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

Author

Listed:
  • 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)

Abstract

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
    DOI: 10.1287/mnsc.44.12.S243
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    References listed on IDEAS

    as
    1. Sridhar Bashyam & Michael C. Fu, 1994. "Application of perturbation analysis to a class of periodic review (s, S) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 47-80, February.
    2. 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.
    3. Richard Ehrhardt, 1984. "( s , S ) Policies for a Dynamic Inventory Model with Stochastic Lead Times," Operations Research, INFORMS, vol. 32(1), pages 121-132, February.
    4. 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.
    5. 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.
    6. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
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