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Online scheduling of two job types on a set of multipurpose machines

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  • Karhi, Shlomo
  • Shabtay, Dvir

Abstract

We study an online-list scheduling problem on a set of m multipurpose machines for which the objective is to minimize the makespan. It is assumed that there are two different job types, and each job type can be processed on a unique subset of machines. We provide an online algorithm with a competitive ratio of 1+k(m−1)/(k(m−s)+s2) where M1={M1,…,Mk} is the set of machines eligible to process jobs of type 1 and where M2={Ms+1,…,Mm} is the set of machines eligible to process jobs of type 2 with k≥s. By analyzing the competitive ratio function, we show that the worst competitive ratio is obtained for an inclusive processing set structure in which the number of machines (m) is even, the first job type can be processed on any of the m machines and the second job type can be processed only on a subset of m/2 machines. Moreover, we provide a lower bound as a function of the processing set structure.

Suggested Citation

  • Karhi, Shlomo & Shabtay, Dvir, 2014. "Online scheduling of two job types on a set of multipurpose machines," International Journal of Production Economics, Elsevier, vol. 150(C), pages 155-162.
    • Handle: RePEc:eee:proeco:v:150:y:2014:i:c:p:155-162
    DOI: 10.1016/j.ijpe.2013.12.015
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    References listed on IDEAS

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    1. Yiwei Jiang, 2008. "Online scheduling on parallel machines with two GoS levels," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 28-38, July.
    2. 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.
    3. Wu, Yong & Ji, Min & Yang, Qifan, 2012. "Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision," International Journal of Production Economics, Elsevier, vol. 135(1), pages 367-371.
    4. 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.
    5. 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.
    6. Lin, Yixun & Li, Wenhua, 2004. "Parallel machine scheduling of machine-dependent jobs with unit-length," European Journal of Operational Research, Elsevier, vol. 156(1), pages 261-266, July.
    7. 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. 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.
    2. Goldberg, Noam & Karhi, Shlomo, 2019. "Online packing of arbitrary sized items into designated and multipurpose bins," European Journal of Operational Research, Elsevier, vol. 279(1), pages 54-67.
    3. Ma, Ran & Yuan, Jinjiang, 2014. "Online tradeoff scheduling on a single machine to minimize makespan and total weighted completion time," International Journal of Production Economics, Elsevier, vol. 158(C), pages 114-119.
    4. Goldberg, Noam & Karhi, Shlomo, 2017. "Packing into designated and multipurpose bins: A theoretical study and application to the cold chain," Omega, Elsevier, vol. 71(C), pages 85-92.

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