Use of Sample Information in Stochastic Recourse and Chance-Constrained Programming Models

In probabilistic linear programming models the decision maker is typically assumed to know the probability distribution of the random parameters. Here it is assumed that the distribution functions of the parameters have a specified functional form F(t, \theta ), where \theta is an unknown (real) vector parameter. We suppose that the decision maker has the opportunity of observing a random sample drawn from F(t, \theta ). For a two-stage stochastic programming with recourse model the deterministic equivalent model is found using a Bayesian approach. Properties are presented for the deterministic equivalents in general and in the special case of the simple recourse model. Expressions for Expected Value of Sample Information (EVSI) and Expected Net Gain from Sampling (ENGS) are also derived. In the final section similar results are obtained for chance constrained programming models.