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On SIP algorithms for minimizing the mean-risk function in the multi-period single-source problem under uncertainty

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  • A. Alonso-Ayuso
  • L. Escudero
  • C. Pizarro

Abstract

We present an algorithmic framework for solving the strategic problem of assigning retailers to facilities in a multi-period single-sourcing product environment under uncertainty in the demand from the retailers and the costs of production, inventory holding, backlogging and distribution of the product. The functional to minimize is included by the expected objective function and the excess probability functional. By considering a splitting variable mathematical representation of the Deterministic Equivalent Model, we introduce several so-called Fix-and-Relax procedures that exploit the excess probability functional structure in addition to the structure of the special ordered sets related to the non-anticipativity constraints for the assignment variables. Some computational experience is reported. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • A. Alonso-Ayuso & L. Escudero & C. Pizarro, 2009. "On SIP algorithms for minimizing the mean-risk function in the multi-period single-source problem under uncertainty," Annals of Operations Research, Springer, vol. 166(1), pages 223-242, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:223-242:10.1007/s10479-008-0411-5
    DOI: 10.1007/s10479-008-0411-5
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    References listed on IDEAS

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    1. Guglielmo Lulli & Suvrajeet Sen, 2004. "A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems," Management Science, INFORMS, vol. 50(6), pages 786-796, June.
    2. 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).
    3. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    4. Dillenberger, Christof & Escudero, Laureano F. & Wollensak, Artur & Zhang, Wu, 1994. "On practical resource allocation for production planning and scheduling with period overlapping setups," European Journal of Operational Research, Elsevier, vol. 75(2), pages 275-286, June.
    5. repec:dgr:rugsom:03a21 is not listed on IDEAS
    6. A. Alonso-Ayuso & L. Escudero & C. Pizarro & H. Romeijn & D. Morales, 2006. "On solving the multi-period single-sourcing problem under uncertainty," Computational Management Science, Springer, vol. 3(1), pages 29-53, January.
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    Cited by:

    1. Kristin Uggen & Marte Fodstad & Vibeke Nørstebø, 2013. "Using and extending fix-and-relax to solve maritime inventory routing problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 355-377, July.

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