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Order-Based Backorders and Their Implications in Multi-Item Inventory Systems

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  • Jing-Sheng Song

    (Graduate School of Management, University of California, Irvine, California 92697)

Abstract

In a multi-item inventory system, such as an assemble-to-order manufacturing system or an online-retailing system, a customer order typically consists of several different items in different amounts. The average order-based backorders are the average number of customer orders that are not yet completely filled. While this is an important measure of customer satisfaction, it has not been widely studied in the operations management literature. This is largely because its evaluation involves the joint distribution of inventory levels of different items and other intricate relations, which is computationally dreadful. Taking a novel approach, this paper develops a tractable way of evaluating this measure exactly. We also develop easy-to-compute bounds, which require the evaluation of item-based backorders only. Numerical experiments indicate that the average of the lower and upper bounds is very effective. The exact results show surprisingly simple structures, which shed light on how system parameters affect the performance. Using these results, we study several examples to gain managerial insights. Questions addressed include: What are the implications of item-based inventory planning decisions on the order-based performance? What is the impact of introducing common components on inventory and service trade-offs? Would order-delivery performance be improved if we restrict the number of choices in product configurations?

Suggested Citation

  • Jing-Sheng Song, 2002. "Order-Based Backorders and Their Implications in Multi-Item Inventory Systems," Management Science, INFORMS, vol. 48(4), pages 499-516, April.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:4:p:499-516
    DOI: 10.1287/mnsc.48.4.499.207
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    References listed on IDEAS

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    1. Bruce L. Miller, 1971. "A Multi-Item Inventory Model with Joint Backorder Criterion," Operations Research, INFORMS, vol. 19(6), pages 1467-1476, October.
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    4. Jing-Sheng Song, 2000. "A Note on Assemble-to-Order Systems with Batch Ordering," Management Science, INFORMS, vol. 46(5), pages 739-743, May.
    5. Jing-Sheng Song & Susan H. Xu & Bin Liu, 1999. "Order-Fulfillment Performance Measures in an Assemble-to-Order System with Stochastic Leadtimes," Operations Research, INFORMS, vol. 47(1), pages 131-149, February.
    6. Jing-Sheng Song, 1998. "On the Order Fill Rate in a Multi-Item, Base-Stock Inventory System," Operations Research, INFORMS, vol. 46(6), pages 831-845, December.
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    Cited by:

    1. Levi DeValve & Saša Pekeč & Yehua Wei, 2020. "A Primal-Dual Approach to Analyzing ATO Systems," Management Science, INFORMS, vol. 66(11), pages 5389-5407, November.
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    3. van Jaarsveld, Willem & Dollevoet, Twan & Dekker, Rommert, 2015. "Improving spare parts inventory control at a repair shop," Omega, Elsevier, vol. 57(PB), pages 217-229.
    4. Yao Zhao & David Simchi-Levi, 2006. "Performance Analysis and Evaluation of Assemble-to-Order Systems with Stochastic Sequential Lead Times," Operations Research, INFORMS, vol. 54(4), pages 706-724, August.
    5. Gregory A. DeCroix & Jing-Sheng Song & Paul H. Zipkin, 2009. "Managing an Assemble-to-Order System with Returns," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 144-159, October.
    6. van Jaarsveld, W.L. & Dollevoet, T.A.B., 2011. "Spare parts inventory control for an aircraft component repair shop," Econometric Institute Research Papers EI2011-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Hill, R.M. & Pakkala, T.P.M., 2007. "Base stock inventory policies for a multi-item demand process," International Journal of Production Economics, Elsevier, vol. 109(1-2), pages 137-148, September.
    8. Jing-Sheng Song & David D. Yao, 2002. "Performance Analysis and Optimization of Assemble-to-Order Systems with Random Lead Times," Operations Research, INFORMS, vol. 50(5), pages 889-903, October.
    9. Willem van Jaarsveld & Alan Scheller-Wolf, 2015. "Optimization of Industrial-Scale Assemble-to-Order Systems," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 544-560, August.
    10. Karaarslan, A.G. & Kiesmüller, G.P. & de Kok, A.G., 2013. "Analysis of an assemble-to-order system with different review periods," International Journal of Production Economics, Elsevier, vol. 143(2), pages 335-341.
    11. Cheng, T.C.E. & Gao, Chunyan & Shen, Houcai, 2011. "Production planning and inventory allocation of a single-product assemble-to-order system with failure-prone machines," International Journal of Production Economics, Elsevier, vol. 131(2), pages 604-617, June.
    12. Zhao, Yao, 2009. "Analysis and evaluation of an Assemble-to-Order system with batch ordering policy and compound Poisson demand," European Journal of Operational Research, Elsevier, vol. 198(3), pages 800-809, November.
    13. Ana Bušić & Ingrid Vliegen & Alan Scheller-Wolf, 2012. "Comparing Markov Chains: Aggregation and Precedence Relations Applied to Sets of States, with Applications to Assemble-to-Order Systems," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 259-287, May.
    14. Mustafa K. Doğru & Martin I. Reiman & Qiong Wang, 2010. "A Stochastic Programming Based Inventory Policy for Assemble-to-Order Systems with Application to the W Model," Operations Research, INFORMS, vol. 58(4-part-1), pages 849-864, August.
    15. Gongbing Bi & Lei Song & Yalei Fei, 2020. "Dynamic mixed-item inventory control with limited capital and short-term financing," Annals of Operations Research, Springer, vol. 284(1), pages 99-130, January.
    16. Yingdong Lu & Jing-Sheng Song & Yao Zhao, 2010. "No-Holdback Allocation Rules for Continuous-Time Assemble-to-Order Systems," Operations Research, INFORMS, vol. 58(3), pages 691-705, June.
    17. Jan A. Van Mieghem, 2004. "Note--Commonality Strategies: Value Drivers and Equivalence with Flexible Capacity and Inventory Substitution," Management Science, INFORMS, vol. 50(3), pages 419-424, March.
    18. Vernon Ning Hsu & Chung Yee Lee & Kut C. So, 2006. "Optimal Component Stocking Policy for Assemble-to-Order Systems with Lead-Time-Dependent Component and Product Pricing," Management Science, INFORMS, vol. 52(3), pages 337-351, March.
    19. Yao Zhao, 2008. "Evaluation and Optimization of Installation Base-Stock Policies in Supply Chains with Compound Poisson Demand," Operations Research, INFORMS, vol. 56(2), pages 437-452, April.
    20. Jing-Sheng Song & Yao Zhao, 2009. "The Value of Component Commonality in a Dynamic Inventory System with Lead Times," Manufacturing & Service Operations Management, INFORMS, vol. 11(3), pages 493-508, March.
    21. Mohammad Ebrahim Arbabian & Shi Chen & Kamran Moinzadeh, 2021. "Capacity Expansions with Bundled Supplies of Attributes: An Application to Server Procurement in Cloud Computing," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 191-209, 1-2.
    22. Albrecht, Martin, 2017. "Optimization of safety stocks in models with an order service level objective or constraint," European Journal of Operational Research, Elsevier, vol. 263(3), pages 900-909.
    23. Yingdong Lu & Jing-Sheng Song, 2005. "Order-Based Cost Optimization in Assemble-to-Order Systems," Operations Research, INFORMS, vol. 53(1), pages 151-169, February.
    24. Yingdong Lu & Jing-Sheng Song & David D. Yao, 2003. "Order Fill Rate, Leadtime Variability, and Advance Demand Information in an Assemble-to-Order System," Operations Research, INFORMS, vol. 51(2), pages 292-308, April.

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