Mathematical Programming

, Volume 159, Issue 1–2, pp 557–569 | Cite as

A comment on “computational complexity of stochastic programming problems”

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Wolfram Wiesemann
Short Communication Series A

Abstract

Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Math Program A 106(3):423–432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem data is governed by independent uniform distributions. We show that Dyer and Stougie’s proof is not correct, and we offer a correction which establishes the stronger result that even the approximate solution of such problems is #P-hard for a sufficiently high accuracy. We also provide new results which indicate that linear two-stage stochastic programs with random recourse seem even more challenging to solve.

Keywords

Stochastic programming Complexity theory Two-stage problems 

Mathematics Subject Classification

90C15 

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2015

Authors and Affiliations

  • Grani A. Hanasusanto
    • 1
  • Daniel Kuhn
    • 1
  • Wolfram Wiesemann
    • 2
  1. 1.Risk Analytics and Optimization ChairÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Imperial College Business SchoolImperial College LondonLondonUnited Kingdom

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