8 - Analysis of Competitive Situations

Abstract

This chapter presents an analysis of competitive situations. An important class of problems in the domain of modern mathematics and system theory involves selecting a combination of variables that maximizes or minimizes some predefined variable or function of the problem. This problem, called the optimization problem, becomes formidable when a number of combinations in which the variables can be combined are large. With the development of modern computers, the computational difficulties are no longer insurmountable. The chapter describes linear programming. The general problem of finding the maximum or minimum value of a function of one or many variables—when the function might be linear or non-linear, discrete valued or continuous, constrained or unconstrained—is a difficult problem to solve. The twin concepts maximum and minimum have been distinguished. Mathematically, the minimum value that is attained by a function f(x) is the same as the maximum value attained by the function -f(x). It is possible to talk about maximization or minimization, interchangeably, without a loss of generality.