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Convex approximations for complete integer recourse models

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  • Vlerk, Maarten H. van der

    (Groningen University)

Abstract

We consider convex approximations of the expected value function of a two-stage integer recourse problem. The convex approximations are obtained by perturbing the distribution of the random right-hand side vector. It is shown that the approximation is optimal for the class of problems with totally unimodular recourse matrices. For problems not in this class, the result is a convex lower bound that is strictly better than the one obtained from the LP relaxation.

Suggested Citation

  • Vlerk, Maarten H. van der, 2002. "Convex approximations for complete integer recourse models," Research Report 02A21, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:02a21
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    File URL: http://irs.ub.rug.nl/ppn/239644395
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    References listed on IDEAS

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    1. 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.
    2. Rüdiger Schultz, 1993. "Continuity Properties of Expectation Functions in Stochastic Integer Programming," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 578-589, August.
    3. Vlerk, Maarten H. van der, 2002. "On multiple simple recourse models," Research Report 02A06, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    4. KLEIN HANEVELD, Willem K. & STOUGIE, Leen & VAN der VLERK, M.H., 1995. "On the Convex Hull of the Composition of a Separable and a Linear Function," LIDAM Discussion Papers CORE 1995070, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, University Library of Munich, Germany, revised 13 Nov 2003.
    6. repec:dgr:rugsom:02a06 is not listed on IDEAS
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    Cited by:

    1. Vlerk, Maarten H. van der, 2003. "Integrated chance constraints in an ALM model for pension funds," Research Report 03A21, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    2. repec:dgr:rugsom:02a06 is not listed on IDEAS
    3. Vlerk, Maarten H. van der, 2002. "On multiple simple recourse models," Research Report 02A06, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    4. repec:dgr:rugsom:03a01 is not listed on IDEAS
    5. Klein Haneveld, Willem K. & Vlerk, Maarten H. van der, 2002. "Integrated chance constraints: reduced forms and an algorithm," Research Report 02A33, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. repec:dgr:rugsom:03a14 is not listed on IDEAS
    7. repec:dgr:rugsom:03a21 is not listed on IDEAS
    8. Vlerk, Maarten H. van der, 2003. "Simplification of recourse models by modification of recourse data," Research Report 03A01, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    9. repec:dgr:rugsom:02a33 is not listed on IDEAS
    10. 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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