A column-and-constraint generation algorithm for two-stage stochastic programming problems

Denise D. Tönissen*, Joachim J. Arts, Zuo Jun Max Shen

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

This paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

Original languageEnglish
Pages (from-to)781-798
Number of pages18
JournalTOP
Volume29
Issue number3
Early online date16 Feb 2021
DOIs
Publication statusPublished - Oct 2021

Bibliographical note

Funding Information:
The study was funded by Nedtrain. Furthermore, the authors thank Geert-Jan van Houtum and Nicole Perez-Becker for giving valuable input.

Publisher Copyright:
© 2021, The Author(s).

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

  • Benders decomposition
  • Column-and-constraint generation
  • Facility location
  • Stochastic programming

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