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Strategies for a Centralized Single Product Multiclass M/G/ 1 Make-to-Stock Queue

Author

Listed:
  • Hossein Abouee-Mehrizi

    (Department of Management Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

  • Barış Balcıoğlu

    (Faculty of Engineering and Natural Sciences, Sabancı University, Orhanlı-Tuzla, 34956 Istanbul, Turkey)

  • Opher Baron

    (Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

Abstract

Make-to-stock queues are typically investigated in the M/M /1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G /1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition : the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G /1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G /1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G /1 make-to-stock queues.

Suggested Citation

  • Hossein Abouee-Mehrizi & Barış Balcıoğlu & Opher Baron, 2012. "Strategies for a Centralized Single Product Multiclass M/G/ 1 Make-to-Stock Queue," Operations Research, INFORMS, vol. 60(4), pages 803-812, August.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:4:p:803-812
    DOI: 10.1287/opre.1120.1062
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    References listed on IDEAS

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    1. 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.
    2. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
    3. Francis de Véricourt & Fikri Karaesmen & Yves Dallery, 2002. "Optimal Stock Allocation for a Capacitated Supply System," Management Science, INFORMS, vol. 48(11), pages 1486-1501, November.
    4. Hasan Arslan & Stephen C. Graves & Thomas A. Roemer, 2007. "A Single-Product Inventory Model for Multiple Demand Classes," Management Science, INFORMS, vol. 53(9), pages 1486-1500, September.
    5. Francis de Véricourt & Fikri Karaesmen & Yves Dallery, 2001. "Assessing the Benefits of Different Stock-Allocation Policies for a Make-to-Stock Production System," Manufacturing & Service Operations Management, INFORMS, vol. 3(2), pages 105-121, December.
    6. Opher Baron, 2008. "Regulated Random Walks and the LCFS Backlog Probability: Analysis and Application," Operations Research, INFORMS, vol. 56(2), pages 471-486, April.
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    Cited by:

    1. Jianfu Wang & Opher Baron & Alan Scheller-Wolf, 2015. "M/M/c Queue with Two Priority Classes," Operations Research, INFORMS, vol. 63(3), pages 733-749, June.
    2. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2018. "Multilevel rationing policy for spare parts when demand is state dependent," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 751-780, July.
    3. Hossein Abouee-Mehrizi & Opher Baron & Oded Berman, 2014. "Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 561-577, October.
    4. Antonis Economou & Athanasia Manou, 2022. "A probabilistic approach for the analysis of the $$M_n/G/1$$ M n / G / 1 queue," Annals of Operations Research, Springer, vol. 317(1), pages 19-27, October.

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