Thursday, 30 June 2011

Modelling Magic

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!

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