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Analysis and Optimization of a Multistage Inventory-Queue System

Author

Listed:
  • Liming Liu

    (Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • Xiaoming Liu

    (Faculty of Business Adminstration, University of Macau, Macau, China)

  • David D. Yao

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

An important issue in the management of supply chains and manufacturing systems is to control inventory costs at different locations throughout the system while satisfying an end-customer service-level requirement. The challenge involved is to solve a nonlinear constrained optimization problem that captures the key dynamics of a complex production-inventory system. In this paper, we first develop a multistage inventory-queue model and a job-queue decomposition approach that evaluates the performance of serial manufacturing and supply systems with inventory control at every stage. We then present an efficient procedure to minimize the overall inventory in the system while meeting the required service level. Our technique is relatively simple and delivers accurate performance estimates. Furthermore, numerical studies generate certain managerial insights into related design and control issues.

Suggested Citation

  • Liming Liu & Xiaoming Liu & David D. Yao, 2004. "Analysis and Optimization of a Multistage Inventory-Queue System," Management Science, INFORMS, vol. 50(3), pages 365-380, March.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:3:p:365-380
    DOI: 10.1287/mnsc.1030.0196
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    References listed on IDEAS

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    1. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
    2. Frederick S. Hillier & Ronald W. Boling, 1979. "On the Optimal Allocation of Work in Symmetrically Unbalanced Production Line Systems with Variable Operation Times," Management Science, INFORMS, vol. 25(8), pages 721-728, August.
    3. Yong-Joo Lee & Paul Zipkin, 1995. "Processing Networks with Inventories: Sequential Refinement Systems," Operations Research, INFORMS, vol. 43(6), pages 1025-1036, December.
    4. Paul Glasserman & Sridhar Tayur, 1994. "The Stability of a Capacitated, Multi-Echelon Production-Inventory System Under a Base-Stock Policy," Operations Research, INFORMS, vol. 42(5), pages 913-925, October.
    5. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    6. Gabriel R. Bitran & Devanath Tirupati, 1988. "Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference," Management Science, INFORMS, vol. 34(1), pages 75-100, January.
    7. Paul Glasserman, 1997. "Bounds and Asymptotics for Planning Critical Safety Stocks," Operations Research, INFORMS, vol. 45(2), pages 244-257, April.
    8. Zipkin, Paul, 1995. "Processing networks with planned inventories: Tandem queues with feedback," European Journal of Operational Research, Elsevier, vol. 80(2), pages 344-349, January.
    9. Craig C. Sherbrooke, 1968. "Metric: A Multi-Echelon Technique for Recoverable Item Control," Operations Research, INFORMS, vol. 16(1), pages 122-141, February.
    10. Sven Axsäter & Kaj Rosling, 1993. "Notes: Installation vs. Echelon Stock Policies for Multilevel Inventory Control," Management Science, INFORMS, vol. 39(10), pages 1274-1280, October.
    11. Yong-Joo Lee & Paul Zipkin, 1992. "Tandem Queues with Planned Inventories," Operations Research, INFORMS, vol. 40(5), pages 936-947, October.
    12. M. Berg & M. J. M. Posner, 1990. "Customer Delay in M/G/∞ Repair Systems with Spares," Operations Research, INFORMS, vol. 38(2), pages 344-348, April.
    13. Markus Ettl & Gerald E. Feigin & Grace Y. Lin & David D. Yao, 2000. "A Supply Network Model with Base-Stock Control and Service Requirements," Operations Research, INFORMS, vol. 48(2), pages 216-232, April.
    14. Hau L. Lee & Corey Billington, 1993. "Material Management in Decentralized Supply Chains," Operations Research, INFORMS, vol. 41(5), pages 835-847, October.
    15. Duri, C. & Frein, Y. & Di Mascolo, M., 2000. "Performance evaluation and design of base stock systems," European Journal of Operational Research, Elsevier, vol. 127(1), pages 172-188, November.
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    Cited by:

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    3. Boute, Robert N. & Disney, Stephen M. & Lambrecht, Marc R. & Houdt, Benny Van, 2014. "Coordinating lead times and safety stocks under autocorrelated demand," European Journal of Operational Research, Elsevier, vol. 232(1), pages 52-63.
    4. Skintzi, Georgia & Ioannou, George & Prastacos, Gregory, 2008. "Investigating warehousing policies," International Journal of Production Economics, Elsevier, vol. 112(2), pages 955-970, April.
    5. Bo Li & Antonio Arreola‐Risa, 2022. "Minimizing conditional value‐at‐risk under a modified basestock policy," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1822-1838, April.
    6. Sanajian, Nima & BalcIog[small tilde]lu, BarIs, 2009. "The impact of production time variability on make-to-stock queue performance," European Journal of Operational Research, Elsevier, vol. 194(3), pages 847-855, May.
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    8. Avṣar, Zeynep Müge & Henk Zijm, W., 2014. "Approximate queueing models for capacitated multi-stage inventory systems under base-stock control," European Journal of Operational Research, Elsevier, vol. 236(1), pages 135-146.

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