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A Brownian Approximation of a Production-Inventory System with a Manufacturer That Subcontracts

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  • James R. Bradley

    (The S. C. Johnson Graduate School of Management, Cornell University, 321 Sage Hall, Ithaca, New York 14853-6201)

Abstract

This paper considers a production-inventory problem where a manufacturer fulfills stochastic, stationary demand for a single product from a finished-goods inventory. The inventory can be replenished by two production resources, in-house production and a subcontractor, which both have finite capacity. We construct a Brownian approximation of the optimal control problem, assuming that the manufacturer uses a “dual base-stock” policy to control replenishment from the two sources and that her objective is to minimize average cost. A closed-form expression is obtained for one optimal base-stock policy and an analytical expression is derived from which the other optimal base stock can be computed numerically. We show conditions under which the objective is convex in capacity, and the unique globally optimal capacity can be computed numerically. We thus provide a tractable approximation to the two-source problem, which is generally intractable. We demonstrate the accuracy of this approximation for an M / M /1 model. We also draw managerial insight from the Brownian optimal base-stock results into how the optimal base-stock policies control the inventory distribution and under what conditions the contingent source is used to build inventory or to resolve backorders.

Suggested Citation

  • James R. Bradley, 2004. "A Brownian Approximation of a Production-Inventory System with a Manufacturer That Subcontracts," Operations Research, INFORMS, vol. 52(5), pages 765-784, October.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:5:p:765-784
    DOI: 10.1287/opre.1040.0135
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    References listed on IDEAS

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    Cited by:

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    2. Aouam, Tarik & Kumar, Kunal, 2019. "On the effect of overtime and subcontracting on supply chain safety stocks," Omega, Elsevier, vol. 89(C), pages 1-20.
    3. Sabri Çelik & Costis Maglaras, 2008. "Dynamic Pricing and Lead-Time Quotation for a Multiclass Make-to-Order Queue," Management Science, INFORMS, vol. 54(6), pages 1132-1146, June.
    4. Eric Logan Huggins & Tava Lennon Olsen, 2010. "Inventory Control with Generalized Expediting," Operations Research, INFORMS, vol. 58(5), pages 1414-1426, October.
    5. Gad Allon & Jan A. Van Mieghem, 2010. "Global Dual Sourcing: Tailored Base-Surge Allocation to Near- and Offshore Production," Management Science, INFORMS, vol. 56(1), pages 110-124, January.
    6. Jian Yang & Xiangtong Qi & Yusen Xia, 2005. "A Production-Inventory System with Markovian Capacity and Outsourcing Option," Operations Research, INFORMS, vol. 53(2), pages 328-349, April.
    7. Gallego, Guillermo & Jin, Yue & Muriel, Ana & Zhang, Ge & Yildiz, V. Taylan, 2007. "Optimal ordering policies with convertible lead times," European Journal of Operational Research, Elsevier, vol. 176(2), pages 892-910, January.
    8. Sean X. Zhou & Chaolin Yang, 2016. "Continuous-Review ( R, nQ ) Policies for Inventory Systems with Dual Delivery Modes," Operations Research, INFORMS, vol. 64(6), pages 1302-1319, December.
    9. Senthil Veeraraghavan & Alan Scheller-Wolf, 2008. "Now or Later: A Simple Policy for Effective Dual Sourcing in Capacitated Systems," Operations Research, INFORMS, vol. 56(4), pages 850-864, August.
    10. Ruiz-Torres, Alex J. & Ho, Johnny C. & Lopez, Francisco J., 2006. "Generating Pareto schedules with outsource and internal parallel resources," International Journal of Production Economics, Elsevier, vol. 103(2), pages 810-825, October.
    11. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.
    12. Lee, Kangbok & Choi, Byung-Cheon, 2011. "Two-stage production scheduling with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(3), pages 489-497, September.
    13. Qi, Xiangtong, 2011. "Outsourcing and production scheduling for a two-stage flow shop," International Journal of Production Economics, Elsevier, vol. 129(1), pages 43-50, January.

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