Objective function bounds for the inexact linear programming problem with generalized cost coefficients

Abstract

This paper addresses the inexact linear programming problem in which the objective function coefficients are not fixed but lie in some predetermined set, C. Under certain convexity assumptions, standard mathematical programming techniques are employed to determine worst case and best case solutions. Simulation is then used to explore the properties of the general problem: max ( cx: Ax ≦ b) for some c ϵ C. A wide range of configurations is examined and it is statistically demonstrated that the variance of objective function values is proportional to the size and shape of C. A number of examples are given to highlight the results.