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

Hossein Abouee-Mehrizi (), Barış Balcıoğlu () and Opher Baron ()
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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

Operations Research, 2012, vol. 60, issue 4, 803-812

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.

Keywords: make-to-stock; M/G/1 queue; priority classes; customer composition; multilevel rationing; strict priority (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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