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Solution-Method-Free Modeling Campaign

This is one of my recent campaigns.

The point is this: the

Operations Researchliterature -- especially introductory textbooks -- is dominated by modeling paradigms that are solution-methods oriented. By this I mean that the choice of the mathematical model that is used to formulate a specific problem is "dictated", from the start, by the decision to use a specific solution-method for the problem in question.But the fact is that problems typically lend themselves to various formulations. That is, the same problem can be formulated via different models. The implication is then that the solution-method-based model that you may have envisaged for a specific problem need not necessarily offer the best formulation for this problem. This is particularly true if your objective is not necessarily to solve the problem in question but to describe it by means of a mathematical formulation.

I am a strong advocate of the "generic modeling" paradigm.

This paradigm is based on the fact that in operations research we have a rich collection of "generic problems" such as the knapsack problem, the shortest path problem, the transportation problem, the assignment problem, the maximum flow problem, the minimum cost network flow problem, the traveling salesman problem, the diet problem, and the list go on ...

Of course, these catchy appellations are little more than metaphors. For, the knapsack problem has very little to do with jute knapsacks, or the traveling salesman with flesh and blood traveling salesmen, and so on. Still, as metaphors these terms give an apt description of the types of situations (problems) that OR takes on and strives to solve.

So, as OR students/analysts/practitioners know all too well, very often OR modelling is all about striving to fit a specific problem that one happens to be investigating into one of these given molds. Or in other words, one's main task is to translate the problem considered into the framework of one of the above "generic problems" or, a slightly modified version thereof.

Of course the main difficulty here is that often it is not easy to recognize the "generic problem" in the problem considered, nor indeed is it easy to see that the problem considered has any affinity with any one of the "generic problems".

So, often the task one faces first of all is to figure out which of the above "generic problems" -- or a slightly modified version thereof -- provides the right framework for formulating the problem considered.

My extensive experience in this area has shown that the conventional solution-method-based modeling paradigm is of little help here.

As I consider mastering what I call "solution-method-free" modeling in Operations Research of the utmost importance, I am trying to promote it as a practice. I have been practicing this idea in my teaching for many years and I am now preparing lecture notes on this topic.

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