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

Kan Fang (zjumath***at***gmail.com)
Nelson A. Uhan (uhan***at***usna.edu)
Fu Zhao (fzhao***at***purdue.edu)
John W. Sutherland (jwsuther***at***purdue.edu)

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. We consider both uniform-speed and speed-scalable machine environments. For the uniform-speed case, we prove that this problem is strongly NP-hard, and in fact inapproximable within a constant factor, unless P = NP. We also propose an exact polynomial-time algorithm for this problem when all the jobs have the same workload and the electricity prices follow a so-called pyramidal structure. 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 this problem is strongly NP-hard. In addition, we present different approximation algorithms for this case and test the computational performance of these approximation algorithms on randomly generated instances.

Keywords: scheduling; time-of-use tariff; electricity cost; dynamic speed scaling; approxima- tion algorithm

Category 1: Applications -- OR and Management Sciences (Scheduling )

Category 2: Combinatorial Optimization

Citation: Annals of Operations Research, available online first, September 2015. DOI: 10.1007/s10479-015-2003-5

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Entry Submitted: 04/10/2014
Entry Accepted: 04/10/2014
Entry Last Modified: 10/17/2015

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