Satisficing techniques in stochastic linear programming

Abstract

Stochastic linear programs (SLP), i.e. linear programs with random data, are handled usually by replacing them by certain determinitsic substitutes, using e.g. a penalty function or a chance-constrained programming approach. Instead of solving then approximatively the resulting difficult mean value minimization problems or dealing with difficult chance-constraints, here, using structural properties of the SLP being available under many distribution assumptions, a new, relatively simple interactive method (satisficing trade-off method) is suggested for finding a satisfactory efficient solution of the SLP, where the Pareto optimal solutions of the SLP are defined with respect to a vector valued linear/quadratic criterion depending on certain moments of the random data of the underlying linear program. It turns out that the optimal solutions of standard substituting problems, e.g. SLP with recourse, are contained in the closed hull of the set of efficient solutions of the SLP.