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A branch‐and‐price algorithm for parallel machine scheduling with time windows and job priorities

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  • Jonathan F. Bard
  • Siwate Rojanasoonthon

Abstract

This paper presents a branch‐and‐price algorithm for scheduling n jobs on m nonhomogeneous parallel machines with multiple time windows. An additional feature of the problem is that each job falls into one of ρ priority classes and may require two operations. The objective is to maximize the weighted number of jobs scheduled, where a job in a higher priority class has “infinitely” more weight or value than a job in a lower priority class. The methodology makes use of a greedy randomized adaptive search procedure (GRASP) to find feasible solutions during implicit enumeration and a two‐cycle elimination heuristic when solving the pricing subproblems. Extensive computational results are presented based on data from an application involving the use of communications relay satellites. Many 100‐job instances that were believed to be beyond the capability of exact methods, were solved within minutes. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • Jonathan F. Bard & Siwate Rojanasoonthon, 2006. "A branch‐and‐price algorithm for parallel machine scheduling with time windows and job priorities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 24-44, February.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:1:p:24-44
    DOI: 10.1002/nav.20118
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    1. Bruce L. Golden & Larry Levy & Rakesh Vohra, 1987. "The orienteering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 307-318, June.
    2. Jonathan F. Bard & George Kontoravdis & Gang Yu, 2002. "A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 36(2), pages 250-269, May.
    3. Desrochers, Martin & Soumis, Francois, 1988. "A reoptimization algorithm for the shortest path problem with time windows," European Journal of Operational Research, Elsevier, vol. 35(2), pages 242-254, May.
    4. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
    5. Gabrel, Virginie, 1995. "Scheduling jobs within time windows on identical parallel machines: New model and algorithms," European Journal of Operational Research, Elsevier, vol. 83(2), pages 320-329, June.
    6. Lap Mui Ann Chan & Ana Muriel & David Simchi-Levi, 1998. "Parallel Machine Scheduling, Linear Programming, and Parameter List Scheduling Heuristics," Operations Research, INFORMS, vol. 46(5), pages 729-741, October.
    7. Moshe Dror, 1994. "Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW," Operations Research, INFORMS, vol. 42(5), pages 977-978, October.
    8. Kolen, Antoon W. J. & Kroon, Leo G., 1993. "On the computational complexity of (maximum) shift class scheduling," European Journal of Operational Research, Elsevier, vol. 64(1), pages 138-151, January.
    9. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    10. Blazewicz, Jacek & Dror, Moshe & Weglarz, Jan, 1991. "Mathematical programming formulations for machine scheduling: A survey," European Journal of Operational Research, Elsevier, vol. 51(3), pages 283-300, April.
    11. S Rojanasoonthon & J F Bard & S D Reddy, 2003. "Algorithms for parallel machine scheduling: a case study of the tracking and data relay satellite system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 806-821, August.
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    Cited by:

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    2. Xiaoyun Xiong & Peng Zhou & Yunqiang Yin & T. C. E. Cheng & Dengfeng Li, 2019. "An exact branch‐and‐price algorithm for multitasking scheduling on unrelated parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 502-516, September.
    3. Yunqiang Yin & Youhua Chen & Kaida Qin & Dujuan Wang, 2019. "Two-agent scheduling on unrelated parallel machines with total completion time and weighted number of tardy jobs criteria," Journal of Scheduling, Springer, vol. 22(3), pages 315-333, June.

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