Saturday, April 11, 2009

O.R Practice: The paradox of optimality

Operations Research in practice is, as one would expect, a different animal compared to O.R in academia. I choose to call it 'applied O.R'. OR dwells a lot on optimality, and there's no ambiguity there. AOR deals with optimalities. They come in different shades (some shadier than the others :-). We'll just touch upon a couple of them here.

Every analytic firm sells stuff with the word 'optimizer' somewhere. In most cases they dont really optimize anything. But some of them do; atleast they hope to 'improve' something. But optimizer sounds cooler than 'improver' because we understand that one cant really do better than 'optimal'. Management folks so love this word they'll use it in the most non-optimal manner!

Now, something is 'optimal' to you unless you find something better. It's 'user optimal'; something that your user cannot replicate visually (or if you are a good OR guy, neither can excel). If the user doesnt get to interact with your product much, user-optimality is great. A quick and dirty AOR heuristic is good enough. Minimum effort, maximum benefit. Dr. Hari J. Balasubramanian at the University of Mass, Amherst has a great article in ORMS-Today on a user-optimal solution to the land-reallocation problem after the 1947 partition of India. He's got a nice blog going (follow the 'thirty letters' blog link on this page).

The user-optimal solution approach looks good until the day a user insists he wants to play with the tool to what-if analyze scenarios and use it for decision support. Thats when they see that user-optimal doesnt cut it. They dont know it, but they actually require real (global) optimality. Therein lies the paradox. Nobody really cares about global optimality since your model is but a fading shadow of reality. However, if your interactive AOR product cant consistently hit solutions close to optimality, its just a scattergun. Its a car that turns by random amounts and directions. Or think of it this way - if you are an OR student - when do you expect to defend your OR dissertation and graduate if the CPLEX or GUROBI solver in your university lab suddenly solves your LPs to only within 25-50% of optimality but doesnt tell you that.

Your optimal answer and objective value is itself pretty useless, but the method you employed to generate that on a consistent basis is priceless; your customer can actually take decisions and make policies based on the response of your AOR product. Everything looks good until somebody says something about 'degeneracy' .... to be continued.

1 comment:

  1. >> They come in different shades (some shadier than the others :-).

    Nice! I should use this sometime :)


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