Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty

We study server scheduling in multiclass service systems under uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels and then determine schedules for the servers that cover these levels. We propose a new stochastic integer programming (SIP)...

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Bibliographic Details
Published in:Management science Vol. 63; no. 7; pp. 2073 - 2091
Main Authors: Bodur, Merve, Luedtke, James R.
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.07.2017
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Integer programming
Methods
mixed-integer rounding
Quality of service
Relaxation
Scheduling
Scheduling (Management)
service-system scheduling
Staffing
stochastic integer programming
Strength
Uncertainty
ISSN:0025-1909, 1526-5501
Online Access:Get full text
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Summary:We study server scheduling in multiclass service systems under uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels and then determine schedules for the servers that cover these levels. We propose a new stochastic integer programming (SIP) model that integrates these two decisions, which can yield lower scheduling costs by exploiting the presence of alternative server configurations that yield similar quality of service. We find that a branch-and-cut algorithm based on Benders decomposition may fail due to the weakness of the relaxation bound. We propose a novel application of mixed-integer rounding to improve the Benders cuts used in this algorithm, a technique that is applicable to any SIP with integer first-stage decision variables. Numerical examples illustrate the computational efficiency of the proposed approach and the potential benefit of solving the integrated model compared to considering the staffing and scheduling problems separately. This paper was accepted by Yinyu Ye, optimization .
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ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.2016.2455