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Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals

Author

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  • Xiuli Chao

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

  • Sean X. Zhou

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong)

Abstract

In many production/distribution systems, materials flow in fixed lot sizes (e.g., in full truckloads or full containers) and under regular schedules (e.g., delivery every week). In this paper, we study a multiechelon serial system with batch ordering and fixed replenishment intervals. We derive the optimal inventory control policy, provide a distribution-function solution for its optimal control parameters, and present an efficient algorithm for computing those parameters. Further, we show that the optimal expected system cost is minimized when the ordering times for all stages are synchronized. In contrast to the known approach in the literature that develops a lower bound for the average cost of a given period for the classical serial system, we develop a lower bound for the average total cost over an appropriately defined cycle and then construct a policy that reaches the lower bound. We also discuss its extension to the nonlinear shortage cost case (i.e., the nonlinear cost case). This paper generalizes several recent results on the analysis of multiechelon systems.

Suggested Citation

  • Xiuli Chao & Sean X. Zhou, 2009. "Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals," Operations Research, INFORMS, vol. 57(2), pages 377-390, April.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:2:p:377-390
    DOI: 10.1287/opre.1080.0636
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    References listed on IDEAS

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    1. 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.
    2. Xiuli Chao & Sean X. Zhou, 2007. "Probabilistic solution and bounds for serial inventory systems with discounted and average costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 623-631, September.
    3. Jing-Sheng Song, 1994. "The Effect of Leadtime Uncertainty in a Simple Stochastic Inventory Model," Management Science, INFORMS, vol. 40(5), pages 603-613, May.
    4. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    5. 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.
    6. Arthur F. Veinott, 1965. "The Optimal Inventory Policy for Batch Ordering," Operations Research, INFORMS, vol. 13(3), pages 424-432, June.
    7. Chen, Fangruo & Zheng, Yu-Sheng, 1993. "Inventory models with general backorder costs," European Journal of Operational Research, Elsevier, vol. 65(2), pages 175-186, March.
    8. Stephen C. Graves, 1996. "A Multiechelon Inventory Model with Fixed Replenishment Intervals," Management Science, INFORMS, vol. 42(1), pages 1-18, January.
    9. Fangruo Chen & Yu-Sheng Zheng, 1998. "Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems," Operations Research, INFORMS, vol. 46(4), pages 592-602, August.
    10. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.
    11. Gérard P. Cachon, 1999. "Managing Supply Chain Demand Variability with Scheduled Ordering Policies," Management Science, INFORMS, vol. 45(6), pages 843-856, June.
    12. Awi Federgruen & Paul Zipkin, 1984. "Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model," Operations Research, INFORMS, vol. 32(4), pages 818-836, August.
    13. Kaj Rosling, 2002. "Inventory Cost Rate Functions with Nonlinear Shortage Costs," Operations Research, INFORMS, vol. 50(6), pages 1007-1017, December.
    14. Marc A. De Bodt & Stephen C. Graves, 1985. "Continuous-Review Policies for a Multi-Echelon Inventory Problem with Stochastic Demand," Management Science, INFORMS, vol. 31(10), pages 1286-1299, October.
    15. Geert-Jan van Houtum & Alan Scheller-Wolf & Jinxin Yi, 2007. "Optimal Control of Serial Inventory Systems with Fixed Replenishment Intervals," Operations Research, INFORMS, vol. 55(4), pages 674-687, August.
    16. Kaj Rosling, 1989. "Optimal Inventory Policies for Assembly Systems Under Random Demands," Operations Research, INFORMS, vol. 37(4), pages 565-579, August.
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    Cited by:

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    4. Qinan Wang & Sven Axsäter, 2013. "Fixed‐interval joint‐replenishment policies for distribution systems with multiple retailers and stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 637-651, December.
    5. Woonghee Tim Huh & Ganesh Janakiraman, 2012. "Technical Note---On Optimal Policies for Inventory Systems with Batch Ordering," Operations Research, INFORMS, vol. 60(4), pages 797-802, August.
    6. Zhu, Han & Liu, Xing & Chen, Youhua (Frank), 2015. "Effective inventory control policies with a minimum order quantity and batch ordering," International Journal of Production Economics, Elsevier, vol. 168(C), pages 21-30.
    7. Huang, Boray & Wu, Andy, 2017. "Reduce shortage with self-reservation policy for a manufacturer paying both fixed and variable stockout expenditure," European Journal of Operational Research, Elsevier, vol. 262(3), pages 944-953.
    8. Agrawal, Narendra & Smith, Stephen A., 2019. "Optimal inventory management using retail prepacks," European Journal of Operational Research, Elsevier, vol. 274(2), pages 531-544.
    9. Yi Yang & Youhua (Frank) Chen & Yun Zhou, 2014. "Coordinating Inventory Control and Pricing Strategies Under Batch Ordering," Operations Research, INFORMS, vol. 62(1), pages 25-37, February.
    10. Yang, Yi & Yuan, Quan & Xue, Weili & Zhou, Yun, 2014. "Analysis of batch ordering inventory models with setup cost and capacity constraint," International Journal of Production Economics, Elsevier, vol. 155(C), pages 340-350.
    11. Alkaabneh, Faisal & Diabat, Ali & Gao, Huaizhu Oliver, 2021. "A unified framework for efficient, effective, and fair resource allocation by food banks using an Approximate Dynamic Programming approach," Omega, Elsevier, vol. 100(C).
    12. Ming Hu & Yi Yang, 2014. "Modified Echelon ( r, Q ) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems," Operations Research, INFORMS, vol. 62(4), pages 812-828, August.
    13. 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.
    14. Johan Marklund & Kaj Rosling, 2012. "Lower Bounds and Heuristics for Supply Chain Stock Allocation," Operations Research, INFORMS, vol. 60(1), pages 92-105, February.
    15. Saif Benjaafar & David Chen & Rowan Wang, 2017. "Managing Production-Inventory Systems with Scarce Resources," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 216-229, May.
    16. Cong Shi & Huanan Zhang & Xiuli Chao & Retsef Levi, 2014. "Approximation algorithms for capacitated stochastic inventory systems with setup costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 304-319, June.
    17. 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.
    18. 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.
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    21. Kevin H. Shang & Sean X. Zhou & Geert-Jan van Houtum, 2010. "Improving Supply Chain Performance: Real-Time Demand Information and Flexible Deliveries," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 430-448, May.

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