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Scheduling on a single machine under time-of-use electricity tariffs

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Abstract

We consider the problem of scheduling jobs on a single machine to minimize the total electricity cost of processing these jobs under time-of-use electricity tariffs. For the uniform-speed case, in which all jobs have arbitrary power demands and must be processed at a single uniform speed, we prove that the non-preemptive version of this problem is inapproximable within a constant factor unless \(\text {P} = \text {NP}\). On the other hand, when all the jobs have the same workload and the electricity prices follow a so-called pyramidal structure, we show that this problem can be solved in polynomial time. For the speed-scalable case, in which jobs can be processed at an arbitrary speed with a trade-off between speed and power demand, we show that the non-preemptive version of the problem is strongly NP-hard. We also present different approximation algorithms for this case, and test the computational performance of these approximation algorithms on randomly generated instances. In addition, for both the uniform-speed and speed-scaling cases, we show how to compute optimal schedules for the preemptive version of the problem in polynomial time.

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Notes

  1. A \(\rho \) -approximation algorithm finds a solution whose objective value is within a factor \(\rho \) of the optimal value, and runs in time polynomial in the input size. The factor \(\rho \) is known as the performance guarantee.

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Author information

Authors and Affiliations

  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Kan Fang

  2. Mathematics Department, United States Naval Academy, Annapolis, MD, 21402, USA

    Nelson A. Uhan

  3. Environmental and Ecological Engineering and School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47904, USA

    Fu Zhao

  4. Environmental and Ecological Engineering, Purdue University, West Lafayette, IN, 47904, USA

    John W. Sutherland

Authors
  1. Kan Fang
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  2. Nelson A. Uhan
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  3. Fu Zhao
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  4. John W. Sutherland
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Corresponding author

Correspondence to Nelson A. Uhan.

Appendix: Tables of results from computational experiments

Appendix: Tables of results from computational experiments

See Tables 2, 3, 4 and 5.

Table 2 Average ratio between the total electricity costs of schedules obtained by Algorithms 4.2, 4.3, 4.4 and an optimal preemptive schedule
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Table 3 Average ratio between total electricity costs of schedules obtained by Algorithm 4.2 and an optimal preemptive schedule
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Table 4 Average ratio between total electricity costs of schedules obtained by Algorithm 4.3 and an optimal preemptive schedule
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Table 5 Average ratio between total electricity costs of schedules obtained by Algorithms 4.3 and 4.2
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Fang, K., Uhan, N.A., Zhao, F. et al. Scheduling on a single machine under time-of-use electricity tariffs. Ann Oper Res 238, 199–227 (2016). https://doi.org/10.1007/s10479-015-2003-5

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  • DOI: https://doi.org/10.1007/s10479-015-2003-5

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