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Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint


Author Info

  • Sridhar Bashyam

    (KPMG Peat Marwick LLP, 2300 Clarendon Boulevard, Arlington, Virginia 22201)

  • Michael C. Fu

    (The Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

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    A major assumption in the analysis of (s, S) inventory systems with stochastic lead times is that orders are received in the same sequence as they are placed. Even under this assumption, much of the work to date has focused on the unconstrained optimization of the system, in which a penalty cost for unsatisfied demand is assigned. The literature on constrained optimization, wherein a service level requirement needs to be met, is more sparse. In this paper, we consider the constrained optimization problem, where orders are allowed to cross in time. We propose a feasible directions procedure that is simulation based, and present computational results for a large number of test cases. In the vast majority of cases, we come within 5% of estimated optimality.

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 44 (1998)
    Issue (Month): 12-Part-2 (December)
    Pages: S243-S256

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    Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-2:p:s243-s256

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    Keywords: (s; S) Inventory Systems; Random Lead Times; Service Level Constraint; Constrained Simulation Optimization; Feasible Directions Search; Perturbation Analysis;


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    Cited by:
    1. Kleijnen, Jack P.C. & Beers, W.C.M. van & Nieuwenhuyse, I. van, 2010. "Constrained optimization in simulation: A novel approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3583585, Tilburg University.
    2. Bekker, James & Aldrich, Chris, 2011. "The cross-entropy method in multi-objective optimisation: An assessment," European Journal of Operational Research, Elsevier, vol. 211(1), pages 112-121, May.
    3. Rossi, Roberto & Tarim, S. Armagan & Hnich, Brahim & Prestwich, Steven, 2010. "Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times," International Journal of Production Economics, Elsevier, vol. 127(1), pages 180-189, September.
    4. Sumit Kunnumkal & Huseyin Topaloglu, 2009. "A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions," Computational Statistics, Springer, vol. 70(3), pages 477-504, December.
    5. Duan, Qinglin & Warren Liao, T., 2013. "Optimization of replenishment policies for decentralized and centralized capacitated supply chains under various demands," International Journal of Production Economics, Elsevier, vol. 142(1), pages 194-204.
    6. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping: A Survey (Revision of CentER DP 2011-064)," Discussion Paper 2013-064, Tilburg University, Center for Economic Research.
    7. Fang, Xin & Zhang, Cheng & Robb, David J. & Blackburn, Joseph D., 2013. "Decision support for lead time and demand variability reduction," Omega, Elsevier, vol. 41(2), pages 390-396.


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