategies during the project.

At the start of the project the total investment for the metro line was estimated to be €430 million. Based on this estimation the Amsterdam council decided to go ahead with the plan. Besides the relief the metro would bring to the dense traffic in the centre of the city, making it more healthier to live in, it would also make the centre of the city more appealing. No walls of trams blocking your view of Amsterdam. Constructing the metro would take some time and would cause a lot of inconvenience during that period. By the end of 2011 all work would have been done and everybody, either citizen or tourist, would benefit from fast and comfortable transport under the city. The actual situation is much different. Cost are now estimated to sum up to €3.1 billion (that’s more than 7 times the initial estimate!) and the project will finish no sooner than 2017.

These things can happen of course, but all big infrastructural projects in the Netherlands seem to go this way. To name a few, the construction of a high speed railway track is over budget, delayed and still not operational. A new railway track for freight trains towards Germany is operational, cost more than estimated and has a lower than estimated utilization, making it less profitable. And yesterday the construction of the new campus of the university of Maastricht was stopped, because of excessive cost overruns. What questions me is, didn’t the decision makers in each of these projects ever hear of quantitative risk management?

The project plan for the Amsterdam metro included a risk analysis both financially and technically. The tubes of the metro and the underground stations need to be constructed in very wet grounds. Many of the old houses are build on wooden poles and digging deep holes near them might case damages to the houses. Past experience and even tests had shown the construction workers how to deal with it. The total addition for risk in the budget was set to 4%. This number really makes me laugh. When I compare that risk measure with the risk measure normally taken into account in for example IT developments (10%) that would mean that constructing the new Amsterdam metro is far less risky that making a IT system. Is this really true?

The trouble with risk is than we can perfectly look back and see the cause and effect relationship of every incident, but how to asses or even forecast consequences of risks? As Nassim Taleb already described we (as humans) are not capable of dealing with probability. We tend to underestimate the bad (see the financial crisis) and overestimate the positive risks (we all think we will win the €27.5 million price in next months lottery). So we need some help to deal with it. I don not mean the simple risk mapping tools that were probably used in the assessing risks of the above disasters. These methods are not fit for assigning risks, it is far better to use quantative models. It has been shown (see for example the work of Fiona MacMillan in assessing risks in oil exploration) that companies using quantitative risk methods have a better financial performance, this should also hold for (local) governments.

One of the methods that I use a lot is Monte Carlo simulation. It is flexible, pretty straightforward to program and very easy to use. I used it to asses risks for pension funds and insurers and to identify robust strategies in for example investments. I also used to calculate dredging lanes. In one of the projects for insurers I used is to asses the financial risks involved when a catastrophe, like a hurricane or flood, occurred to oil rigs or refineries. That last example is comparable to the construction projects mentioned above.

How come nobody in government uses these methods? It will probably save us all a lot of money and probably also some careers in politics. I think it should be part of legislation. No new big infrastructural project should be started with a certified and quantative risk assessment, using state of the art models.

Strategic value of OR

2009-08-19T13:23:00.003+02:00

In the CPMS group of INFORMS on LinkedIn a discussion was started on the contribution Operations Research can have in Strategic Planning. This discussion triggered me to think about if and when Operations Research offers added value in boardroom decision making. You might think that because the name of our profession starts with Operations, that it is the only area of business where it can be applied. My experience is different.

This year’s winner of the Edelman award is a perfect example of how OR can support Strategic Planning. HP has used Operations Research to transform their complete product portfolio and saved $500 million over a three year period. The challenges faced by HP were huge. HP had tens of thousands of products in over 170 countries. By applying OR techniques HP has redesigned their complete supply chain and improved on profitability and agility.

From my own experience I can give several examples in which OR plays a crucial role in boardroom decision making. One of them is the Global Optimisation programme of TNT Express. The programme objective is to enable the strategic goal of TNT Express, focus in networks. TNT Express has identified that using OR supplies them with a competitive advantage. Using OR models we created insight on the strengths and weaknesses of the current network and service offerings of TNT. With this knowledge and in cooperation with senior management future scenarios were formulated based on which new network designs and service offerings were identified. With these results senior management of TNT Express is able to achieve $M cost savings for the short term and make fact based strategic decisions on future network design and service offerings.

TNT is not the only example. Other examples of the application of OR within strategic decision making are optimised pricing strategies in the airline and travel industry and the identification of the contribution, investment and indexation policies for pension funds and insurers. In each of the examples OR is applied first to understand the dynamics of the arena in which the decision needs to be made, leading to a mathematical model that provides the insight. Than the model is used to identify and evaluate possible alternatives (= scenario’s) and decide on the best way forward (=strategy/policy). How the alternatives are constructed or generated very much depends on the type of questions that need to be answered. This also applies to the environment in which the decision is made. In many cases, because nobody can predict the future, Monte Carlo simulation is used to generate viable future scenario’s based on which the most robust future strategy is identified.

More and more companies use OR as part of their strategic decision making. But there is still much ground to cover for us as OR professionals. To “compete on analytics” companies need to better understand what OR can offer them, but also its limitations. OR is no magic lamp or crystal bowl offering the answer to any strategic question. The responsibility for the decisions on strategy lies with senior management, OR can help them unravel complexity, quantify risks, understand consequences of decisions and in the end beat competition.

Does Operations Research sell?

2009-05-25T13:27:00.004+02:00

No, it does not; nobody is looking for an Operations Research specialist. What companies seek is a solution, not a tool or skill. We will have to convince them that Operations Research can lead them to a solution. In the current climate of economic downturn companies seek strategies to survive. They have many questions like how to cut costs, improve profitability or want to review their total supply chain. Questions that require the support of Operations Research to solve them. Although companies need support, it does not imply that it is easy to get a new project. There is no standard “algorithm” that gives you a new project every time you run it. Acquiring a new project can be hard and it requires skill that can not be learned form a textbook. Here are some of my experiences.

Create Some Buzz
First step in acquiring a new project obviously is to get an appointment. When you are very lucky you get a call and are invited to have a talk about the questions that need to be addressed. But unfortunately this is often not the case. Before you are invited to have a talk and possibly acquire a new project, you need to get yourself noticed or get introduced. To accomplish that you need to make some buzz about your work and achievements in the media that your customers are most likely to read. Think about business magazines, blogs, websites, speeches at conferences, etc. The most effective way is to ask your customers to make the buzz. For example by means of a short statement on the project you performed for them and what you have achieved. Do not forget to let them include a statement on the project cost and the cost reduction or increased revenue you have accomplished. Getting noticed also requires you to build up a network, which enables you to get introduced to the right people. Moreover since your customers are happy with the result of the project, you can ask them to help you find new projects.

Golden Nuggets
Operations Research is a relative young area of expertise. Although it has been around for over 60 years now, we as OR professionals still need to carefully explain what OR has to offer. Managers many times mistake OR for some kind of application of IT. Operations Research requires IT as an enabler very often, like in Advanced Planning Software or as part of a larger ERP system like SAP, but it surely is not the same. It is far more than that. During the acquisition phase of the project we therefore have to explain in non technical terms what can be achieved with OR, preferably in terms used by the potential customer and with examples from the business area of the potential customer. The examples should come from your own (or your colleagues) experience, like the testimonials from your customers. These golden nuggets will provide you with some ease of mind during your conversation, while the potential customer will be amazed by the things that can be achieved with OR.

Cherish your customer
So creating Buzz and some nuggets is enough? No, but they help a lot. The far easiest way to get a new project is at your current customers. It is a rule that applies to any business; it sure does apply to ours. Your current customer knows you and knows what you can achieve for him. So make sure to do your best during your current projects. If it is successful, acquiring the next project will be as easy as picking up the phone. Operations Research sells after all!

Hip Hip Hooray!

2009-04-19T12:17:00.010+02:00

This year it has been 50 years since a Dutch Mathematician Edsger W. Dijkstra published his famous algorithm to solve the shortest path problem. Time for a celebration! Although not always visible, we depend on the algorithm every day. The algorithm has many examples, starting from the obvious application in the satellite navigation system in your car. But also less straight forward applications like in Internet routing protocols like IS-IS and OSPF, without it no Internet and you would not be able to read this blog entry.

Edsger Dijkstra was a brilliant computer scientist, who strang enough was not very found of using computers himself. He was well known for his use of a fountain pen, instead of a word processor. It has been said that he even went so far as to create his own ink because he was not happy with the quality of the ink that was available. Besides the Shortest Path algorithm he has many other accomplishments in the area of program correctness, mathematical methodology, algorithms, and systems. He considered the GOTO statement as disastrous as you can read from his article in the Communications of the ACM 11, 147-148 in 1968.

