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


  • 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)


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.

Suggested Citation

  • Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
  • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-2:p:s243-s256

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    References listed on IDEAS

    1. Pierre L'Ecuyer & Nataly Giroux & Peter W. Glynn, 1994. "Stochastic Optimization by Simulation: Numerical Experiments with the M/M/1 Queue in Steady-State," Management Science, INFORMS, vol. 40(10), pages 1245-1261, October.
    2. Tijms, H. C. & Groenevelt, H., 1984. "Simple approximations for the reorder point in periodic and continuous review (s, S) inventory systems with service level constraints," European Journal of Operational Research, Elsevier, vol. 17(2), pages 175-190, August.
    3. Helmut Schneider & Jeffrey L. Ringuest, 1990. "Power Approximation for Computing (s, S) Policies Using Service Level," Management Science, INFORMS, vol. 36(7), pages 822-834, July.
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    Cited by:

    1. 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.
    2. 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.
    3. Ebru Angün & Jack Kleijnen, 2012. "An Asymptotic Test of Optimality Conditions in Multiresponse Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 53-65, February.
    4. 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.
    5. Kleijnen, J.P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2008. "Constrained Optimization in Simulation : A Novel Approach," Discussion Paper 2008-95, Tilburg University, Center for Economic Research.
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    7. repec:spr:compst:v:70:y:2009:i:3:p:477-504 is not listed on IDEAS
    8. Bettonvil, B.W.M. & Del Castillo, E. & Kleijnen, J.P.C., 2007. "Statistical Testing of Optimality Conditions in Multiresponse Simulation-based Optimization (Revision of 2005-81)," Discussion Paper 2007-45, Tilburg University, Center for Economic Research.
    9. Kleijnen, J.P.C. & Wan, J., 2006. "Optimization of Simulated Inventory Systems : OptQuest and Alternatives," Discussion Paper 2006-75, Tilburg University, Center for Economic Research.
    10. Kleijnen, J.P.C., 2006. "Generalized Response Surface Methodology : A New Metaheuristic," Discussion Paper 2006-77, Tilburg University, Center for Economic Research.
    11. 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.
    12. repec:pal:jorsoc:v:53:y:2002:i:11:d:10.1057_palgrave.jors.2601441 is not listed on IDEAS
    13. Sumit Kunnumkal & Huseyin Topaloglu, 2009. "A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 477-504, December.
    14. Mario Guajardo & Mikael Rönnqvist & Ann Mari Halvorsen & Svein Inge Kallevik, 2015. "Inventory management of spare parts in an energy company," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(2), pages 331-341, February.
    15. van Beers, Wim C.M. & Kleijnen, Jack P.C., 2008. "Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1099-1113, May.
    16. 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.
    17. J J A Moors & L W G Strijbosch, 2002. "Exact fill rates for (R, s, S) inventory control with gamma distributed demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1268-1274, November.
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    19. Kleijnen, Jack P.C. & Beers, Wim van & Nieuwenhuyse, Inneke van, 2010. "Constrained optimization in expensive simulation: Novel approach," European Journal of Operational Research, Elsevier, vol. 202(1), pages 164-174, April.
    20. Ramesh Bollapragada & Uday S. Rao & Jun Zhang, 2004. "Managing Inventory and Supply Performance in Assembly Systems with Random Supply Capacity and Demand," Management Science, INFORMS, vol. 50(12), pages 1729-1743, December.


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