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On the design of a tandem queue with blocking: Modeling, analysis, and gradient estimation

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  • Dinah W. Cheng

Abstract

We demonstrate here how recent advances in the study of discrete‐event stochastic systems provide fruitful results for the modeling, analysis, and design of manufacturing systems. We consider a multistage make‐to‐stock system where outputs from the final stage are used to satisfy customer demands. We address the problem of finding the appropriate trade‐off between reduced order waiting time and increased process speeds. Using the idea of infinitesimal perturbation analysis (IPA), we establish a simple procedure where sample‐path derivatives can be obtained along an arbitrary sample path. Under suitable conditions, we demonstrate that these derivative estimators are unbiased and strongly consistent and can be used in a classical stochastic optimization scheme to solve the problem. The role of continuity and convexity on the validity of the estimator is also addressed. Although the focus of this article is not to solve for the optimal solution, we provide a theoretical justification for such a pursuit. The approach is appealing as it is numerically stable, easy to implement, and can be extended to other system performance measures. © 1994 John Wiley & Sons, Inc.

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  • Dinah W. Cheng, 1994. "On the design of a tandem queue with blocking: Modeling, analysis, and gradient estimation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 759-770, October.
  • Handle: RePEc:wly:navres:v:41:y:1994:i:6:p:759-770
    DOI: 10.1002/1520-6750(199410)41:63.0.CO;2-1
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    1. Debasis Mitra & Isi Mitrani, 1990. "Analysis of a Kanban Discipline for Cell Coordination in Production Lines. I," Management Science, INFORMS, vol. 36(12), pages 1548-1566, December.
    2. Paul Glasserman, 1991. "Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices," Operations Research, INFORMS, vol. 39(5), pages 724-738, October.
    3. Rajan Suri & Michael A. Zazanis, 1988. "Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue," Management Science, INFORMS, vol. 34(1), pages 39-64, January.
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    1. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.

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