The Purpose of Mathematical Programming is Insight, Not Numbers

Abstract

The ostensible purpose of a mathematical programming model is to optimize a stipulated objective function subject to stipulated constraints. But its true purpose, at least in strategic applications as every experienced practitioner should know, is to help develop insights into system behavior which in turn can be used to guide the development of effective plans and decisions. Such insights are seldom evident from the output of an optimization run. One must know not only what the optimal solution is for a given set of input data, but also why. The desired insights usually have more to do with the “why” than the “what.” This paper advocates the use of highly simplified analytic models to help explain the “whys” behind the solutions of conventional mathematical programming models. A methodological approach is described which permits the development of richer insights than would otherwise be possible. This approach is illustrated with reference to a facility location study carried out recently for a consumer products manufacturer.