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Some insights into the solution algorithms for SLP problems

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  • Peter Kall
  • János Mayer

Abstract

We consider classes of stochastic linear programming problems which can be efficiently solved by deterministic algorithms. For two–stage recourse problems we identify two such classes. The first one consists of problems where the number of stochastically independent random variables is relatively low; the second class is the class of simple recourse problems. The proposed deterministic algorithm is successive discrete approximation. We also illustrate the impact of required accuracy on the efficiency of this algorithm. For jointly chance constrained problems with a random right–hand–side and multivariate normal distribution we demonstrate the increase in efficiency when lower accuracy is required, for a central cutting plane method. We support our argumentation and findings with computational results. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Peter Kall & János Mayer, 2006. "Some insights into the solution algorithms for SLP problems," Annals of Operations Research, Springer, vol. 142(1), pages 147-164, February.
    • Handle: RePEc:spr:annopr:v:142:y:2006:i:1:p:147-164:10.1007/s10479-006-6166-y
    DOI: 10.1007/s10479-006-6166-y
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    1. Gilbert Laporte & François Louveaux & Hélène Mercure, 1992. "The Vehicle Routing Problem with Stochastic Travel Times," Transportation Science, INFORMS, vol. 26(3), pages 161-170, August.
    2. Peter Kall & János Mayer, 2005. "Stochastic Linear Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-24440-2, September.
    3. Gondzio, Jacek, 1995. "HOPDM (version 2.12) -- A fast LP solver based on a primal-dual interior point method," European Journal of Operational Research, Elsevier, vol. 85(1), pages 221-225, August.
    4. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    5. repec:dgr:rugsom:02a06 is not listed on IDEAS
    6. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
    7. Vlerk, Maarten H. van der, 2002. "On multiple simple recourse models," Research Report 02A06, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
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