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Scheduling a Make-To-Stock Queue: Index Policies and Hedging Points

Author

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  • Michael H. Veatch

    (Gordon College, Wenham, Massachusetts)

  • Lawrence M. Wein

    (Massachusetts Institute of Technology Cambridge, Massachusetts)

Abstract

A single machine produces several different classes of items in a make-to-stock mode. We consider the problem of scheduling the machine to regulate finished goods inventory, minimizing holding and backorder, or holding and lost sales costs. Demands are Poisson, service times are exponentially distributed, and there are no delays or costs associated with switching products. A scheduling policy dictates whether the machine is idle or busy and specifies the job class to serve in the latter case. Since the optimal solution can be numerically computed only for problems with several products, our goal is to develop effective policies that are computationally tractable for a large number of products. We develop index policies to decide which class to produce, including Whittle's “restless bandit” index, which possesses a certain asymptotic optimality. Several idleness policies are derived, and the best policy is obtained from a heavy traffic diffusion approximation. Nine sample problems are considered in a numerical study, and the average suboptimality of the best policy is less than 3%.

Suggested Citation

  • Michael H. Veatch & Lawrence M. Wein, 1996. "Scheduling a Make-To-Stock Queue: Index Policies and Hedging Points," Operations Research, INFORMS, vol. 44(4), pages 634-647, August.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:4:p:634-647
    DOI: 10.1287/opre.44.4.634
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    Cited by:

    1. Rezaei Somarin, Aghil & Chen, Songlin & Asian, Sobhan & Wang, David Z.W., 2017. "A heuristic stock allocation rule for repairable service parts," International Journal of Production Economics, Elsevier, vol. 184(C), pages 131-140.
    2. Arreola-Risa, Antonio & Giménez-García, Víctor M. & Martínez-Parra, José Luis, 2011. "Optimizing stochastic production-inventory systems: A heuristic based on simulation and regression analysis," European Journal of Operational Research, Elsevier, vol. 213(1), pages 107-118, August.
    3. Zhou, Bin & Zhao, Yao & Katehakis, Michael N., 2007. "Effective control policies for stochastic inventory systems with a minimum order quantity and linear costs," International Journal of Production Economics, Elsevier, vol. 106(2), pages 523-531, April.
    4. Hongler, Max-Olivier & Ciprut, Philippe, 2001. "Production indices obtained by a myopic policy for non-Markovian dynamics," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 115-123, December.
    5. Arts, Joachim, 2017. "A multi-item approach to repairable stocking and expediting in a fluctuating demand environment," European Journal of Operational Research, Elsevier, vol. 256(1), pages 102-115.
    6. ElHafsi, Mohsen & Fang, Jianxin & Camus, Herve, 2018. "Optimal control of a continuous-time W-configuration assemble-to-order system," European Journal of Operational Research, Elsevier, vol. 267(3), pages 917-932.
    7. Gayon, Jean-Philippe & Vercraene, Samuel & Flapper, Simme Douwe P., 2017. "Optimal control of a production-inventory system with product returns and two disposal options," European Journal of Operational Research, Elsevier, vol. 262(2), pages 499-508.
    8. Flapper, Simme Douwe & Gayon, Jean-Philippe & Lim, Lâm Laurent, 2014. "On the optimal control of manufacturing and remanufacturing activities with a single shared server," European Journal of Operational Research, Elsevier, vol. 234(1), pages 86-98.
    9. Zerhouni, Hichem & Gayon, Jean-Philippe & Frein, Yannick, 2013. "Influence of dependency between demands and returns in a reverse logistics system," International Journal of Production Economics, Elsevier, vol. 143(1), pages 62-71.
    10. N. Srivatsan & Yves Dallery, 1998. "Partial Characterization of Optimal Hedging Point Policies in Unreliable Two-Part-Type Manufacturing Systems," Operations Research, INFORMS, vol. 46(1), pages 36-45, February.
    11. Chao, Gary H., 2013. "Production and availability policies through the Markov Decision Process and myopic methods for contractual and selective orders," European Journal of Operational Research, Elsevier, vol. 225(3), pages 383-392.
    12. Jemai, Zied & Karaesmen, Fikri, 2005. "The influence of demand variability on the performance of a make-to-stock queue," European Journal of Operational Research, Elsevier, vol. 164(1), pages 195-205, July.
    13. Sanajian, Nima & BalcIog[small tilde]lu, BarIs, 2009. "The impact of production time variability on make-to-stock queue performance," European Journal of Operational Research, Elsevier, vol. 194(3), pages 847-855, May.

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