On minimax solutions of stochastic linear programming problems

Abstract

1. Our starting point is the formulation of a stochastic linear program as a strategic game. This formulation differs only slightly from that given by IOSIFESCU and THEO-DORESCU [3]. Secondly, we state a minimax theorem for that game and study the methods of solution. In some special but important cases it is shown that the minimax solution of a stochastic linear program is equivalent to the solution of an ordinary linear program (of greater dimension, in general). The existence of a finite solution is also discussed. 2. Let E* denote the non-negative orthant of the n-dimensional Euclidean space. Let (A, 5, c)-where A = (a fJ), b = (b £), c = (c,), i = 1,..., m, j = 1,..., n-be a random vector; let its distribution F(-4, b, c) belong to a set of distributions ;#". Let r f (y), i = 1,..., m be real functions such that r t (y) = 0 for y g 0 and r^y) > 0 for y > 0.