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Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

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  • Joseph Y‐T. Leung
  • Haibing Li
  • Michael Pinedo

Abstract

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • Joseph Y‐T. Leung & Haibing Li & Michael Pinedo, 2006. "Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 243-260, June.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:4:p:243-260
    DOI: 10.1002/nav.20138
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    References listed on IDEAS

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    1. Chang Sup Sung & Sang Hum Yoon, 1998. "Minimizing total weighted completion time at a pre-assembly stage composed of two feeding machines," International Journal of Production Economics, Elsevier, vol. 54(3), pages 247-255, May.
    2. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
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    Cited by:

    1. José R. Correa & Martin Skutella & José Verschae, 2012. "The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 379-398, May.
    2. Xiaoling Cao & Wen-Hsing Wu & Wen-Hung Wu & Chin-Chia Wu, 2018. "Some two-agent single-machine scheduling problems to minimize minmax and minsum of completion times," Operational Research, Springer, vol. 18(2), pages 293-314, July.
    3. Joseph Leung & Haibing Li & Michael Pinedo, 2008. "Scheduling orders on either dedicated or flexible machines in parallel to minimize total weighted completion time," Annals of Operations Research, Springer, vol. 159(1), pages 107-123, March.
    4. Lung-Yu Li & Jian-You Xu & Shuenn-Ren Cheng & Xingong Zhang & Win-Chin Lin & Jia-Cheng Lin & Zong-Lin Wu & Chin-Chia Wu, 2022. "A Genetic Hyper-Heuristic for an Order Scheduling Problem with Two Scenario-Dependent Parameters in a Parallel-Machine Environment," Mathematics, MDPI, vol. 10(21), pages 1-22, November.
    5. Framinan, Jose M. & Perez-Gonzalez, Paz & Fernandez-Viagas, Victor, 2019. "Deterministic assembly scheduling problems: A review and classification of concurrent-type scheduling models and solution procedures," European Journal of Operational Research, Elsevier, vol. 273(2), pages 401-417.

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