"For a number of years I have been familiar with the observation that the quality of programmers is a decreasing function of the density of go to statements in the programs they produce. More recently I discovered why the use of the go to statement has such disastrous effects, and I became convinced that the go to statement should be abolished from all "higher level" programming languages."

Dijkstra’s algorithm is a greedy algorithm to find the shortest distance from a starting point (or vertex) to any other point in a network (or graph). Actually it is an undirected weighted graph, the edges (or lines between points) all have a value, for example cost or duration. I have used it many times, even programmed in VB using GOTO statements (sorry Edsger!). It is any easy to use algorithm, and simple to programme or adapt to specific applications. It should be part of any OR practitioners toolbox. The obvious application is to calculate the travel times and shortest distances in a network. Based on the result infrastructure analysis and network design studies can be performed or optimal routes can be calculated. But I also used the same algorithm to generate schedules for bus drivers.

Dijkstra’s algorithm has many real world applications. One of them is in telephone networks. In a telephone network the lines have bandwidth; a phone call needs to be routed through the network via the highest BW. By representing the switching stations as vertices and the transmission lines as edges and the weight of edges to represent the band width, with Dijkstra’s algorithm we are able to find the best routing. This example is similar to the situation in which you want to plan your holiday or business visit. Given the available flights, airports and arrival and departure times, you can find out the earliest arrival time at your destination given the airport you want to start form and the start time with Dijkstra.

With Dijkstra’s algorithm we can put Operations Research into practice! Therefore three cheers for Edsger, Hip Hip Hooray, Hip Hip Hooray, Hip Hip Hooray!

SiCKO

2009-03-21T16:41:00.004+01:00

In the past few weeks the Dutch hospitals were in the news several times. The hospitals in the Flevopolder (IJsselmeer hospitals) went broke and have now been taken over by an investment company. In Zeeland negotiations to merge two hospitals were stopped. In Limburg one of the 3 hospitals in that area nearly went broke because of financial mismanagement, now over 600 nurses may lose their job. Seems that healthcare itself should go for a check up. When looking at the number and geographic spread of hospitals in the Netherlands, I wondered if we don’t have too many of them. Researching some statistics, this hunch seems to be right. Over 70% of the Dutch population can reach a hospital within 20 minutes, which is 22% above the EU average. Also the average distance to a hospital in the Netherlands is only 7 kilometres. We can do with fewer hospitals and still be well within the safety limits.

People in the US are less fortunate with respect to healthcare. 20% of the US population lives in areas with only 9% of the doctors. Moreover the cost of healthcare is 2.5 times the cost of OECD countries and continues to rise. So people in the US get less care at a higher price. More than 50 million people of the US lack insurance and as a consequence do not receive treatment when required; even Medicaid patients sometimes are not accepted. Access to healthcare can be an issue when you live in the US. Michel Moore can tell you all about it.

How to address such a challenge then? The Dutch and US situation with respect to access to hospital care is comparable to a location decision similar to the decision on where to place antennas to set up a UMTS network. The hospitals need to be located in such a way that the longest travel time of a patient is within the safety access time. The safety access time is different for emergency care than for example paediatric care, so different care types require different service times. Besides access time also the demographic characteristics of the population should be taken into account. The demographic characteristics determine the kind and demand for healthcare, elderly people usually demand more and specialised care. To give you a flavour, 80% of the cost of your life time healthcare is generated in the last 5 years of your life. Most of it is hospital care. More demand for healthcare means more doctors and beds and therefore a larger location. As such, the hospital location decision looks very much like the facility location problem, a problem that we know how to solve.

Decisions on location, size and kinds of healthcare offered are political decisions. With the use of techniques from the area Operations Research better and more objective decisions can be made on number, size and location. This will lower the cost for healthcare or enabling more care for the same Euro/Dollar. That is not the only subject were Operations Research has added value in healthcare, to name a few:

Improve on the allocation of drugs
Improve on the efficiency of the distribution of vaccines, redesign of vaccine programmes
Improve blood supply chain
Reduce organ transplants that go to waste.
Improved budget allocation, use the available money better
Better allocation of medical personnel; geographic spread, better schedules, improve productivity.
Improvement on the screening programmes; early disease detection like certain cancers.

I all of these areas good work has been done, but to my opinion not known to the decision makers in healthcare. I would to invite them to read about it and to challenge us, the Operations Research practitioners, to come up with a challenge that we can not help to solve.

Excellence in Industry

2009-02-06T17:58:00.005+01:00

Yesterday I was at the 23rd Belgian Conference on Operations Research (http://www.orbel09.be/). It was hosted by the University of Leuven in the ancient city of Leuven, a wonderful setting for such a conference at wich also Martin Grötschel and Maurice Queryanne were present as plenary speakers. I really recommend you to visit Leuven, even if you have little time available. A very good way to plan for such a trip is to use http://www.citytripplanner.com/ .

I was in Leuven as a member of the committee for the Excellence in Industry award that is sponsored by the company I work for, ORTEC. For the award 6 projects were nominated. Each submitted project was asked to present the project in a 20 minute speech. Since the award is about Excellence in Industry criteria such a business relevance and practicality of the solution were very important in evaluating each of the submitted projects. But than again, that is what Operations research is about, improve and enhance operations.

The winner of the award was the integrated berth allocation and crane assignment model of Rowan van Schaeren. In his project he succeeded to combine the berth allocation and the quay crane planning for a container terminal in the Antwerp harbour. The combination of the two is unique, but more important, the model was applied in practice in such a way that the container terminal is able to lessen the time required for a ship to spend at the terminal. It therefore saves money. Second, the model also assists the planners of the terminal in creating a plan, reducing their effort. Before the model was available, the berth allocation and crane assignment was done manually and separate from each other. Getting a feasible plan was a first priority. With the model in place, the planners can now focus on the quality of the plans and also better manage the cost of manpower on the terminal. This is what Operations research is about, improving Operations!

The runner up for the award actually was the project that resulted in the city trip planner I mentioned above. It also is a wonderful and very practical application of Operations Research; it even works on a smart phone. The idea was born out of a need of tourists to select locations in Leuven that they could visit given their available time. Leuven has many points of interest (around 170) that make it impossible to visit them all in a short time (say a weekend or a day trip). To help the tourist decide on which points of interest to visit a website was developed, with behind it a model to support the tourist in planning the city trip. On the website you can fill in a short questionnaire on the kind of points of interest you would like to visit and your available time. What is interesting is that questionnaire also asks you to add keywords on subjects or general interests you have. These keywords are used to query the descriptions of the points of interest to select the best matches. Based on the scores of each point of interest, the travel time between each of the points, expected length of stay and the available time for the trip, a plan is suggested including a route which you can print or download on your cell phone. Again a very practical application of Operations Research.

Given the possibilities Google offers in real time tracking of cell phones I can imagine that extending the city trip model to reduce queuing at popular sites or even using the length of stay at each location to better estimate trip length is easy. Not to mention the possibility to have the model order your beer in advance, so it’s waiting for you when you arrive at the end of your city trip. Not sure if I would like that.

From Politics to Maintenance

2009-01-28T12:36:00.003+01:00

On my way to the office I listened to an interview on the radio. The reporter was interviewing the project manager of the largest infrastructural building site in the Netherlands, the construction of the orbital motorway around Eindhoven. The project manager indicated that the project would take 4 years. During that time the current traffic, around 150.000 vehicles per day, needs to by-pass Eindhoven using temporary roads. During the project these temporary roads will change constantly. Today nearly every driver in the Netherlands has a TomTom kind of navigation system in the car, which is trusted without question on directing the user to its end destination. These systems are a very good example of how practical Operations Research can be. The situation around Eindhoven however changes every few weeks, which causes some of the drivers that blindly follow the directions from their navigation system to end up between the builders. A good example that even though you have a wonderful system available to solve an optimization problem, you still need to be aware of the conditions under which you apply it. At least some of the drivers around Eindhoven know that now.

The interview on the radio also brings back some projects that I did in the past with respect to road construction, that are nice examples of how broad the application of Operations Research can be. To start with, in the Netherlands the Ministry of Transport, Public Works and Water Management is responsible for the maintenance and construction of roads. They develop a long term plan in which specific projects are scheduled to either construct, changes of maintain roads. Based on that long term plan, a yearly budget is determined that is announced on the annual speech of the Throne on the third Tuesday of September. The challenge in developing the long term plan is that projects usually take longer than 1 year, and in each year a certain budget is required. The budget approval from the House of Commons however is for one year only. Also the scheduled projects cannot be stopped as soon as they have started, and as you can imagine, some of the projects take more time and therefore more money. Also the projects are related and have precedence relations. Every year the long term plans needs to be reviewed and revised to come up with a new annual budget. The number of projects is quite large, so manual adjustment is out of the question. This is where Operations Research comes in. Actually, the problem the Ministry of Transport, Public Works and Water Management faces is a capital budgeting question which we solved using a linear programming model. With this model the Ministry was able to decide which projects to start or postpone and so meet the budget requirements, but also have the projects with the highest priority scheduled as soon as possible. The model supported the Ministry to objectify the project scheduling, making it a less political decision. Maybe they should use Operations Research more for example better estimate the risks involved in large infrastructural projects.

