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Minimizing the sum of job completion times on capacitated two-parallel machines

Author

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  • Liao, Ching-Jong
  • Chao, Chien-Wen
  • Lin, Chien-Hung

Abstract

This paper considers a scheduling problem with two identical parallel machines. One has unlimited capacity; the other can only run for a fixed time. A given set of jobs must be scheduled on the two machines with the goal of minimizing the sum of their completion times. The paper proposes an optimal branch and bound algorithm which employs three powerful elements, including an algorithm for computing the upper bound, a lower bound algorithm, and a fathoming condition. The branch and bound algorithm was tested on problems of various sizes and parameters. The results show that the algorithm is quite efficient to solve all the test problems. In particular, the total computation time for the hardest problem is less than 0.1second for a set of 100 problem instances. An important finding of the tests is that the upper bound algorithm can actually find optimal solutions to a quite large number of problems.

Suggested Citation

  • Liao, Ching-Jong & Chao, Chien-Wen & Lin, Chien-Hung, 2009. "Minimizing the sum of job completion times on capacitated two-parallel machines," European Journal of Operational Research, Elsevier, vol. 197(2), pages 475-481, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:475-481
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    References listed on IDEAS

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    1. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    2. 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.
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    Cited by:

    1. Örnek, Arslan & Özpeynirci, Selin & Öztürk, Cemalettin, 2010. "A note on "A mixed integer programming model for advanced planning and scheduling (APS)"," European Journal of Operational Research, Elsevier, vol. 203(3), pages 784-785, June.
    2. Wang, Xiuli & Cheng, T.C.E., 2015. "A heuristic for scheduling jobs on two identical parallel machines with a machine availability constraint," International Journal of Production Economics, Elsevier, vol. 161(C), pages 74-82.
    3. Tan, Zhiyi & Chen, Yong & Zhang, An, 2011. "Parallel machines scheduling with machine maintenance for minsum criteria," European Journal of Operational Research, Elsevier, vol. 212(2), pages 287-292, July.
    4. Guo, Shouwei & Kang, Liying, 2010. "Online scheduling of malleable parallel jobs with setup times on two identical machines," European Journal of Operational Research, Elsevier, vol. 206(3), pages 555-561, November.

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