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GRASP with path-relinking for the non-identical parallel machine scheduling problem with minimising total weighted completion times

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  • F. Rodriguez
  • C. Blum
  • C. García-Martínez
  • M. Lozano

Abstract

In this work, we tackle the problem of scheduling a set of jobs on a set of non-identical parallel machines with the goal of minimising the total weighted completion times. GRASP is a multi-start method that consists of two phases: a solution construction phase, which randomly constructs a greedy solution, and an improvement phase, which uses that solution as an initial starting point. In the last few years, the GRASP methodology has arisen as a prospective metaheuristic approach to find high-quality solutions for several difficult problems in reasonable computational times. With the aim of providing additional results and insights along this line of research, this paper proposes a new GRASP model that combines the basic scheme with two significant elements that have been shown to be very successful in order to improve GRASP performance. These elements are path-relinking and evolutionary path-relinking. The benefits of our proposal in comparison to existing metaheuristics proposed in the literature are experimentally shown. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • F. Rodriguez & C. Blum & C. García-Martínez & M. Lozano, 2012. "GRASP with path-relinking for the non-identical parallel machine scheduling problem with minimising total weighted completion times," Annals of Operations Research, Springer, vol. 201(1), pages 383-401, December.
    • Handle: RePEc:spr:annopr:v:201:y:2012:i:1:p:383-401:10.1007/s10479-012-1164-8
    DOI: 10.1007/s10479-012-1164-8
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    1. Renata M. Aiex & Mauricio G. C. Resende & Panos M. Pardalos & Gerardo Toraldo, 2005. "GRASP with Path Relinking for Three-Index Assignment," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 224-247, May.
    2. Parag Pendharkar & James Rodger, 2000. "Nonlinear programming and genetic search application for production scheduling in coal mines," Annals of Operations Research, Springer, vol. 95(1), pages 251-267, January.
    3. Weng, Michael X. & Lu, John & Ren, Haiying, 2001. "Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective," International Journal of Production Economics, Elsevier, vol. 70(3), pages 215-226, April.
    4. Graham Kendall & Kay Tan & Edmund Burke & Stephen Smith, 2010. "Preface for the special volume on Computational Intelligence in Scheduling," Annals of Operations Research, Springer, vol. 180(1), pages 1-2, November.
    5. Allahverdi, Ali & Gupta, Jatinder N. D. & Aldowaisan, Tariq, 1999. "A review of scheduling research involving setup considerations," Omega, Elsevier, vol. 27(2), pages 219-239, April.
    6. Zhi-Long Chen & Warren B. Powell, 1999. "Solving Parallel Machine Scheduling Problems by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 78-94, February.
    7. Fanjul-Peyro, Luis & Ruiz, Rubén, 2010. "Iterated greedy local search methods for unrelated parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 207(1), pages 55-69, November.
    8. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    9. Manuel Laguna & Rafael Marti, 1999. "GRASP and Path Relinking for 2-Layer Straight Line Crossing Minimization," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 44-52, February.
    10. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    11. Cheng, T. C. E. & Sin, C. C. S., 1990. "A state-of-the-art review of parallel-machine scheduling research," European Journal of Operational Research, Elsevier, vol. 47(3), pages 271-292, August.
    12. Azizoglu, Meral & Kirca, Omer, 1999. "On the minimization of total weighted flow time with identical and uniform parallel machines," European Journal of Operational Research, Elsevier, vol. 113(1), pages 91-100, February.
    13. Rosenbloom, E. S. & Goertzen, N. F., 1987. "Cyclic nurse scheduling," European Journal of Operational Research, Elsevier, vol. 31(1), pages 19-23, July.
    14. Waligóra, Grzegorz, 2009. "Tabu search for discrete-continuous scheduling problems with heuristic continuous resource allocation," European Journal of Operational Research, Elsevier, vol. 193(3), pages 849-856, March.
    15. Celso C. Ribeiro & Eduardo Uchoa & Renato F. Werneck, 2002. "A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 228-246, August.
    16. Guang Feng & Hoong Lau, 2008. "Efficient algorithms for machine scheduling problems with earliness and tardiness penalties," Annals of Operations Research, Springer, vol. 159(1), pages 83-95, March.
    17. Jacek Błażewicz & Klaus H. Ecker & Erwin Pesch & Günter Schmidt & Jan Węglarz, 2007. "Handbook on Scheduling," International Handbooks on Information Systems, Springer, number 978-3-540-32220-7, November.
    18. Jarrah, Ahmad I. Z. & Bard, Jonathan F. & de Silva, Anura H., 1992. "A heuristic for machine scheduling at general mail facilities," European Journal of Operational Research, Elsevier, vol. 63(2), pages 192-206, December.
    19. Dodin, Bajis & Huang Chan, K., 1991. "Application of production scheduling methods to external and internal audit scheduling," European Journal of Operational Research, Elsevier, vol. 52(3), pages 267-279, June.
    20. Buxey, Geoff, 1989. "Production scheduling: Practice and theory," European Journal of Operational Research, Elsevier, vol. 39(1), pages 17-31, March.
    21. Tjark Vredeveld & Cor Hurkens, 2002. "Experimental Comparison of Approximation Algorithms for Scheduling Unrelated Parallel Machines," INFORMS Journal on Computing, INFORMS, vol. 14(2), pages 175-189, May.
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    Cited by:

    1. García-Martínez, C. & Rodriguez, F.J. & Lozano, M., 2014. "Tabu-enhanced iterated greedy algorithm: A case study in the quadratic multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 454-463.
    2. Zhi Pei & Mingzhong Wan & Ziteng Wang, 2020. "A new approximation algorithm for unrelated parallel machine scheduling with release dates," Annals of Operations Research, Springer, vol. 285(1), pages 397-425, February.
    3. Kramer, Arthur & Dell’Amico, Mauro & Iori, Manuel, 2019. "Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines," European Journal of Operational Research, Elsevier, vol. 275(1), pages 67-79.
    4. Wang, Haibo & Alidaee, Bahram, 2019. "Effective heuristic for large-scale unrelated parallel machines scheduling problems," Omega, Elsevier, vol. 83(C), pages 261-274.
    5. Kerem Bülbül & Halil Şen, 2017. "An exact extended formulation for the unrelated parallel machine total weighted completion time problem," Journal of Scheduling, Springer, vol. 20(4), pages 373-389, August.

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