On the other side of the spectrum, I was also involved in a project in which the objective was to find the cost optimal strategy to maintain road section. The cost identified was used for the above budgeting process but also to compare it with the offers submitted by the road construction companies that would like to get the maintenance contract. So Operations Research enabled a sanity check on the offers done by the road construction companies. With the optimal maintenance strategy available, the government was able to challenge the construction companies, leading to more efficient road maintenance at a lower cost. Finding the optimal maintenance strategy was a challenge in itself. Based on actual the road conditions (holes, bumps, wear and tear) the model we developed was able to define the best maintenance strategy for each part of the road. We accomplished that by dividing the road into (virtual) tiles en for each tile decide to either lower it (scraping of the tarmac) or raise it (put on tarmac). Using a dynamic programming formulation the optimal maintenance strategy was identified, taking restrictions on bumpiness of the road, angle, etc, into account.

So Operations Research can be very hands-on giving you an exact plan on how to maintain a road segment and helps to identify the best maintenance offer. On the other hand it also supports decisions on governmental level, making the difference between what’s logical and politics.

Forecasting; Witchcraft or Science?

2008-12-26T12:39:00.004+01:00

At years end, we start thinking about next year. What will it bring us? How will our lives look like in one year’s time? Some people visit a palm reader or fortune-teller, maybe even a ghost whisperer to learn about the future. Others, like Albert Einstein, never think of the future, because it will come fast enough. To look into the future we need tools other than Tarot cards or tea leaves or people like Sybill Trelawney. But are these tools good enough?

Everybody knows that no one can accurately predict the future, at least that’s my view. However, companies depend on accurate forecasts to survive. In the current economic decline, forecasts about how long and deep the decline will be are required to take the appropriate measures. In the Netherlands, several companies that depend heavily on the tendency of the market, like ASML, TNT Express, Corus, need to act quickly in order to survive. They have to (temporarily) lay off people, close down plants or reduce costs very fast. Getting this right reduces the impact of the measures that need to be taken, also it reduces the probability that too harsh measures are applied, setting back the company’s ability to take advantage when the economy booms again. Can Operations Research be of any help?

In forecasting, Operations Research offers techniques that can offer some assistance. These techniques come from the area of Econometrics and have a statistical background. They can be divided into two groups, time series analysis and regression analysis. In time series analysis a formal pattern in a sequence of observations is identified and used to predict future values. In regression analysis a formal relationship is determined between a dependent variable and one or more explanatory variables or predictors. Note that both assume that the pattern that was identified prevails in the future. A lot of research has been done in developing and improving these statistical techniques. Major problem is that these techniques require enough reliable data and should be applied by specialists.

I have encountered many examples in projects in which time series or regression analysis was applied without a sound theoretical fundament, leading to ill defined relations and therefore bad forecasts. One of the examples was in the travel & leisure business. In that particular project statistical techniques were used to identify factors that determined the demand for hotels and residential leisure parks. The idea was to use these factors to predict the future demand, based on which the price was determined to maximise the firm’s revenue. The error in the approach was that to forecast future demand, each of the identified predictors of demand needed to be forecasted. No data to support that was available. So, instead of forecasting the future demand alone, the company ended up with having to forecast several unknowns.

In forecasting I have obtained the best results when combining the statistical techniques with judgemental methods. Judgemental methods are subjective, but allow you to incorporate intuition, expert opinion and experience (so still a bit of palm-reading is required). By interviewing experts in different areas of expertise a qualitative vision on the future can be developed. Combining these views with what has been identified with statistical techniques leads to better forecasts. When constructing different (expert) views of the future, scenario analysis helps you to even better determine the strategy for the future. This way you can support companies to identify the best way forward, but also show them what the future can possible bring them (not just a point estimate, but a range of possibilities) improving the quality of the strategy.

Of black sheep and black swans

2008-11-23T12:16:00.004+01:00

The credit crisis is spreading more and more. Banks will tumble over without governmental support, companies like General Motors and Toyota have to layoff people because they are not selling enough new cars and pension funds have to apply serious cutbacks in order to keep a healthy balance between assets and liabilities. It has become commonly accepted that the cause of the credit crisis lies in the introduction of complex financial product that have been constructed in the backrooms of banks by financial mathematicians and econometricians. So it is all to blame on math? Math has become a black sheep, a scapegoat to blame the credit crisis on. But math doesn’t introduce new financial products, it is the bankers themselves. Moreover it was not the math that caused the prices of houses to drop, causing the sub prime mortgages to default. Bankers didn’t anticipate on a significant drop in real estate prices, a rare but disastrous event. They didn’t (want to) see that black swan.

Math is the mother of many sciences, it is very important in our profession, also in the financial markets. I have spent several years in applying math in modelling financial products in optimisation models for pension funds and insurers. Aim of the models was to analyse strategies in funding and investments against the uncertain future. In most cases Monte Carlo simulation was used, to generate as many as possible future scenarios and find the most robust investment and funding strategy. Math gives you the possibility to describe a financial product in a handy, accurate, objective and quantitative way, giving insight it its behaviour under different economic circumstances. Key is of course to think of the circumstances you want to analyse, as in any optimisation project. This requires an open mind, not one pre-occupied with making money.

The core of the credit crisis lies in supplying mortgages to families that normally wouldn’t get one. By adjusting the conditions of a mortgage (introducing the sub prime mortgage), banks in the US created a possibility to increase the number of mortgages sold. When the family no longer could fulfil the payments on the mortgage, the banks would simply sell the house. In selling the house they expected to make a profit, because of ever increasing prices of real estate. There is no math involved in that process, just a focus on making money, whatever you may think of that. To even more increase revenues (and profit) derivatives were created to split up the sub prime mortgage portfolios, selling it to other banks and investors, spreading the risk across the world. This created a setting compared to Domino day. Again no math involved here, the only driver here is money.

The first domino’s started to tumble when banks in the US were only able to sell the real estate of defaulted sub prime mortgages with substantial losses. A situation that was impossible according to the bankers. This is a typical example of a black swan as has been described by Nassim Nicholas Taleb. As he states: “Banks hire dull people and train them to be even more dull. If they look conservative, it's only because their loans go bust on rare, very rare occasions. But (...) bankers are not conservative at all. They are just phenomenally skilled at self-deception by burying the possibility of a large, devastating loss under the rug”

So it is wrong to blame math for the credit crisis. Math is a powerful tool that supports us in many ways. It helps us in optimising logistic chains, schedule manpower, build telecom networks, search Mars for water, organise humanitarian support and much more. When the bankers had used it in a proper way, maybe they would have been able to identify the risks involved when introducing sub prime mortgages.

Operations Research Economics

2008-10-19T17:27:00.004+02:00

I seem to be one of the OR-bloggers that didn’t attend the INFORMS DC meeting. Sorry for that, I would have liked to meet all that did attend but I was too busy. With the current economical developments in which governments spent billions to save banks from falling over, also my clients call me in distress and ask for support. This seems weird since, in times of economic distress, companies tend to reduce spending money on external consulting, but it seems that OR consulting is the one type that companies much like to spend money on even when things get rough.

When the economic mills slow down or even stop, companies face a lot of difficult questions. One of the most important ones is how to keep business profitable and shareholders happy; cost cutting is thought to be the best option because it is a powerful instrument to still make a profit with deceasing revenues. But cost cutting is also very destructive; it will destroy future capabilities and can ruin lives of employees. In times of economic prosperity the focus on costs, building a lean and mean operations, is not the first priority of management. That results in a lot of fat in the origination that can be removed by operating more efficiently. The challenge for the OR professional is to find that the best optimisation diet to revive profitability with the lowest impact on the operation.

In the past years I have been consulted by many different companies to support them in deciding how to best address the consequences of an economic slow down. They wanted to know were to close down factories, which products to stop offering, how to be more cost efficient, even who to lay-off. The last one certainly wasn’t easy. As an OR professional you can’t decide what is the best action to take; that is the responsibility of the company itself. In situations in which I was asked to suggest the best decision, I always tell the company that I can show them the impact of the various options, but they have to make the decision.

