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Note: A Separation Principle for a Class of Assemble-to-Order Systems with Expediting

Author

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  • Erica L. Plambeck

    (Graduate School of Business, Stanford University, Stanford, California 94305)

  • Amy R. Ward

    (Marshall School of Business, University of Southern California, Los Angeles, California 90089)

Abstract

In an assemble-to-order system, a wide variety of products are rapidly assembled from component inventories in response to customer orders. We assume that orders must be filled within a product-specific target lead time. In the event that some of the components required to fill an order are out of stock, these components must be expedited. The objective is to minimize the expected infinite-horizon discounted cost of primary component production and expediting. Our formulation captures financial holding costs but implicitly assumes that physical holding costs are negligible. The controls are (1) sequencing orders for assembly, (2) primary component production, and (3) component expediting. We prove that the multidimensional assemble-to-order control problem separates into single-item inventory control problems. In particular, under an optimal policy for assembly sequencing, the optimal production and expediting policy for each component is independent of all other components. Hence, the literature on single-item inventory management with expediting or lost sales is directly relevant to the control of assemble-to-order systems.

Suggested Citation

  • Erica L. Plambeck & Amy R. Ward, 2007. "Note: A Separation Principle for a Class of Assemble-to-Order Systems with Expediting," Operations Research, INFORMS, vol. 55(3), pages 603-609, June.
  • Handle: RePEc:inm:oropre:v:55:y:2007:i:3:p:603-609
    DOI: 10.1287/opre.1060.0372
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    References listed on IDEAS

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    Cited by:

    1. Arts, Joachim & Kiesmüller, Gudrun P., 2013. "Analysis of a two-echelon inventory system with two supply modes," European Journal of Operational Research, Elsevier, vol. 225(2), pages 263-272.
    2. 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.
    3. Gunasekaran, Angappa & Ngai, Eric W.T., 2009. "Modeling and analysis of build-to-order supply chains," European Journal of Operational Research, Elsevier, vol. 195(2), pages 319-334, June.
    4. 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.
    5. Mor Armony & Erica Plambeck & Sridhar Seshadri, 2009. "Sensitivity of Optimal Capacity to Customer Impatience in an Unobservable M/M/S Queue (Why You Shouldn't Shout at the DMV)," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 19-32, June.
    6. 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.
    7. Atan, Zümbül & Ahmadi, Taher & Stegehuis, Clara & Kok, Ton de & Adan, Ivo, 2017. "Assemble-to-order systems: A review," European Journal of Operational Research, Elsevier, vol. 261(3), pages 866-879.
    8. 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.
    9. Fu, Ke & Xu, Jiayan & Miao, Zhaowei, 2013. "Newsvendor with multiple options of expediting," European Journal of Operational Research, Elsevier, vol. 226(1), pages 94-99.
    10. Ghadimi, Foad & Aouam, Tarik, 2021. "Planning capacity and safety stocks in a serial production–distribution system with multiple products," European Journal of Operational Research, Elsevier, vol. 289(2), pages 533-552.
    11. Jiri Chod & David Pyke & Nils Rudi, 2010. "The Value of Flexibility in Make-to-Order Systems: The Effect of Demand Correlation," Operations Research, INFORMS, vol. 58(4-part-1), pages 834-848, August.
    12. 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.
    13. Süleyman Demirel & Izak Duenyas & Roman Kapuscinski, 2015. "Production and Inventory Control for a Make-to-Stock/Calibrate-to-Order System with Dedicated and Shared Resources," Operations Research, INFORMS, vol. 63(4), pages 823-839, August.
    14. Lijian Lu & Jing‐Sheng Song & Hanqin Zhang, 2015. "Optimal and asymptotically optimal policies for assemble‐to‐order n‐ and W‐systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 617-645, December.
    15. 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.

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