Response surface analysis of two-stage stochastic linear programming with recourse

We apply the techniques of response surface methodology to approximate the objective function of a two-stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first-stage decision variables. The resulting response surface can provide valuable modeling insight, such as direction of minimum and maximum sensitivity to changes in the first-stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers and the Schruben–Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two-stage problems which includes the classical capacity expansion model.