Most of the times the questions raised have to be solved on a very short notice. The stock market annalists are waiting for action and they want it fast. For all stock market listed companies this means less than three months of time to get results, since every quarter an update to the shareholders must be given on the financial soundness of the company and the plans for the future. The projects executed to regain profitability are of high strategic importance and were executed in or very close to the boardroom. This brings operations research professionals were they should be, at boardroom level. Many times I was surprised to see that CEO’s and the like know so little of the added value an Operations research professional can offer them.

So, even though the economy is coming to a stand still, I still am very busy. A job in the OR consulting business therefore is probably the best hedge against unemployment. In times of prosperity companies hire you because the have money to spent to work on ideas they have on expanding their business. In times of economic distress they also hire you, to find out the best strategy to keep them in business.

Planes, Trains and Express services

2008-09-14T12:25:00.002+02:00

Resource schedules play an important role in everyday life. Simply think of the airline schedules and bus and train schedules. This year the Franz Edelman award went to the Dutch Railways for their accomplishments in improving the schedules of the commuter rails system of the Netherlands. The Dutch Railways got the price for applying Operations Research to construct an improved timetable. As a result, the percentage of trains arriving within 3 minutes of the scheduled time increased from 84.8 % in 2006 to 87.0 % in 2007. This may not seem much, but it is a great achievement since the Dutch railway system is one of the worlds busiest. Even the public opinion changed because of the new schedules. The number of jokes on the trains arriving on time dropped significantly (now how can I proof that?)
Schedules like the ones used in railways are also present in other areas, for example in the Express market. Since Express services are all about on time delivery, they face the same challenge as the Dutch railways. In designing their schedules a much used approach is to start with an estimation of the amount of freight (parcels) that have to be moved between each origin and destination combination in the network. Based on the forecasted volumes the required schedules are than developed. Designing the network is not an easy task (see http://john-poppelaars.blogspot.com/2008/04/express-network-design.html) As you can imagine the data and parameters used in such a case are not fixed. For example think of vehicle capacities. How many parcels could a vehicle carry? This depends on the composition of parcels that have to be transported. These can be either bulky but light, but also compact and heavy (like a machine or engine). Normally a certain gross capacity is assumed for the vehicle, talking into account the freight profile of the past, assuming that that will be the same in the future.

A main cost driver in an Express network is the line haul cost, in road networks as well as air based networks. A network schedules consists of movements which designate the time of departure from the origin and the time of arrival at the destination and vehicle type. For trains it is exactly the same. Getting the vehicle type wrong (either to large or to big) is not efficient from a cost perspective. Since the Express market is a highly competitive one, you cannot effort to loose money that way. However, changing the vehicle in accordance with the actual volumes, most of the time, is impossible, as is the case with trains. Having a good estimate of the amount and composition of the parcels is therefore a must.

Obviously the amount and composition of parcels is not static but random over time. There are some characteristics of the time series that will repeat themselves, like the increase in number of parcels during the Christmas period. But estimating the amount and composition on a daily basis is really hard, if not impossible. How to address this issue than, because we still need reliable volume forecasts to construct the network. Trying to model the stochastic nature of the time series and incorporating it in the model to find the best line haul schedule will clearly complicate that model immensely. That under the assumption that an econometric model can be fitted to model both number, volume and weight of the parcels for each of the origin and destination combinations to be served by the network.

My way to deal with this random nature is to except it in designing the network and go for the average or some percentage of that average volume (say 90% or 110% of the average). Based on this static forecast the network can be designed. This works fine in practice, also because many times my customers are not able to supply my with the data to estimate a volume forecast model. To improve on this we do a sensitivity analysis based on volumes used using scenario’s that are discusses and approved by the customers.

Tactical Manpower Planning

2008-07-27T15:41:00.010+02:00

Manpower, for many companies, is their most important source of production capacity. Simply look at healthcare, mail delivery or the retail business. According to the Fortune 500, Wal-mart is the world’s biggest employer, employing over 2 million people. Number 4 is US postal. Both are examples of industries where the demand for manpower will vary over time.
Identifying the best staffing levels to meet the requested manpower at each moment in time is a challenge for them, one that can be addressed effectively with the use of Operation Research. I have performed various projects on this, in a wide variety of industries. In this blog entry I will explain how I addressed this challenge. I will focus on the question of how to determine the staffing levels; in a later entry I will address the challenge of generating good shift schedules.

First step in identifying the right staffing levels is to have a good estimate on the required manpower. As mentioned before, the required manpower varies over time, sometimes due to seasonal influences, like in agriculture or for airlines, but it can also vary on a very short term, like in call centres. A clear understanding of how the work is organized helps in identifying the right levels of staffing. In the airline business for example most of the activities performed are depended on the schedule of the aircraft. At a hub of an Express company the activities to be performed are depended on the arrival and departure of trucks or aircraft, also at railways, bus companies, etc. Focussing on the airline example, when an aircraft arrives at the airport all kinds of activities need to be performed before it can depart again. It needs to have a technical check up (to make sure it doesn’t fall apart), small repairs are performed, it needs to be cleaned, refuelled, etc. Also the baggage handling, passenger check in, airport security checks and boarding are all processes that are depended on the airline schedule. Scheduling these activities is a challenge in itself, also because in most cases special skills are required to perform them. As you can imagine the scheduling of these activities influences the demand for manpower a lot. When you do a bad job at this, for example by scheduling them all at the same time, it will create a peak in the required manpower. When you are able to create a flat as possible manpower requirement profile, it is much easier to create efficient staffing levels, for each skill, as you can imagine. Sometimes the company that hires you supplies you with the required manpower and is therefore taken as given. An easy job, you might be tempted to think. However my experience indicates that having a detailed look at it and trying to influence the organisation of work is worthwhile to consider, before identifying the best staffing levels.

A typical picture of the required manpower looks like the profile of the toughest stage in the Tour the France, many peaks and valleys that need to be covered with a set of shifts of certain lengths. The objective can either be to cover the peaks at all time, or at a certain ambition level. Part of the work is then covered with hired workers. Identifying a new set of shifts involves taking into account a vast number of conditions. Collective labour agreements and governmental regulation give guidelines on the minimal and maximum duration of shifts, the number of breaks in a shift and appropriate start times of shifts. Last but not least also employee preferences or scheduling principles applied influence the shift set to be modelled. Each of these conditions needs to be translated into formal restrictions of the model, most of the time leading to a mixed integer programming model. I usually solve this kind of models by generating all possible shifts using different start times, breaks required and duration of the shifts and breaks and let the management and employee representation of the company review them. After approval I feed the shifts that are acceptable to both management and employees into the model that identifies the best set. Sometimes new shift times are out of the question, because the shifts are part of the collective agreement. In that case it is still possible to improve, since the amount of shift can still be optimized. The same model as before can be used but now the shift set is fixed to the shifts now in use. The objective function needs some attention, especially when you want to use the model also for less than 100% coverage of the required manpower. I have some good experience with an objective function that minimizes the absolute difference between the required and available manpower.

The result of the optimization could look like this. Possible savings due to better shift times or number can be large. The savings obtained varied between 5% - 30% in the projects I performed. In case of variable demand for manpower, it pays of to regularly run the analysis to see if the current shift times and number still fits the required manpower.

Instant Optimisation

2008-06-26T11:30:00.005+02:00

Get your organisation optimised! All you need is our optimisation software package OptimalAll, install it on your computer, add some data and hit the OPT button. After only a few minutes of number crunching, your computer will come up with the optimal solution for your optimisation challenge. You can get OptimalAll at your local store for only €99.95. Ask for the special offer to have the software installed and run with support of one of our optimisation experts for only €150,- all in.

Visit any trade fair, look in any magazine and you will find companies that offer this kind of optimisation solutions. As with any ad, things are presented a little brighter than reality. Don’t expect that buying optimisation software solves you optimisation challenge. There is more to optimisation than you think. Many troubled managers that face optimisation challenges are often tempted by the tales that are told by salesman about the capabilities of the solution they sell. Because of their focus on selling, salesmen tend to exaggerate a bit, leaving the troubled manager in seventh heaven with his just bought answer to everything. (Note: As some of you may know, you don’t need software to figure that out, it is 42). After a while he wakes up and realizes that there is more to optimisation than just buying a tool.

