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Stochastic scheduling on parallel machines to minimize discounted holding costs

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Abstract

We study stochastic scheduling on m parallel identical machines with random processing times. The cost involved in the problem is discounted to the present value and the objective is to minimize the expected discounted holding cost, which covers in a unified framework many performance measures discussed in the literature as special cases, including discounted rewards, flowtime, and makespan. We prove that the SEPT rule is optimal, on a fairly general ground, in the class of preemptive dynamic policies, the class of nonpreemptive dynamic policies, and the class of nonpreemptive static list policies. The LEPT rule, on the other hand, is optimal to minimize the expected discounted makespan only under certain restrictive conditions. Without such conditions, the LEPT rule is found no longer optimal for discounted makespan by a counterexample, in contrast to the case without discounting.

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Authors and Affiliations

  1. Department of Systems Engineering & Management Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    Xiaoqiang Cai

  2. Department of Statistics and Actuarial Science, East China Normal University, Zhongshan Road North, Shanghai, China

    Xianyi Wu

  3. Department of Actuarial Studies, Macquarie University, North Ryde, Sydney, Australia

    Xian Zhou

Authors
  1. Xiaoqiang Cai
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  2. Xianyi Wu
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  3. Xian Zhou
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Corresponding author

Correspondence to Xianyi Wu.

Additional information

This research was partially supported by the National Natural Science Foundation of China under Grant No. 70671043, Research Grants Council of Hong Kong Under Project No. 410208, NSFC/RGC Joint Research Grant No. N-CUHK442/05 (NSFC Ref: 70518002), and Macquarie University Research Development Grant.

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Cai, X., Wu, X. & Zhou, X. Stochastic scheduling on parallel machines to minimize discounted holding costs. J Sched 12, 375–388 (2009). https://doi.org/10.1007/s10951-009-0103-2

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