Restricted-recourse bounds for stochastic linear programming

David P. Morton, R. Kevin Wood

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We consider 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. Our `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, we apply the bounds to a two-stage stochastic program for semiconductor manufacturing with uncertain demand and production rates.

Original languageEnglish (US)
Pages (from-to)943-956
Number of pages14
JournalOperations Research
Volume47
Issue number6
DOIs
StatePublished - 1999

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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