In my work as an optimisation consultant I come across many of these managers. Because of their past experience they think optimisation is something for the academic world, not as something that can deliver results for them. I tell them a different story. About one thing the troubled manager is right, successful optimisation in practice is not just buying software. In my opinion is consists of the combination of three things. First of all, thorough understanding of the business that the manager is in. Without that knowledge you don’t know square about the challenges that the manager faces and what the do’s and don’ts are in his/her business. Talking to people of the manager’s organisation, having a look around, gather data, analyse it, etc. will help you build up that knowledge. In that process you will also build up a clear understanding what needs to be optimized and to what extend.

Next ingredient of successful optimisation project is using that knowledge to build and tune a fit-for-purpose optimisation model. This can be a one-off model or a model that is part of optimisation software like a scheduling, rostering or vehicle routing software package. The model enables you to generate and rank various alternatives to the challenge the manager faces. When the model has been tested, the best solution can be identified. Next step than is to implement the model. This is where the software comes in as the third ingredient of a successful optimisation project.

Software is an enabler for transferring you optimisation knowledge to the organisation. Main step is training employees that will use the model in the future. The organisation needs to have some basic optimisation knowledge to use the model effectively. Another thing is integrating your model with the business ICT systems to be able to feed your model with the required data and feed the results from the optimisation run back into those systems. This will enable the organisation to perform the optimisation runs in the future by themselves and capitalize on their investment in optimization software and consulting.

And the winner is....

2008-05-17T16:27:00.006+02:00

In the Netherlands every year lists are published on the performance of Dutch hospitals. The lists tell the consumer which hospital scores best on a variety of key performance indicators such as customer friendliness, the number of cancelled OR sessions and the number of caesareans performed. Consulting firms, consumer agencies and even newspapers present rankings of the hospitals, each are using their own methodology. This leads to different rankings for the same hospital, leaving the to-be patient confused about the results. How should a (potential) patient decide on which hospital to go to? Wouldn’t it be better to have an overall score for each of the hospitals, so a simple ranking based on that figure can be constructed? Question is of course how to create such a ranking.

It is not only the consumer that is interested in the ranking of the hospital. Hospitals themselves also like to know where they stand compared to their piers. Since the Dutch healthcare market is changing from regulated (with fixed prices for services) to a more liberated market (with free pricing for some standardized products) a low ranking could implicate less “customers” leading to lower revenues. Also the liberation of the market leads to more pressure on effectiveness and efficiency of the hospitals. But how can we compare the performance of hospitals? How to benchmark the performance of each of them and rank the hospitals on an objective and simple way?

I came across this question in a project a few months ago. Hospitals are accustomed to benchmarking, but the drawbacks of the techniques used were something they would like to get rid of. In most cases some kind of ratio analysis is used. Clearly this doesn’t give you objective measures and does not allow for a simple ranking. Various ratios can direct in contradictory directions. So we had to search for better techniques. We came a cross a linear programming based technique, Data Envelopment Analysis. This technique supports the benchmarking questions for the hospitals but also can also be used in ranking hospitals either as a whole or per type of care.

Data envelopment analysis (DEA) is a much used technique in benchmarking, also in healthcare. Is has been developed in the 1970’s by Charens, Cooper and Rhodes. In DEA the most efficient combination of production units is constructed, called the efficient frontier. Efficiency is then measured as the distance to that efficient frontier. See http://www.emp.pdx.edu/dea/wvedea.html for more details on DEA. By modelling the hospitals as production units with certain inputs and outputs, DEA can be used to identify which hospital converts the inputs into outputs the most efficient. The efficiency score can than be used to rank the hospitals.

A nice feature of DEA is that it can be used to determine how a hospital can improve its performance, either by lowering its use of inputs (i.e people, cost, equipment, etc), of increasing the outputs (patients served, quality, etc).

The project was performed at middle sized hospitals in the Netherlands for the clinic and day care departments. The results were received very well; next step will be to extend the benchmark to other parts of the hospital like the OR and out patient clinic.

Express netwORk design

2008-04-27T15:04:00.005+02:00

The last view mounts I have been busy with several projects to improve, or design from scratch, the infrastructure of the domestic networks of an express company in several countries around the world. In infrastructure planning the number and location of hubs/depots and the network design are determined. In express networks (but also in passenger, freight and communications networks) hubs are used to reduce total cost because of more efficient vehicle/network utilization. With hubs a better match can be achieved between available capacity and requested demand for it. For sure, using a hub will increase the distance traveled between origin and destination depot, but the consolidation possibilities will offset this.

Infrastructure planning is quite a challenging puzzle and one that is of high strategic importance to an express company. Getting it wrong will cause the company to invest or disinvest in the wrong locations leading to a poor overall performance of the express supply chain. Apart from the complex puzzle to solve, performing these international projects is also challenging. Especially when it is not possible to talk to each other face to face frequently enough and cultural differences also influence the project. A prerequisite in any optimization project is to have a clear idea on the objectives and requirements. As I mentioned before, this is already hard when you are speaking the same language. Guess what happens if you have to take that hurdle first. A lot of effort goes into making sure that you understand each other before you even can get to optimization part.

Let us have a look at the supply chain of an express company to see how we can address the infrastructure planning problem. The supply chain starts when a parcel is offered to be transported to a certain end destination, within a given timeframe. For example, the parcel needs to go from Amsterdam to Liege and needs to be there at 9:00 in the morning. The parcel is picked up and taken to the depot assigned to the origin location. At the depot it is decided to which hub the parcel is sent to reach its final destination within the available service window.
Using either air or road the parcel is transported to the hub, were it is sorted and put on either a line haul to another hub or to its destination depot. From the depot it is taken to its destination location. To be able to deliver the parcel on time, an express company uses a time definite network schedule to plan the transportation of the parcel in advance. In that way the express company knows the time before which a parcel needs to be picked up in order to deliver it on time at its destination, so called cut off times.

In designing an infrastructure plan, one has to decide how many depots and hubs are needed and where they should be located. Besides that, the connections between depots and hubs need to be determined. These can either be depot-depot, hub-hub or depot-hub (or vice versa) connections. For the depots you have to determine which service areas it is assigned to. Opening a depot or hub will require investments, land needs to be acquired; a building is required to store parcels and parking/maneuvering space for the vehicles. Determining size and layout of the site is a puzzle in it self. I will come back on that in a later blog entry. With the connections between the depots and the hubs also costs are involved. These costs depend on the distance traveled and the vehicles used. Since we are designing the infrastructure of an express company we also need to take the service capabilities into account. To my knowledge there is no published research that solves this kind of puzzles, taking into account the fixed cost of opening a location, the variable cost of handling material at that location and the cost involved in operating a connection between two locations, either hub or depot. So we need to be pragmatic and creative to solve it.

Our approach is to split the hub and depot location decision. In a stepwise approach we can than start identifying the best infrastructure and network design. With our specially designed model, BOSS, we determine the best possible set up of the network. BOSS determines the best possible hub location set up, minimizing the cost of the line haul (connections between the locations). Line haul cost is the major cost driver for an express network. After optimization the (fixed and variable) cost for the hubs are added. Inputs for this kind of studies are expected volumes, service offerings and possible locations. We discuss these inputs with the local management. Since infrastructure is of strategic importance several scenario’s on service and volume are taken into account. Also possible locations are discussed since not all available locations are suitable. With our analysis results we support the management in their decision on the best infrastructure plan for now and in the near future, making the trade off on cost, service and volume. Next to these criteria also carbon emission is becoming an important decision criterion in these studies.

The OR in HR; Manpower planning

2008-03-24T12:29:00.003+01:00

There are many challenges that will make the HR manager use a more quantitative approach to HR. In this blog-entry I will focus on one of them, aging. In future entries I will present more. Human resource management is seen as a “soft” discipline and is often not treated with the respect that is deserves from other managerial disciplines. Many times the HR manager is seen as obstructive, creating obstacles that hamper the other managers of the company. Also personnel are not an explicit subject discussed in the board, other than in terms of costs. On average, personnel amounts 60% to 70% of the total capital expenditure of a company. But investments in human capital are hardly measured. The CFO/CEO takes care of these decisions because the HR manager is often not accustomed to using figures or models. It is something that will be changing rapidly in the next years. Techniques from the field of Operations Research can support the HR manager and will ensure that attention for HR subjects, other than the cost involved, will increase in the board.

Aging
Many companies are or will be facing the consequences of aging and diminishing population growth. These trends will lower the available workforce over the next years; even with stable workforce requirements it will become harder and harder to keep the available workforce at the required level.

As can be seen from the above figure, the available workforce within the company will diminish over time because of aging, increasing the gap between the required and available workforce. This means that every year, even when the company stays at the same size, more people need to be recruited to fulfil the workforce demand, putting the recruitment department under a lot of pressure. This pressure even increases because the available group of people to recruit from will decrease, because of diminishing population growth. This situation will even worsen more because companies don’t tend to be stable in terms size, also service offerings will change leading to a different set of required capabilities. How can the HR manager address all this?

