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Application of perturbation analysis to a class of periodic review (s, S) inventory systems

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  • Sridhar Bashyam
  • Michael C. Fu

Abstract

In this article we apply perturbation analysis (PA), combined with conditional Monte Carlo, to obtain derivative estimators of the expected cost per period with respect to s and S, for a class of periodic review (s, S) inventory systems with full backlogging, linear holding and shortage costs, and where the arrivals of demands follow a renewal process. We first develop the general form of four different estimators of the gradient for the finite‐horizon case, and prove that they are unbiased. We next consider the problem of implementing our estimators, and develop efficient methodologies for the infinite‐horizon case. For the case of exponentially distributed demand interarrival times, we implement our estimators using a single sample path. Generally distributed interarrival times are modeled as phase‐type distributions, and the implementation of this more general case requires a number of additional off‐line simulations. The resulting estimators are still efficient and practical, provided that the number of phases is not too large. We conclude by reporting the results of simulation experiments. The results provide further validity of our methodology and also indicate that our estimators have very low variance. © 1994 John Wiley & Sons, Inc.

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  • 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.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:1:p:47-80
    DOI: 10.1002/1520-6750(199402)41:13.0.CO;2-I
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    References listed on IDEAS

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    1. Reuven Y. Rubinstein, 1989. "Sensitivity Analysis and Performance Extrapolation for Computer Simulation Models," Operations Research, INFORMS, vol. 37(1), pages 72-81, February.
    2. M. Hossein Safizadeh, 1990. "Optimization in simulation: Current issues and the future outlook," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(6), pages 807-825, December.
    3. Paul Glasserman, 1991. "Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices," Operations Research, INFORMS, vol. 39(5), pages 724-738, October.
    4. Martin I. Reiman & Alan Weiss, 1989. "Sensitivity Analysis for Simulations via Likelihood Ratios," Operations Research, INFORMS, vol. 37(5), pages 830-844, October.
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    Cited by:

    1. Ravi Anupindi & Sridhar Tayur, 1998. "Managing Stochastic Multiproduct Systems: Model, Measures, and Analysis," Operations Research, INFORMS, vol. 46(3-supplem), pages 98-111, June.
    2. 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.
    3. Michael C. Fu, 2008. "What you should know about simulation and derivatives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 723-736, December.
    4. Sridhar Tayur, 2000. "Improving Operations and Quoting Accurate Lead Times in a Laminate Plant," Interfaces, INFORMS, vol. 30(5), pages 1-15, October.

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