The Probability Distribution Function of the Optimum of a 0-1 Linear Program with Randomly Distributed Coefficients of the Objective Function and the Right-Hand Side

This paper proposes and discusses exact and approximate methods for solving the distribution problem of a linear 0-1 program with stochastic b and c. It shows that, in decision-making situations, severe errors can arise when mathematical expectations are substituted for the stochastic coefficients and the problem is treated as a deterministic one. Thus, a knowledge of the distribution function of the optimal value of the objective function as a function of the distributions of the coefficients—or close bounds on it—is a genuine help for the decision maker in situations of risk or uncertainty.