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Preemptive multiprocessor order scheduling to minimize total weighted flowtime

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  • Leung, Joseph Y.-T.
  • Lee, C.Y.
  • Ng, C.W.
  • Young, G.H.

Abstract

Consider m identical machines in parallel, each of which can produce k different product types. There is no setup cost when the machines switch from producing one product type to another. There are n orders each of which requests various quantities of the different product types. All orders are available for processing at time t = 0, and preemption is allowed. Order i has a weight wi and its completion time is the time when its last requested product type finishes. Our goal is to find a preemptive schedule such that the total weighted completion time [summation operator]wiCi is minimized. We show that this problem is NP-hard even when all jobs have identical weights and there are only two machines. Motivated by the computational complexity of the problem, we propose a simple heuristic and show that it obeys a worst-case bound of 2 - 1/m. Finally, empirical studies show that our heuristic performs very well when compared with a lower bound of the optimal cost.

Suggested Citation

  • Leung, Joseph Y.-T. & Lee, C.Y. & Ng, C.W. & Young, G.H., 2008. "Preemptive multiprocessor order scheduling to minimize total weighted flowtime," European Journal of Operational Research, Elsevier, vol. 190(1), pages 40-51, October.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:1:p:40-51
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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. Leung, Joseph Y-T. & Li, Haibing & Pinedo, Michael & Sriskandarajah, Chelliah, 2005. "Open shops with jobs overlap--revisited," European Journal of Operational Research, Elsevier, vol. 163(2), pages 569-571, June.
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    6. A.E. Gerodimos & C.A. Glass & C.N. Potts & T. Tautenhahn, 1999. "Scheduling multi‐operation jobs on a single machine," Annals of Operations Research, Springer, vol. 92(0), pages 87-105, January.
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    Cited by:

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    3. 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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