Sensitivity Analysis and Parametric Programming

Abstract

There are three groups of parameters in a linear programming problem: the “technological” coefficients, a _ij (representing, for example, machine time per unit of product); the constant terms on the right-hand sides of the restrictions, b _i (e.g., capacity limits); and the coefficients in the linear preference function, c _j (for example, unit profits). In practical applications of linear programming it is important to explore the sensitivity of the numerical solution with respect to changes in these parameters¹. Some of them may be subject to known variations in time — prices or cost elements change, machine times are reduced and capacities increased because of rationalization or technological change, output stipulations vary from period to period, etc. — or it may not be possible to determine them exactly but only within certain intervals. (When these variations are of a random nature, the coefficients should be thought of as probability distributions rather than numbers and the problem becomes a stochastic programming problem.)