A NOTE ON DECISION RULES FOR STOCHASTIC PROGRAMS

Abstract

It is shown that a two-stage stochastic program with recourse with right-hand sides random (i.e., a two-stage programming under uncertainty problem) has optimal decision rules which are continuous and piecewise linear. However, this result does not extend to programs with three or more stages. An example is given of a simple inventory-type three-stage stochastic program with recourse for which the the optimal second-stage decision rule is not piecewise linear. The example is also recast in the framework of the conditional probability E-model of chance-constrained programming showing that the Charnes- Kirby theorem on the existence of piecewise linear decision rules for such programs is invalid for more than two stages.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1968
Accession Number
AD0673120

Entities

People

  • David W. Walkup
  • Roger J. B. Wets

Organizations

  • Boeing

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Computer Programming
  • Computing-Related Activities
  • Distribution Functions
  • Functions (Mathematics)
  • Integrals
  • Interdisciplinary Science
  • Linear Programming
  • Mathematical Analysis
  • Mathematics
  • Probability
  • Probability Distributions
  • Random Variables
  • Scientific Research
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Operations Research