Discovering the Properties of a Problem of Scheduling Battery Charging Jobs to Minimize the Total Time with the Use of Harmonic Numbers

Rafał Różycki, Zofia Walczak and Grzegorz Waligóra ()
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Rafał Różycki: Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
Zofia Walczak: Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
Grzegorz Waligóra: Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland

Energies, 2024, vol. 17, issue 15, 1-18

Abstract: In this work, we consider a problem from the field of power-aware scheduling in which a fleet of electric vehicles have to be charged in a minimum time. Each vehicle is equipped with a lithium-ion battery of a given capacity. The initial power used for charging each battery is known, whereas it is assumed that the power drops to zero at the moment when the battery gets fully loaded. The power usage function is linear and decreasing. The charging jobs are nonpreemptable and independent, whereas the total available amount of power is limited. The objective is to minimize the schedule length. In this paper, we analyze the case of a problem with identical jobs that already cover a wide variety of practical situations. By employing inverses of natural numbers, similar to harmonic series, we prove two properties of this case, and we also discuss the phenomenon of the stabilization of the difference between the start times of two successive jobs in a schedule. We also take under examination a few special cases of the problem. Some conclusions and directions for future research are given.

Keywords: electric vehicle; battery; charging; power; energy; scheduling; harmonic numbers (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2024
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