Manpower planning
OR can assist the HR manager to identify the current and future effect of aging and diminishing population growth. Changes in company strategy can be analysed as well, enabling the HR manager to set its recruitment strategy in support of the company goals. As in any other OR project, the first step is to analyse the current situation, identify what the current age distribution is, what are the company goals in terms of size and capabilities of the required workforce. This will give insight in the current impact of aging. Using scenario analysis, company growth scenario’s can be identified together with the management of the company. This will give insight in the size and capabilities of the required future workforce.

Using Markov theory the current and future development of the workforce of the company can be modelled. When incorporating age, insight is created into the positions for which either aging will become a problem or for which the supply of manpower will diminish. These manpower planning models are characterized by transition probabilities that either pull employees to the next step in their carrier or push them when promotions are based on years experience or personnel motivation. In practice a combination of Push and Pull models are used. The transition probabilities for these models need to be estimated from the past.

When both the development of the required and available workforce is modelled, strategies to align the available and required workforce can be formulated and evaluated. Internal measures, the area of the HR manager, can be modelled as changes to the transition probabilities representing for example additional training, changes in remuneration or extending the time people work (over 65). External measures, the area of the other board members, like using new technologies can be modelled as changes in the future workforce demand. Using this approach the HR manager will be able to identify, together with the other managers in the board, the best strategy to ensure that the right amount and quality of people will be available at all times.

The above approach is not new, it is much used in the military, this because of the strict order of promotion. But it is not restricted to it. For example airlines use it to make sure that enough people start training to eventually become a pilot of a Boeing 747, as you can imagine an airline cannot afford to have no pilot available to fly it. More companies should use it, to make sure that they know what they will be facing in the near future. Already many companies face difficulties is attracting enough qualified people. It is time to start up Excel, build the model and start the analysis.

The correct answer to the wrong question!

2008-02-07T22:11:00.001+01:00

In my job I sometimes take on a student from an operations research course who is in her or his final year, to work on a master thesis. The objective of such an assignment is to get the experience of bringing OR knowledge into practice, either by working on a project within our company or getting out in the field, working for one of our customers. I prefer the students to get out in the field, as it is the most interesting for them as well as it is for me. Many times it is the first time that the students are confronted with real world challenges, giving the student a rude awakening. They discover that the real world cases that are used to train them in class are not that “real world” as they were told they are. Also, in the field they learn a very important (maybe even the most important) lesson that practicing OR is not about getting a complex mathematical model drawn up and solving it, unless they prefer a career at university.

When I was at university, seems ages ago, the primary focus of the courses was to teach us the basic techniques. We were taught fundamentals like algebra, statistics, modeling, linear programming, integer programming, simulation, Markov decision theory and queuing theory, just to name some. A few courses were on applying these techniques. During 2 to 3 semesters we were supplied with a couple of “real world” cases that we had to solve. It was fun, but far away from the world I am now working in as an operations research professional. I learned more about OR in practice in the first mounts at ORTEC than all the years at university. There was a lot of focus on the “Research”, but what about the “Operational”?

Solving the right problem and data availability were two things, among others, I never had to worry about in class, but it was my first lesson of OR in practice. How to make sure that you get data and use the correct model? The solution is not to think about data in the first place, not even think of a model. The first thing to do is to get a better understanding of what the problem is about that you are asked to solve. And no better way of understanding the problem then to go out there and see what the problem is about. See why it is a problem, how it is caused and learn what the acceptable directions to solve it are. Talking to the people that have to deal with the problem every day is the best way of learning about it. It helps you identifying what the problem really is. The management may have told you that the utilization of a machine is very low and the scheduling of jobs on the machine needs to be improved. It might be tempting to model that, but the real problem maybe in the scheduling of personnel that operates the machine. You don’t want to be the consultant that brings the correct answer to the wrong question. You will be out of business soon.

When you have identified the real problem then data gathering can start. Because you now have a good understanding of the problem, you can precisely define what data is needed taking into account the data that is available. This way nobody at the IT department gets frustrated from all of your questions. After checking the data and quantifying the problem you can start solving it. Sometimes you already have finished, because your analysis directed the management to the real problem, not the perceived one. Next step is build and solve the model. My experience is that the best result for a real world problem is not the optimal one; it is the one that provides the company with the best possible result, simplifying every day work and saving lots of money quickly. Many times a company cannot effort to wait for the optimal solution, they need results and they need it now. And that is what OR in practice is about, getting the best possible results now!

To my opinion this is an experience students taking a course in operations research should also have at university. They therefore should be working on real world challenges, supplied by real companies, with the involvement of the management of that company. They should visit the company and work there so they get to learn how to identify the real problem and acceptable directions to solve it. No nice and easy approach, in which the professor thinks up a case based on a text book example, with all the data ready on a plate.

Express OR

2008-01-26T18:30:00.000+01:00

I have been involved in a project for an express company for a few months now and I am quite enthusiastic about it. The express company is faced with a lot of challenges that can be viewed from an operations research professional’s perspective as being in a candy store. The supply chain that a typical express company has is rather simple. Parcels are picked up and brought to a depot using small vans. Sometimes customers bring there freight directly to the depot. From the depot, in most of the cases, the parcel is transported to a hub. There all the parcels are sorted and put on trucks. Depending on the available time to transport the parcel, it is transported via one or more hubs using either road- or air-transport. Eventually it is transported from the last hub to the depot of its destination. There it is put on a small van to transport it to its final destination.

Depending on the kind of freight, the parcel has to be delivered at a certain time. For example if you sent a document and want it to be at its destination before 9’oclock, this would be a premium service. When the document or parcel is not requested to be at its final destination that soon, it is considered to be normal freight, giving the express company more time to deliver it at is final destination. Because the transportation of the parcel or document, also called consignment, takes time, it has to be available on time at the origin depot for transport. This is also the case for the destination depot; otherwise the express company will not be able to deliver it on time at its destination.

An express company has to take various decisions in building its network. It needs to decide how many depots and hubs it wants to use (infrastructure) and how to connect the depots to the hubs (line haul schedule, including modality). Also it needs to decide on how to assign different regions to a depot to pick up or deliver (PUD) the freight and construct efficient PUD routes. A large number of depots will lower the cost of the pick up and delivery of the freight, but will increase the infrastructure cost and line haul cost. How many locations should it therefore use? Clearly there is a trade-off as can be seen in the below graph.

At the express company I have performed several projects on this subject, in several countries. Currently we are having a look at the hub infrastructure in a South American country. To solve it a network flow kind of approach could be applied, similar to the one I used for the UNJLC assignment. There is a difference however and that is the time constraint. The freight has to be on time, something that is not easy to incorporate in such a model. To solve the challenge of the express company we therefore designed a model that is capable of constructing a high level line haul schedule, including timing of the freight. The model is fed a set of possible hub locations from which a predefined number of hubs is by selected by the model. These will be the optimal infrastructure. We feed the model with a set of predefined locations because you wouldn’t want a hub to be located “in the middle of nowhere”, far away from important highways or junctions. Also the management of the express company has have special interest in certain locations, or want to fix locations in the current infrastructure. We run the model several times, varying the number of hubs to be selected. This way the best set of hub locations can be identified the set with the lowest total cost. Next step is than to construct the network schedule in detail, something that I will take up in a future blog entry. Using our model the express company is able to identify the locations which they should keep and were to invest in new ones, saving a lot of money.

Mail delivery for safer roads?

2007-12-28T17:21:00.000+01:00

Winter is here, in the Netherlands this means that we start wondering if this year it will be possible to skate the eleven-city marathon. We already had a first skate championship on natural ice, which according to the diehards in skating is a more pure experience than skating on artificial ice. Apart from wondering about the marathon, there is another issue to worry about when clearing the ice of our car windows, road safety.

Because the temperatures in the winter are around 0 °C or below the roads can become slippery because of ice or snow. Deicing is necessary otherwise accidents will happen. In fact, temporary friction enhancement through the application of salt is seen as an effective safety countermeasure. In the Netherlands, the government together with local and district authorities are responsible for the deicing of roads. Each of them covers their own roads. The government is responsible for the highways, the local and district authorities for the local roads and the road network within the cities. The deicing of roads is performed with special trucks that can be used to apply deicing salt or snow clearance. To give you an idea, in the Netherlands more than 100 depots and over 500 trucks are involved in deicing the highways alone.

