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Rare-Event Simulation for Multistage Production-Inventory Systems

Author

Listed:
  • Paul Glasserman

    (Columbia Business School, New York, New York 10027)

  • Tai-Wen Liu

    (Rutgers University, Newark, New Jersey 07102)

Abstract

We consider the problem of precise estimation of service-level measures in multistage production-inventory systems when the system is managed for high levels of service. Precisely because the service level is high, stockouts, large backorders, and unfilled demands are rare and thus difficult to estimate by straightforward simulation. We propose and analyze alternative estimators, based on changing the demand distribution to make these rare events less rare. Whereas straightforward simulation for a fixed relative error results in computational requirements that grow exponentially in certain stock-level parameters, the requirements for our importance sampling estimators remain bounded for all parameter values. We provide bounds making it possible to determine the maximum number of replications required before any are generated. Numerical examples illustrate the effectiveness of our method.

Suggested Citation

  • Paul Glasserman & Tai-Wen Liu, 1996. "Rare-Event Simulation for Multistage Production-Inventory Systems," Management Science, INFORMS, vol. 42(9), pages 1292-1307, September.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:9:p:1292-1307
    DOI: 10.1287/mnsc.42.9.1292
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    Citations

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    Cited by:

    1. Paul Glasserman & Yashan Wang, 1999. "Fill-Rate Bottlenecks in Production-Inventory Networks," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 62-76.
    2. Daniel R. Jiang & Warren B. Powell, 2018. "Risk-Averse Approximate Dynamic Programming with Quantile-Based Risk Measures," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 554-579, May.
    3. Apostolos Burnetas & Michael Katehakis, 1997. "On confidence intervals from simulation of finite Markov chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 241-250, June.

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