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


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.


Stochastic programming Complexity theory Two-stage problems 

Mathematics Subject Classification




The authors are grateful to the anonymous referees for their thoughtful comments which substantially improved the paper. This research was supported by the Swiss National Science Foundation Grant BSCGI0_157733 and the EPSRC Grants EP/M028240/1 and EP/M027856/1.


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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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