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Evaluating Echelon Stock (R, nQ) Policies in Serial Production/Inventory Systems with Stochastic Demand

Author

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  • Fangruo Chen

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Yu-Sheng Zheng

    (Operations and Information Management Department, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

This paper studies echelon stock (R, nQ) policies in serial production/inventory systems with stochastic demand. We provide a recursive procedure to compute the steady state echelon inventory levels of the systems, which can be used to evaluate the long-run average holding and backorder costs as well as other performance measures. The procedure is based upon an observation of a relationship between the inventory status of adjacent stages in a serial system. We also device exact formulas for replenishment frequencies and setup costs. Our results apply to both continuous-review systems with compound Poisson demand and periodic-review systems with independent, identically distributed demands. A preliminary numerical study was conducted to explore the cost effectiveness of echelon stock (R, nQ) policies. For two-stage systems with simple Poisson demand, we compared among the minimum costs of echelon stock (R, nQ) policies, a lower bound on the minimum achievable costs, and the minimum costs of installation stock (R, nQ) policies. Finally, we present a modification of an existing approximate evaluation procedure.

Suggested Citation

  • Fangruo Chen & Yu-Sheng Zheng, 1994. "Evaluating Echelon Stock (R, nQ) Policies in Serial Production/Inventory Systems with Stochastic Demand," Management Science, INFORMS, vol. 40(10), pages 1262-1275, October.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:10:p:1262-1275
    DOI: 10.1287/mnsc.40.10.1262
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    Cited by:

    1. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    2. Kevin H. Shang & Sean X. Zhou, 2010. "Optimal and Heuristic Echelon ( r, nQ, T ) Policies in Serial Inventory Systems with Fixed Costs," Operations Research, INFORMS, vol. 58(2), pages 414-427, April.
    3. Agrawal, Narendra & Smith, Stephen A., 2019. "Optimal inventory management using retail prepacks," European Journal of Operational Research, Elsevier, vol. 274(2), pages 531-544.
    4. He, Q. -M. & Jewkes, E. M. & Buzacott, J., 2002. "Optimal and near-optimal inventory control policies for a make-to-order inventory-production system," European Journal of Operational Research, Elsevier, vol. 141(1), pages 113-132, August.
    5. Ki Ling Cheung & Warren H. Hausman, 2000. "An Exact Performance Evaluation for the Supplier in a Two-Echelon Inventory System," Operations Research, INFORMS, vol. 48(4), pages 646-653, August.
    6. Ki Ling Cheung & Hau L. Lee, 2002. "The Inventory Benefit of Shipment Coordination and Stock Rebalancing in a Supply Chain," Management Science, INFORMS, vol. 48(2), pages 300-306, February.
    7. Robert L. Bray & Yuliang Yao & Yongrui Duan & Jiazhen Huo, 2019. "Ration Gaming and the Bullwhip Effect," Operations Research, INFORMS, vol. 67(2), pages 453-467, March.
    8. Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
    9. Ng, C. T. & Li, Leon Y. O. & Chakhlevitch, K., 2001. "Coordinated replenishments with alternative supply sources in two-level supply chains," International Journal of Production Economics, Elsevier, vol. 73(3), pages 227-240, October.
    10. Amir Hosein Afshar Sedigh & Rasoul Haji & Seyed Mehdi Sajadifar, 2023. "The Cost Function of a Two-Level Inventory System with identical retailers benefitting from Information Sharing," Papers 2312.03898, arXiv.org.
    11. Hsien-Jen Lin, 2015. "Two-echelon stochastic inventory system with returns and partial backlogging," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 966-975, April.
    12. Kevin H. Shang & Jing-Sheng Song, 2007. "Serial Supply Chains with Economies of Scale: Bounds and Approximations," Operations Research, INFORMS, vol. 55(5), pages 843-853, October.
    13. Fangruo Chen, 1998. "Echelon Reorder Points, Installation Reorder Points, and the Value of Centralized Demand Information," Management Science, INFORMS, vol. 44(12-Part-2), pages 221-234, December.
    14. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.
    15. Boray Huang & Seyed M. R. Iravani, 2005. "Production Control Policies in Supply Chains with Selective-Information Sharing," Operations Research, INFORMS, vol. 53(4), pages 662-674, August.
    16. Diks, E. B. & de Kok, A. G. & Lagodimos, A. G., 1996. "Multi-echelon systems: A service measure perspective," European Journal of Operational Research, Elsevier, vol. 95(2), pages 241-263, December.
    17. Fangruo Chen & Rungson Samroengraja, 2004. "Order Volatility and Supply Chain Costs," Operations Research, INFORMS, vol. 52(5), pages 707-722, October.
    18. Leon Yang Chu & Zuo-Jun Max Shen, 2010. "A Power-of-Two Ordering Policy for One-Warehouse Multiretailer Systems with Stochastic Demand," Operations Research, INFORMS, vol. 58(2), pages 492-502, April.
    19. Ying Zhang & Jayashankar M. Swaminathan, 2020. "Warehouse Location in An Emerging Country: A Win–Win Proposition?," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1487-1505, June.
    20. van Houtum, G. J. & Inderfurth, K. & Zijm, W. H. M., 1996. "Materials coordination in stochastic multi-echelon systems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 1-23, November.
    21. Wei Xu & Dong-Ping Song, 2022. "Integrated optimisation for production capacity, raw material ordering and production planning under time and quantity uncertainties based on two case studies," Operational Research, Springer, vol. 22(3), pages 2343-2371, July.
    22. Yang, Lei & Yang, Jian & Yu, Gang & Zhang, Hanqin, 2011. "Near-optimal (r,Q) policies for a two-stage serial inventory system with Poisson demand," International Journal of Production Economics, Elsevier, vol. 133(2), pages 728-735, October.
    23. Mitra, Subrata & Chatterjee, A. K., 2004. "Echelon stock based continuous review (R,Q) policy for fast moving items," Omega, Elsevier, vol. 32(2), pages 161-166, April.
    24. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.

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