On Stochastic Linear Frogramming

The general linear programming problem Is considered In vhich the coefficients of the objective function to be maximized are assumed to be random variables vlth a knovn multinomial distribution. Three deterministic reformulations Involve maximizing the expected value, the a-fractlle (a fixed, 0 < a < ^), and the probability of exceeding a predetermined level of payoff, respectively. In this paper the author's previous work on "bl-criterion programs" Is applied to derive an algorithm for routinely and efficiently solving the second and third reformulations. A by-product of the calculations in each case is the tradeoff-curve betveen the criterion being maximized and expected payoff. The intimate relationships betveen all three reformulations are illuminated.