Parametric programming

Introduction

The meaning of a parameter as used here is best explained by a simple example. Recall that a parabola can be expressed as follows: y = ax ², a ≠ 0. Setting a = 1, we obtain a parabola that has a different shape from the parabola when we set, for example, a = 5. In both cases, however, we have parabolas that obey specific relationships; only the shapes are different. Hence, the parabola y = ax ² describes a family of parabolas and the parameter a specifies the shape.

Consider the general mathematical-programming model:

(1)

(2)

If we introduce one or more parameters, the model stays the same, but for each value of the parameter(s) we obtain a specific problem.

In setting up a mathematical optimization model, one of the first tasks is to collect data. The collected data might, however, be inaccurate, be of a stochastic character, be uncertain or be deficient in other ways. Therefore, it is appropriate to introduce parameters that enable us to analyze the influence of specific...