Stochastic programming

Abstract

This chapter focuses on stochastic programming. The stochastic programming model can be viewed as an extension of the linear and nonlinear programming models to decision models where the coefficients that are not known with certainty have been given a probabilistic representation. In the context of the mathematical programming models, some versions of this model were introduced and there had been a number of simple stochastic programming models, which had been formulated in inventory theory—micro-economics and system maintenance. The chapter reviews the useful properties of expectation functionals and analyzes the type of constraints and objective functions that arise in various stochastic programming. The questions of sensitivity and stability of the solution with respect to perturbations of the underlying probability measure, and the implications of these results for stochastic programs are presented in the chapter. © 1989 Elsevier Science Publishers B.V.