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Convex approximations for a class of mixed-integer recourse models

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  • Maarten Vlerk

Abstract

We consider mixed-integer recourse (MIR) models with a single recourse constraint. We relate the second-stage value function of such problems to the expected simple integer recourse (SIR) shortage function. This allows to construct convex approximations for MIR problems by the same approach used for SIR models. Copyright The Author(s) 2010

Suggested Citation

  • Maarten Vlerk, 2010. "Convex approximations for a class of mixed-integer recourse models," Annals of Operations Research, Springer, vol. 177(1), pages 139-150, June.
    • Handle: RePEc:spr:annopr:v:177:y:2010:i:1:p:139-150:10.1007/s10479-009-0591-7
    DOI: 10.1007/s10479-009-0591-7
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    References listed on IDEAS

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    1. KLEIN HANEVELD, W. K. & STOUGIE, L. & van der VLERK, M. H., 1996. "An algorithm for the construction of convex hulls in simple integer recourse programming," LIDAM Reprints CORE 1215, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Willem Klein Haneveld & Maarten van der Vlerk, 1999. "Stochastic integer programming:General models and algorithms," Annals of Operations Research, Springer, vol. 85(0), pages 39-57, January.
    3. repec:dgr:rugsom:03a14 is not listed on IDEAS
    4. Rüdiger Schultz, 1993. "Continuity Properties of Expectation Functions in Stochastic Integer Programming," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 578-589, August.
    5. Caroe, Claus C. & Tind, Jorgen, 1997. "A cutting-plane approach to mixed 0-1 stochastic integer programs," European Journal of Operational Research, Elsevier, vol. 101(2), pages 306-316, September.
    6. Stougie, Leen & Vlerk, Maarten H. van der, 2003. "Approximation in stochastic integer programming," Research Report 03A14, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
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    Cited by:

    1. Ilke Bakir & Natashia Boland & Brian Dandurand & Alan Erera, 2020. "Sampling Scenario Set Partition Dual Bounds for Multistage Stochastic Programs," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 145-163, January.
    2. Ward Romeijnders & Niels van der Laan, 2020. "Pseudo-Valid Cutting Planes for Two-Stage Mixed-Integer Stochastic Programs with Right-Hand-Side Uncertainty," Operations Research, INFORMS, vol. 68(4), pages 1199-1217, July.
    3. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2016. "Monotonic bounds in multistage mixed-integer stochastic programming," Computational Management Science, Springer, vol. 13(3), pages 423-457, July.
    4. Weijun Xie & Shabbir Ahmed, 2018. "Distributionally robust simple integer recourse," Computational Management Science, Springer, vol. 15(3), pages 351-367, October.
    5. Ward Romeijnders & David P. Morton & Maarten H. van der Vlerk, 2017. "Assessing the Quality of Convex Approximations for Two-Stage Totally Unimodular Integer Recourse Models," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 211-231, May.
    6. David P. Morton & Ward Romeijnders & Rüdiger Schultz & Leen Stougie, 2018. "The stochastic programming heritage of Maarten van der Vlerk," Computational Management Science, Springer, vol. 15(3), pages 319-323, October.

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