Restricted-Recourse Bounds for Stochastic Linear Programming
Abstract
This article considers the problem of bounding the expected value of a linear program (LP) containing random coefficients, 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. These "restricted-recourse bounds" are more general and more easily computed than most other bounds because random coefficients may appear anywhere in the LP, neither independence nor boundedness of the coefficients 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, the authors apply the bounds to a two-stage stochastic program for semiconductor manufacturing with uncertain demand and production rates.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1999
- Accession Number
- ADA487309
Entities
People
- David P. Morton
- R. Kevin Wood
Organizations
- Naval Postgraduate School