Restricted-Recourse Bounds for Stochastic Linear Programming

We consider the problem of bounding the expected value of a linear program (LP) containing random coe&cients, with applications to solving two-stage stochastic programs. An upper bound for minimizations is derived from a restriction of an equivalent, penalty-based formulation of the primal stochastic LP, and a lower bound is obtained from a restriction of a reformulation of the dual. Our “restrictedrecourse bounds” are more general and more easily computed than most other bounds because random coe&cients may appear anywhere in the LP, neither independence nor boundedness of the coe&cients is needed, and the bound is computed by solving a single LP or nonlinear program. Analytical examples demonstrate that the new bounds can be stronger than complementary Jensen bounds. (An upper bound is “complementary” to a lower bound, and vice versa). In computational work, we apply the bounds to a two-stage stochastic program for semiconductor manufacturing with uncertain demand and production rates.