Management Science and Operational Research Blog

A couple of days ago I spent a whole afternoon on a quite amusing Barbecue. All guest were police lieutenants, except for me. After a couple of beers I got asked what I was studying in London. Of course, no one has every heard of Operational Research. Fortunately, I remembered one interesting working paper by former professors of mine in order to give an appropriate example¹.

This paper gives an example how the theory of Search Games² could be applied to a practical problem. In the simplified version, villains try to attack distinct targets (i.e. banks) which are located in a well defined area, so that it is expressible as a graph (i.e. road network). The security forces objective is to patrols in such a way that the probability of an attack stays at an minimum. The villains objective is to come up with a plan that maximises their chances of a successful attack.

The police lieutenants could immediately relate to this problem. However, they also were moaning right away that such knowledge shouldn’t be made publicly available. They regarded it as security risk if ‘civil persons’ get to know how the police plans their patrols.

Having thought about their objections for a couple of days, I am now convinced that they are wrong:

• The lieutenants assume that security by obscurity actually works. This might be true under very specific circumstances, but my friends forgot that their patrol-planning is public domain either way. Any person can observe the police’s movements in order to figure out its strategy. So it is better to develop a strategy which optimal even if the opponent knows about it. Search Games treats exactly this kind of problem. (N.B.: A strategy may not be a fixed route, moreover it can have random elements.)
• If the patrols have to be planned for a yet unknown problem (i.e. patrolling in a airport instead of patrolling on the street) the analytical approach helps to detect pitfalls and might lead to better results than a planning based on experience (which might not be applicable if the problem is fundamentally different).
• The theoretical insights of search games might help planners to create facilities which are easier to patrol. For example, the facility must be planned so that the security forces are be able to reach every potential target on a Eulerian path..

But the resentment and comments of my friends made me realise about certain precautions in regard to this application of Search Games.

• No one likes to have his hardly earned experience replaced by some abstract theory. Such objections have been clearly expressed during the barbecue, but they could be easily appeased by the argument that Search Games is supportive rather than substitutive to their patrol plannings.
• The point above is also important in regard to the complexity of the real world problem. Patrolling involves a lot of details which can hardly be included into the Search Game’s model.
• And finally, the security forces must understand what they are doing, otherwise they do not stick to the plans. Hence, any insights gained by a formal analysis should be easily explainable.

I chose to study Search Games because I considered it an exotic and fun class but with little practical relevance. It seems that I was wrong, and I never imagined imagined that exactly this discipline might come handy in order to explain the field of Operational Research.

1. Alpern, S., A. Morton and K. Papadaki, Optimizing randomized patrols, Operational Research working papers, LSEOR 09.116. Operational Research Group, London School of Economics and Political Science, London, UK, 2009 [↩]
2. Alpern, S. and S. Gal, The Theory of Search Games and Rendezvous, Springer, 2003 [↩]