Friday, 30 May 2014

Balancing today’s decisions against tomorrow’s conditions

As organisations move up Tom Davenports’ analytics maturity curve, they encounter new challenges in using the insights from data analysis and optimisation models.  Today, the majority of organisations use descriptive analytics to create insights on what has happened. Also the use of diagnostic analytics to understand why things have happened is becoming more common. Moving up the curve towards predictive and prescriptive analytics is more difficult and requires the development of more advanced analytical capabilities. Gartner surveys indicate that about 13% of the companies are using predictive analytics. Predictive Analytics provides these companies the capability to identify future probabilities and trends. It will also support the discovery of relations in data not readily apparent with traditional analysis. These insights can be used to for example estimate future demand, which in turn supports sourcing and production decisions. Predictive analytics enables organisations to balance the decisions of today against the conditions that they face in the (uncertain) future; it allows them to become proactive instead of reactive. Turning these insights into robust decisions is however not always as straight forward as it seems.

Let’s take the example of a company that manufactures desks, tables and chairs. The desks sell at €60, the tables at €40 and the chairs at €10.  To make the furniture the company needs to source wood and two types of labour, carpentry and finishing. Costs and resource requirements for each type of furniture, including the demand, are shown in the table below.


Given the demand, a simple linear programming model will help the company to figure out that the best decision is to produce 150 desks and 125 tables. It will require the company to source 1950 feet of wood, 487.5 labour hours of carpentry and 850 labour hours of finishing. A net profit of €4,165 will result. In fact, a simple per-item profit analysis provides the answer already as producing chairs will not generate any profit. What is important to note is that in the above approach the sourcing, production and selling decisions are made in one go. In practice this might not be realistic.

Using predictive analytics the company constructed the following scenarios for future demand for desks, tables and chairs with the accompanying probability of occurrence.

Given these scenarios the company wonders how this variability in demand will impact its sourcing and production decisions.  How to deal with the various demand scenarios? The use of predictive analytics has created more insight, but also increased the complexity of the sourcing and production decisions. To find out what is best, the company decides to perform a sensitivity analysis on demand using the LP model with the deterministic demand scenario. The analysis shows that although the number of desks and tables produced in each demand scenario differs, no chairs will be produced in any of the scenarios. Given this observation, the company decides to go for expected demand scenario, also a common way of dealing with multiple scenarios in practice. The impact of this decision becomes apparent when we look at the profit for each of the demand scenarios based on this decision. Expected profit for sure is not what was expected! In the low demand scenario there is a significant loss instead of a small profit, in the most likely scenario there is a slightly lower profit while in the high demand scenario the upward potential doesn’t materialize. So on average the company will be worse off than expected (wheredid we here that before?). The sensitivity analysis on demand didn’t provide any clue that this could happen, it is therefore flawed. Stein Wallace indicates that key to better deal with uncertainty in this case is to have a more thoughtful approach to creating the math model.


Key in developing a better model is to understand when decisions are made and how they are impacted by the uncertainty in demand. There are three possible situations.
  1.  Demand is known before the sourcing and production decision
  2.  Demand is known after the sourcing and production decision
  3.  Demand is known after the sourcing decision but before the production decision.

If demand is known before we need to decide what to produce and source, there is no uncertainty on demand and therefore the first model will provide the optimal production and sourcing decisions for every demand scenario (as shown in the above table). When we need to decide both sourcing and production before we know demand, these decisions must be weighed against all demand scenarios. The production plan and corresponding sourcing decisions in this case will be set trading off the sunk cost of producing furniture that can’t be sold with the upward potential in revenue from the high valued demand scenario.  The best decision in this case is to source and produce 50 desks and 110 tables.

An interesting situation arises when we need to source before we know demand but can adapt the production decisions after demand is known. So if there is a change in demand, the resources can be used to produce furniture for which there is demand. The optimal solution to the model clearly shows this. Compared to the second situation in which demand is known after the sourcing and production decision the model in this case advices to acquire more resources. Also in the low demand scenario it suggests to switch to the production of chairs, which generates additional revenue. It’s a fall-back scenario which justifies the more aggressive sourcing decision.  


In practice the input of mathematical models is assumed to be accurate and deterministic. If accuracy of the data is a worry the conventional wisdom is to perform a sensitivity analysis. With the rise of predictive analytics more and more companies will start using the results of their predictive models in their decision models. As predictions are in their nature uncertain, many of these companies will turn to sensitivity analysis to analyse the impact of the uncertainty on their decisions. Most commercial solvers offer this as a standard feature, which is most convenient. However the above example shows that sensitivity analysis can be seriously flawed. Careful analysis of how uncertainty influences decisions will lead to models that better incorporate uncertainty and therefore will result in better quality decisions. This requires companies not only to invest in predictive analytics tools but in modelling skills as well.


This blog is inspired by an article of Stein Wallace on sensitivity analysis in linear programming which was published in Interfaces. If you want to experiment yourself a download of an Excel workbook is available.
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