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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| Vydané v: | Management science Ročník 63; číslo 7; s. 2073 - 2091 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Linthicum
INFORMS
01.07.2017
Institute for Operations Research and the Management Sciences |
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| ISSN: | 0025-1909, 1526-5501 |
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| Abstract | 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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| AbstractList | History: Accepted by Yinyu Ye, optimization. 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. . 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. History: Accepted by Yinyu Ye, optimization. Funding: This research has been supported in part by the National Science Foundation [Grant CMMI1130266], Supplemental Material: The electronic companion is available at https: //doi.org/ 10.1287/mnsc.2016.2455. Keywords: service-system scheduling * stochastic integer programming * mixed-integer rounding 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. 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 . |
| Audience | Trade Academic |
| Author | Luedtke, James R. Bodur, Merve |
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| SubjectTerms | Algorithms Integer programming Methods mixed-integer rounding Quality of service Relaxation Scheduling Scheduling (Management) service-system scheduling Staffing stochastic integer programming Strength Uncertainty |
| Title | Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty |
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