Annals of Operations Research

, Volume 238, Issue 1–2, pp 199–227 | Cite as

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

  • Kan Fang
  • Nelson A. UhanEmail author
  • Fu Zhao
  • John W. Sutherland


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.


Scheduling Time-of-use tariff Electricity cost  Dynamic speed scaling Approximation algorithm 


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Copyright information

© Springer Science+Business Media New York (outside the USA) 2015

Authors and Affiliations

  • Kan Fang
    • 1
  • Nelson A. Uhan
    • 2
    Email author
  • Fu Zhao
    • 3
  • John W. Sutherland
    • 4
  1. 1.College of Management and EconomicsTianjin UniversityTianjinChina
  2. 2.Mathematics DepartmentUnited States Naval AcademyAnnapolisUSA
  3. 3.Environmental and Ecological Engineering and School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA
  4. 4.Environmental and Ecological EngineeringPurdue UniversityWest LafayetteUSA

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