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

Authors:
Hossein Abouee-Mehrizi;Barış Balcıoğlu;Opher Baron
Affiliations:
Department of Management Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;Faculty of Engineering and Natural Sciences, Sabancı University, Orhanlı-Tuzla, 34956 Istanbul, Turkey;Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Venue:
Operations Research
Year:
2012

Citing 7
Cited 0

Inventory rationing in a make-to-stock production system with several demand classes and lost sales

Management Science
Assessing the Benefits of Different Stock-Allocation Policies for a Make-to-Stock Production System

Manufacturing & Service Operations Management
Optimal Stock Allocation for a Capacitated Supply System

Management Science
Stock Rationing in an M/Ek/1 Make-to-Stock Queue

Management Science
A Single-Product Inventory Model for Multiple Demand Classes

Management Science
Regulated Random Walks and the LCFS Backlog Probability: Analysis and Application

Operations Research
Stationary remaining service time conditional on queue length

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

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.