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Makespan minimization for m parallel identical processors

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  • Johnny C. Ho
  • Johnny S. Wong

Abstract

We introduce an algorithm, called TMO (Two‐Machine Optimal Scheduling) which minimizes the makespan for two identical processors. TMO employs lexicographic search in conjunction with the longest‐processing time sequence to derive an optimal schedule. For the m identical parallel processors problem, we propose an improvement algorithm, which improves the seed solution obtained by any existing heuristic. The improvement algorithm, called Extended TMO, breaks the original m‐machine problem into a set of two‐machine problems and solves them repeatedly by the TMO. A simulation study is performed to evaluate the effectiveness of the proposed algorithms by comparing it against three existing heuristics: LPT (Graham, [11]), MULTIFIT (Coffman, Garey, and Johnson, [6]), and RMG (Lee and Massey, [17]). The simulation results show that: for the two processors case, the TMO performs significantly better than LPT, MULTIFIT, and RMG, and it generally takes considerably less CPU time than MULTIFIT and RMG. For the general parallel processors case, the Extended TMO algorithm is shown to be capable of greatly improving any seed solution. © 1995 John Wiley & Sons, Inc.

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  • Johnny C. Ho & Johnny S. Wong, 1995. "Makespan minimization for m parallel identical processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 935-948, September.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:6:p:935-948
    DOI: 10.1002/1520-6750(199509)42:63.0.CO;2-D
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    References listed on IDEAS

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    1. James D. Blocher & Suresh Chand, 1991. "Scheduling of parallel processors: A posterior bound on LPT sequencing and a two‐step algorithm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 273-287, April.
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    Cited by:

    1. Liao, Ching-Jong & Shyur, Der-Lin & Lin, Chien-Hung, 2005. "Makespan minimization for two parallel machines with an availability constraint," European Journal of Operational Research, Elsevier, vol. 160(2), pages 445-456, January.
    2. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    3. Peruvemba Sundaram Ravi & Levent Tunçel & Michael Huang, 2016. "Worst-case performance analysis of some approximation algorithms for minimizing makespan and flowtime," Journal of Scheduling, Springer, vol. 19(5), pages 547-561, October.
    4. C-J Liao & C-M Chen & C-H Lin, 2007. "Minimizing makespan for two parallel machines with job limit on each availability interval," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 938-947, July.
    5. Chatterjee A K & Mukherjee, Saral, 2006. "Unified Concept of Bottleneck," IIMA Working Papers WP2006-05-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    6. Liao, Ching-Jong & Lin, Chien-Hung, 2003. "Makespan minimization for two uniform parallel machines," International Journal of Production Economics, Elsevier, vol. 84(2), pages 205-213, May.
    7. Navid Hashemian & Claver Diallo & Béla Vizvári, 2014. "Makespan minimization for parallel machines scheduling with multiple availability constraints," Annals of Operations Research, Springer, vol. 213(1), pages 173-186, February.

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