Recently we performed a project to find out if integrating the deicing of highways and local roads would lead to synergies and savings for both government and the local district. The construction of routes for deicing the roads is problem that can easily be solved with the use OR. A lot of restrictions need to be taken into account although. There are several restrictions due to government regulations that state that highways to be deiced within 45 minutes. Road entries and exits need to be deiced within 90 minutes. When constructing the routes you have to take into account the various road types, like very porous or non porous asphalt, since each road type requires a different amount of deicing salt per m2. Sometimes roads are too wide to be covered by one truck, than more than one truck needs to be used. These are only a few of the restrictions that need to be taken in to account when building the deicing routes.

When you think of the problem we need to solve it looks quite similar to the traveling salesman problem. The road network that needs to be deiced consists of vertices and directed edges. The solution to the traveling salesman problem finds the shortest route thru all the vertices of the network. When constructing the deicing routes we need to visit all the directed edges in the network, not the vertices, we will probably visit those several times. The problem we need to solve is called the Chinese Postman Problem and was first described by Mei-Ko Kwan, a Chinese mathematician, in 1962. Today it is sometime called the route inspection problem. To solve it we need to find a circuit, also called an Euler circuit, through the network that only goes along each edge of the network once. If there is such a route and it ends at the same point at which it begun, then the problem is solved. Otherwise we need to adjust the network by adding artificial edges, meaning that we will travel along an edge several times to complete the Euler circuit. After the Euler circuit has been constructed for the complete network we need to split it up in order to have separate circuits that obey the restrictions on time and capacity of the trucks. The project resulted in routes with less use of equipment and depots, leading to savings in cost. So safe roads for less cost thanks to a Chinese postman.

To get an idea of the complexity of the construction of deicing routes try to solve the below example. The length of the optimal circuit is 20, but how does it run?

spORts

2007-11-17T17:12:00.001+01:00

It is the fifth game in a best of 7 series of the national volleyball championship series. The home team is 3 games down to 2 so it must win the next two games in order to win the championship. The coach has to decide which players he will use in the game, especially which opposite hitter. His best opposite hitter has played a lot and could use some rest. The next best opposite hitter is fit and could play the next two games. The coach believes that his best opposite hitter, although not fully rested, is still better than his next best opposite hitter. Letting him play the 6th game would mean that he can’t play the last game. The opponent’s coach has chosen his next best opposite hitter, maybe saving his best player for the last game? The home team coach assesses that the opponent’s opposite hitters have about the same ability as his own opposite hitters. What should the coach decide, let his best opposite hitter play or his next best opposite hitter? Can Operations Research help in this decision?

Traditionally Operations Research has been used in sports for timetabling, like the construction of a round robin tournament schedule. Sports leagues and teams need schedules that satisfy different types of constraints. For example the three soccer teams of Rotterdam cannot play at home at the same time. Other examples are the restrictions due to the international games played by the teams, like the Champions league. Timetable construction in sports competitions is a difficult problem to which several O.R. techniques have been applied. Most of the time a Mixed Integer Problem (MIP) needs to be solved. But Operations Research can be used in other areas of sports as well.

Let’s go back to the decision the coach of the volleyball team has to make. In what way could we assist him in this decision? Should he use his best player in the 6th game and use the next best in the final game, or the other way around? Most people I talked to on this decision say to put up the best player in game 6 and use the next best player in game 7. For obvious reasons they say, because if you don’t win game 6 there won’t be a game 7. Is this the best strategy?

The decision the coach has to make is similar to the examples used by Kahneman and Tversky. They demonstrate that human intuition is notoriously bad at processing even the simplest probability problems. Here is one of their examples:

Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. Which of the following statements is more probable?
A: Linda is a bank teller.
B: Linda is a bank teller and active in the feminist movement.
C: Linda is a bank teller and takes yoga classes.

Most respondents choose B or C. Few choose A. Yet, by the laws of probability Pr(A) ≥ Pr(A ∩ B)

In a similar way we can prove that saving the best player for the last game is the best strategy to win the series and therefore the championship. To see this, let P1 be the probability that the best player wins game 6. Then the probability of winning game 7 for the best player will be P2 = P1 + ε where ε > 0. ε is positive since the player has additional rest and the opposing players are judged to be the same. Let the probability that the next best opposite hitter wins game 6 be P3 = P1 – δ, where δ > 0. Note that this definition takes into account the assessment of the coach that his best opposite hitter is better than his next best even though he isn’t fully fit. The probability of winning game 7 (P4) with the next best player is the same as winning the 6th game, so P3=P4.

The probability of winning the championship starting with the best opposite hitter in game 6 is C1 = P1*P4. Letting the best opposite hitter play in the final game the probability of winning the championship is C2= P3*P2. Now note that C2 = P3*P2 = P3*(P1 + ε) = P3*P1 + P3*ε =P4*P1+ P4*ε. Hence C2 = C1 + P4*ε. Since P4*ε >0, the best strategy therefore would be to save the best opposite hitter for the last game. As you can see, sports can benefit from the application of Operations Research in various ways. Can you think of others?

Uganda flood response

2007-10-26T19:52:00.000+02:00

OR to the aid again! As I stated in my last blog message every Operations Research professional should offer his or her support to initiatives of the UN or other humanitarian organizations to help improve their operations. This way more lives can be saved. Last week I got the chance to put my money where my mouth is.

By coincidence I got in touch with the UNJLC, the United Nations Joint Logistics Centre. They were asked to provide a schedule for delivering relief supplies to schools and settlements in the Amuria district of Uganda. This as part of the Uganda flood response. As you might have read in the newspaper, large parts of eastern Uganda are flooded. At this moment the situation in flood-affected parts of Uganda continues to worsen. The first priorities of the aid are to stabilize the initial food security situation, preventing disease outbreaks, ensuring capacity to respond to health emergencies and re-opening schools.

The task of the UNJLC is to help with the food supply. Tons of cereals, sugar and vegetable oil needs to be transported to schools and settlements. Because the locations cannot be reached by road, helicopters are used to deliver the relief supplies. The helicopter flies from a central point in the area to the locations of the schools and settlements. For each of the locations it is known how much of the relief supplies need to be delivered. The helicopter however has a maximum carrying capacity, which is lower than the demand of some of the schools and settlements. This means that the helicopter has to perform several flights and attend several locations more than once. For each flight it has to be decided which locations to attend and how much of the relief supplies to be delivered at the locations visited. The helicopter range wasn’t an issue in this case, so the length of the flight wasn’t a restriction. You might guess that under the pressure of many people in need no time should be lost in finding the best possible solution. Your (and mine) first reaction would be to load a helicopter and start delivering the supplies. The people at UNJLC wandered if it would be possible to construct the schedules automatically, so the best possible routes could be constructed in the least possible time. A challenge I could not resist.

There are several ways to find the optimal solution. Of course you could startup MS Excel and construct the routes by hand. This can be a very good way when the number of locations to attend is not large. Another way is to use brute force techniques like a set covering approach. In that case you generate all possible routes and use a LP model to select the best routes, assigning the amount of supplies to each of the routes in the same model. I used a Network flow model in which all the nodes in the network represent demand points except the central point (Origin) from which all flights departed. I constructed a complete network, i.e. all demand nodes in the network were connected with directed arcs. The origin was connected to all the demand points in one direction. By setting the appropriate capacity constraints on the arcs, the maximum carrying capacity was modeled. In the objective function the length of the arcs in the network was used as a proxy for cost of using the arc. A flow in the model represents a route, including the amount of relief supplies to be transported. Solving the model was easy and took only a few seconds. The optimal routes are much better than the routes used until now. They save time and money, allowing for more relief supplies to be delivered and therefore lives to be saved. OR to the Aid!

OR to the aid of children

2007-09-26T12:10:00.000+02:00

The world is full of areas in which people and especially children suffer from war or natural hazards like the Tsunami. The United Nations and other humanitarian organizations try and help these people. Of course the aid that is provided is the best possible, but much could be improved with the help of Operations Research, enabling to save more lives and give victims a better chance to build up a new future.

As an example of what can be achieved with the use of Operations research I would like to address a project that was set up by the World Food Program (WFP) of the UN. The UN World Food Program is the world’s largest humanitarian food aid organization. It provides food to about 90 million people in around 80 countries. These people depend on the aid that is provided by the WFP, since no other source for food is available to them. Additional to this aid, the WFP also uses supports 800 million malnourished people in the world with special food aid projects.

