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A Note on Assemble-to-Order Systems with Batch Ordering

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  • Jing-Sheng Song

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

Abstract

We study an assemble-to-order inventory system. The stocks are held for components, with final products assembled only when customer orders are realized. Customer orders form a multivariate compound Poisson process, component replenishment leadtimes are constant, and demands in excess of inventory on hand are backlogged. The component inventories are controlled by (R, nQ) policies. We show that under certain general conditions the inventory position vector has a uniform equilibrium distribution. This result generalizes the corresponding single-item theory considerably. It allows us to express the key performance measures of the system, such as order fill rates and average order-based backorders, as the averages of their counterparts in the base-stock systems.

Suggested Citation

  • Jing-Sheng Song, 2000. "A Note on Assemble-to-Order Systems with Batch Ordering," Management Science, INFORMS, vol. 46(5), pages 739-743, May.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:5:p:739-743
    DOI: 10.1287/mnsc.46.5.739.12043
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    References listed on IDEAS

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    1. F. R. Richards, 1975. "Technical Note—Comments on the Distribution of Inventory Position in a Continuous-Review ( s , S ) Inventory System," Operations Research, INFORMS, vol. 23(2), pages 366-371, April.
    2. 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.
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    4. 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.
    5. Arthur F. Veinott, 1965. "The Optimal Inventory Policy for Batch Ordering," Operations Research, INFORMS, vol. 13(3), pages 424-432, June.
    6. Caplin, Andrew S, 1985. "The Variability of Aggregate Demand with (S, s) Inventory Policies," Econometrica, Econometric Society, vol. 53(6), pages 1395-1409, November.
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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. 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.
    3. Wenhui Zhou & Xiuli Chao, 2012. "Stein–Chen approximation and error bounds for order fill rates in assemble‐to‐order systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(8), pages 643-655, December.
    4. 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.
    5. 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.
    6. Agrawal, Narendra & Smith, Stephen A., 2019. "Optimal inventory management using retail prepacks," European Journal of Operational Research, Elsevier, vol. 274(2), pages 531-544.
    7. 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.
    8. Jiejian Feng & Liming Liu & Yat‐wah Wan, 2012. "Irreducibility of joint inventory positions in an assemble‐to‐order system under (r, nQ) policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 18-25, February.
    9. Emre Nadar & Mustafa Akan & Alan Scheller-Wolf, 2014. "Technical Note---Optimal Structural Results for Assemble-to-Order Generalized M -Systems," Operations Research, INFORMS, vol. 62(3), pages 571-579, June.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Sleptchenko, Andrei & Al Hanbali, Ahmad & Zijm, Henk, 2018. "Joint planning of service engineers and spare parts," European Journal of Operational Research, Elsevier, vol. 271(1), pages 97-108.
    15. Jing-Sheng Song & Yue Zhang, 2020. "Stock or Print? Impact of 3-D Printing on Spare Parts Logistics," Management Science, INFORMS, vol. 66(9), pages 3860-3878, September.
    16. Erica L. Plambeck, 2008. "Asymptotically Optimal Control for an Assemble-to-Order System with Capacitated Component Production and Fixed Transport Costs," Operations Research, INFORMS, vol. 56(5), pages 1158-1171, October.
    17. Li, Xiaoming & Sridharan, V., 2008. "Characterizing order processes of using (R,nQ) inventory policies in supply chains," Omega, Elsevier, vol. 36(6), pages 1096-1104, December.
    18. Marcus Ang & Karl Sigman & Jing-Sheng Song & Hanqin Zhang, 2017. "Closed-Form Approximations for Optimal ( r , q ) and ( S , T ) Policies in a Parallel Processing Environment," Operations Research, INFORMS, vol. 65(5), pages 1414-1428, October.
    19. 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.

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