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Online Bi-Criteria Scheduling on Batch Machines with Machine Costs

Author

Listed:
  • Wenhua Li

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Weina Zhai

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Xing Chai

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

Abstract

We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel batch scheduling, a machine can process several jobs simultaneously as a batch. The processing time of a job and a batch is equal to 1. When job J j is processed on machine M i , it results cost c i j . We only consider two types of cost functions: c i j = a + c j and c i j = a · c j , where a is the fixed cost of machines and c j is the cost of job J j . The number of jobs is n and the number of machines is m . For this problem, we provide two online algorithms, which are showed to be the best possible with a competitive ratio of ( 1 + β m , ⌈ n m ⌉ ) , where β m is the positive root of the equation ( 1 + β m ) m + 1 = β m + 2 .

Suggested Citation

  • Wenhua Li & Weina Zhai & Xing Chai, 2019. "Online Bi-Criteria Scheduling on Batch Machines with Machine Costs," Mathematics, MDPI, vol. 7(10), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:960-:d:275974
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    References listed on IDEAS

    as
    1. Lee, Kangbok & Leung, Joseph Y-T. & Jia, Zhao-hong & Li, Wenhua & Pinedo, Michael L. & Lin, Bertrand M.T., 2014. "Fast approximation algorithms for bi-criteria scheduling with machine assignment costs," European Journal of Operational Research, Elsevier, vol. 238(1), pages 54-64.
    2. Wenhua Li & Jinjiang Yuan & Yixun Lin, 2007. "A note on special optimal batching structures to minimize total weighted completion time," Journal of Combinatorial Optimization, Springer, vol. 14(4), pages 475-480, November.
    3. Wenjie Li, 2015. "A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-10.
    4. Qijia Liu & Jinjiang Yuan, 2016. "Online tradeoff scheduling on a single machine to minimize makespan and maximum lateness," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 385-395, August.
    5. Jianfa Cao & Jinjiang Yuan & Wenjie Li & Hailin Bu, 2011. "Online scheduling on batching machines to minimise the total weighted completion time of jobs with precedence constraints and identical processing times," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(1), pages 51-55.
    6. Yang Fang & Peihai Liu & Xiwen Lu, 2011. "Optimal on-line algorithms for one batch machine with grouped processing times," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 509-516, November.
    7. Wenhua Li & Xing Chai, 2019. "The medical laboratory scheduling for weighted flow-time," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 83-94, January.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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