One of those special food aid projects is the food distribution to schools in Liberia. The project’s aim was to improve the food distribution to children. With the use of Operations Research the WFP distribution network in Liberia was optimized resulting in better locations for the depots from which the food was distributed. Also the distribution of the food to the 1,600 schools in Liberia was optimized, ensuring that 250,000 children receive their food. Initially the routing and scheduling was performed by hand. TNT (which takes part in WFP) together with ORTEC (the company I work for), changed that by automating the scheduling process with the use of state of the art routing software. The scheduling became less time consuming, also the dynamics of the scheduling process could be supported better. As you may guess the road network in Liberia is not that sophisticated. Due to the rain season and mines, not all the roads could be used at all times, even bridges may have collapsed. This introduces a lot of dynamics which is hard to incorporate when every thing is done by hand. Also we improved the distribution network by relocating the depots. The achieved improvements saved al lot of money that can now be used to maintain or further improve the aid that is provided to the children of Liberia.

To my opinion Operations Research professionals should offer more support to the initiatives of the UN and other humanitarian organizations to improve the effectiveness of these operations. This will result in more lives saved and a better future for all victims of humanitarian disasters, especially children.

Complicating Simplifications

2007-07-31T11:52:00.000+02:00

Recently the court of The Hague gave a judgement on the remuneration of resident on call working of the firemen in the Netherlands. Direct cause of the judgement is that the firemen will work less hours a week with no reduction in salary, a loss of productivity of about 11%. The judgement was caused by an attempt of the Dutch government to simplify the rules in the working time directive. These adjustments were necessary because the rules were becoming to complex, also the Dutch working time directive did not follow the agreed working time directive on the European level and the Jaeger as well as the SiMAP judgement. Both judgements state that the hours spend during a resident on call duty should be valued as normal working hours.

From April 1st of 2007 on the simplified working time directive (s-WTD) came into force in the Netherlands. In this new law many rules were simplified or skipped, also some additions were made. The s-WTD sets rules to protect the safety, health and wellbeing of any employee. It contains, for example, rules on the maximum number of hours that employee can work during a shift, a week or consecutive number of weeks. Also it sets rules on the length of a rest period after a shift and after a number of consecutive shifts. The simplifications lead to an increase of possible deployments of employees of about 20%. The question is however if the employers understand the rules well enough to take advantage of the increase in deployment possibilities.

There is one rule in particular that has drawn my attention. I my opinion it is impossible to take that rule into account when construction a roster, without consulting an Operations research specialist or using an advanced planning system, since it requires you to solve the well know multiple knapsack problem. In normal English the rule states that when an employee performs one or more resident on call duties, each period of 7 times 24 hours must contain at least 90 hours of compensatory rest. So far this is simple, we can easily add up all the rest periods an see if it matches the requested 90 hours. There are additional restrictions however on how the compensatory rest period is divided up over the 168 hours period. These restrictions state that there should be at least one period of 24 hours compensatory rest, four of at least 11 hours, one of at least 10 hours and finally one of at least 8 hours. 7 rest periods in total. This still is simple to verify, however these periods of compensatory rest can be joined together. Because of this last condition we have a multiple knapsack problem to solve, which is NP-Hard. (see http://en.wikipedia.org/wiki/Knapsack_problem) I wonder if this crossed the minds of the clerks when writing the new laws. To see the analogy let each period of rest be equal to a knapsack, the capacity of the knapsack is equal to the length of the rest period. Now we have to find out how the 7 rest periods of various sizes can be fitted into the knapsacks. If we succeed, the roster is valid; if not then we need to change it.

To experience what kind of puzzle a planner has to solve, I will give you an example. Assume that an employee has 3 rest periods. The lengths of the periods are 32 hours, 31 hours and 28 hours. I invite you to react and tell me of it is possible to solve this puzzle.

Blood sample logistics

2007-07-25T19:54:00.000+02:00

The diagnostic centre of a hospital asked me to analyze their blood sample collection process from a logistic point of view. They had a feeling that the performance of the collection process could be improved. They asked to verify this and also to provide a set of possibilities to improve the collection process.

The main activity of the diagnostic centre is to take blood samples from patients, analyze them and report the results back to the physician or patient. Sometimes they advise the patient with respect to the medicine they take, for example in the case of diabetes. Some of the patients come to the hospital to have a blood sample taken. Many of the blood samples however are taken at service locations of the diagnostic centre in the area around the location of the hospital. In this case there are about 30 different service locations where a patient can go, to have their blood sample taken.

The employees of the diagnostic center work at the service locations and take the blood samples from the service location to a laboratory to have them analyzed. As an extra service the employees also visits patients at home to take a blood sample. Currently the employees visit the patient at home before and after they work at the service location. This takes careful planning because patients at the service location must not be kept waiting. As you may guess an important condition in the collection process is to have the blood at the laboratory in time. Blood can not be kept indefinitely; it must be delivered on time to the laboratory, otherwise no analyses can be performed.

As you can see this is a rather complex logistic process. Many questions arise, such as

Are there enough locations available for the patients to go to, or should the number be changed?
What should be the opening times and the geographic position of each of these locations?
Should all the blood samples be taken directly to the laboratory, or should they be collected first at specific places in the network. In other words should hubs be used?
Should from an employees point of view the samples taken at the patient’s home be combined with the blood samples taken on the service locations of the diagnostic centre?

This is where Operations Research comes in. We analyzed the blood sample logistics with a model that we developed to analyze and optimize supply chains. With this model we can answer questions like where facilities should be situated, how large they should be and which customers should they serve. With this model we found that introducing a few hubs where blood samples are collected from the service locations before taking them to the laboratory saves about 25% of travel time of the employees. This saves time but also the distance traveled, which reduces the costs for the diagnostic center. This time saved can be used to take more blood samples boosting the workforce effectiveness as well.

OR in the OR

2007-07-13T17:39:00.000+02:00

De Franz Edelman Award wordt elk jaar toegekend aan ‘outstanding examples of Operations Research (OR) – based projects’, die grote veranderingen bewerkstelligen in de samenleving, industrieën en het bedrijfsleven. Deze prestigieuze prijs voor het best wereldwijd toegepaste Operations Research project kan worden gezien als de ‘Superbowl’ in toegepaste O.R. Dit jaar waren onder andere Hewlett Packard, Daimler Chrysler, The Memorial Sloan-Kettering Cancer Centre en Coca Cola genomineerd.

ORTEC, het bedrijf waar ik voor werk, was dit jaar bij een van de genomineerde projecten betrokken. Coca-Cola Enterprises is genomineerd, omdat het bedrijf haar distributienetwerk wist te optimaliseren met rit- en routeplanningsoplossing Shortrec van ORTEC. Het systeem dat in 2004 werd geïmplementeerd heeft Coca-Cola Enterprises een besparing van 45 miljoen dollar per jaar opgeleverd.

De award werd uiteindelijke gewonnen door een zeer innovatief project van OR in het Memorial Sloan-Kettering Cancer Centre. De kern van de toepassing is het vinden van de beste positie voor het inbrengen van radioactieve "zaadjes" in de prostaat. Een soort locatie vraagstuk dus. Veelal wordt dit vraagstuk in het platte vlak opgelost, het feit dat het nu in 3 dimensies plaatsvindt en dat het real time (met de patient op tafel) wordt opgelost maakt het uniek. Kijk voor meer informate over dit project op http://www.lionhrtpub.com/orms/orms-6-07/fredelman.html. De toepassing heeft er toe geleid dat een kostenbesparing van 450 miljoen dollar per jaar kan worden bereikt, maar belangrijker is dat de levensverwachting van de behandelde patiënten vergroot wordt en dat de succeskans van de behandeling enorm is gestegen. Kortom "OR in the OR"

Wat is OR?

2007-06-08T18:15:00.000+02:00

In de Operations Research (OR) worden geavanceerde analytische methoden gebruikt om betere beslissingen te nemen. Operations Research is geen standaardoplossing die meegeleverd wordt met de volgende versie van het operating system van je computer. Het vraagt specialisten met kennis en ervaring om er praktisch bruikbare resultaten mee te behalen. OR is niet alleen theoretisch, de kracht zit hem in de praktische oplossingen die het kan beiden.

OR is in Engeland ontstaan vlak voor het uitbreken van de Tweede Wereldoorlog. De behoefte aan een structurele en praktische benadering van tactische en strategisch militaire vraagstukken leidde tot de initiatie van OR. Het doel van het toenmalige onderzoek was het vinden van de meest effectieve manier om beperkte militaire middelen aan te wenden. Dat hebben ze bereikt door gebruikt te maken van kwantitatieve technieken. De doelstellingen van OR zijn ten opzichte van het toenmalige onderzoek niet veranderd, behalve dan dat het zich niet beperkt tot militaire toepassingen. Vele sectoren plukken nu de vruchten van de mogelijkheden die OR kan bieden. Op deze blog wil ik je daar voorbeelden van laten zien en je laten meekijken in de OR praktijk, OR at Work dus.