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Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan

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  • Li, Shuguang

Abstract

We consider the problem of scheduling n jobs on m parallel batching machines with inclusive processing set restrictions and non-identical capacities. The machines differ in their functionality but have the same processing speed. The inclusive processing set restriction has the following property: the machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. Each job is characterized by a processing time that specifies the minimum time needed to process the job, a release date before which it cannot be processed, and a machine index which is the smallest index among the machines that can process it. Each batching machine has a limited capacity and can process a batch of jobs simultaneously as long as its capacity is not violated. The capacities of the machines are non-identical. The processing time of a batch is the maximum of the processing times of the jobs belonging to it. Jobs in the same batch have a common start time and a common completion time. The goal is to find a non-preemptive schedule so as to minimize makespan (the maximum completion time). When all jobs are released at the same time, we present two fast algorithms with approximation ratios 3 and 9/4, respectively. For the general case with unequal release dates, we develop a polynomial time approximation scheme (PTAS), which is also the first PTAS even for the case with equal release dates and without processing set restrictions.

Suggested Citation

  • Li, Shuguang, 2017. "Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan," European Journal of Operational Research, Elsevier, vol. 260(1), pages 12-20.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:1:p:12-20
    DOI: 10.1016/j.ejor.2016.11.044
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    References listed on IDEAS

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    1. Li, Chung-Lun, 2006. "Scheduling unit-length jobs with machine eligibility restrictions," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1325-1328, October.
    2. Li, Chung-Lun & Wang, Xiuli, 2010. "Scheduling parallel machines with inclusive processing set restrictions and job release times," European Journal of Operational Research, Elsevier, vol. 200(3), pages 702-710, February.
    3. Xiaotie Deng & Haodi Feng & Guojun Li & Benyun Shi, 2005. "A PTAS for Semiconductor Burn-in Scheduling," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 5-17, February.
    4. Leung, Joseph Y.-T. & Li, Chung-Lun, 2016. "Scheduling with processing set restrictions: A literature update," International Journal of Production Economics, Elsevier, vol. 175(C), pages 1-11.
    5. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
    6. Peter Brucker & Bernd Jurisch & Andreas Krämer, 1997. "Complexity of scheduling problems with multi-purpose machines," Annals of Operations Research, Springer, vol. 70(0), pages 57-73, April.
    7. Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "Scheduling with processing set restrictions: A survey," International Journal of Production Economics, Elsevier, vol. 116(2), pages 251-262, December.
    8. Epstein, Leah & Levin, Asaf, 2011. "Scheduling with processing set restrictions: PTAS results for several variants," International Journal of Production Economics, Elsevier, vol. 133(2), pages 586-595, October.
    9. Xiaotie Deng & Chung Keung Poon & Yuzhong Zhang, 2003. "Approximation Algorithms in Batch Processing," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 247-257, September.
    10. Javad H. Ahmadi & Reza H. Ahmadi & Sriram Dasu & Christopher S. Tang, 1992. "Batching and Scheduling Jobs on Batch and Discrete Processors," Operations Research, INFORMS, vol. 40(4), pages 750-763, August.
    11. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    12. Scott Webster & Kenneth R. Baker, 1995. "Scheduling Groups of Jobs on a Single Machine," Operations Research, INFORMS, vol. 43(4), pages 692-703, August.
    13. Hark-Chin Hwang & Soo Y. Chang & Yushin Hong, 2004. "A Posterior Competitiveness For List Scheduling Algorithm On Machines With Eligibility Constraints," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 117-125.
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    Cited by:

    1. Li, Shuguang, 2017. "Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities," European Journal of Operational Research, Elsevier, vol. 263(3), pages 815-826.

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