Fully polynomial time approximation schemes for stochastic dynamic programs

Nir Halman*, Diego Klabjan, Chung Lun Li, James Orlin, David Simchi-Levi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We present a framework for obtaining fully polynomial time approximation schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely, the calculus of K-approximation functions and the calculus of K-approximation sets. Using our framework, we provide the first FPTASs for several NP-hard problems in various fields of research such as knapsack models, logistics, operations management, economics, and mathematical finance. Extensions of our framework via the use of the newly established computational rules are also discussed.

Original languageEnglish (US)
Pages (from-to)1725-1796
Number of pages72
JournalSIAM Journal on Discrete Mathematics
Volume28
Issue number4
DOIs
StatePublished - 2014

Keywords

  • Fully polynomial time approximation schemes
  • K-approximation
  • Stochastic dynamic programming

ASJC Scopus subject areas

  • Mathematics(all)

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