Scheduling on identical machines with preemption and setup times

AbstractIn this paper, we address the problem of scheduling jobs on identical machines for minimising the maximum completion time (makespan). Each job requires a sequence-independent setup time, which represents the time needed to prepare the machines for job execution. Then, we introduce a dynamic programme to solve the case with two machines, and show that this problem admits a fully polynomial time approximation scheme. For the case of m machines, we propose heuristics and an adapted genetic algorithm. Some numerical experiments are done to evaluate the proposed algorithms.Keywords: Schedulingpreemptionsetup timesmakespandynamic programmingFPTAS Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe authors confirm that the data supporting the findings of this study are available within the article.Notes1 mod(n,m) is the remainder of the Euclidean division of n by m.Additional informationNotes on contributorsAmina HanedAmina Haned received her PhD in mathematics at the University USTHB of Algiers. She is a lecturer at the Faculty of Economic Sciences, Commercial Sciences and Management Sciences, University Algiers 3. Amina is deeply interested in the fields of optimisation, operational research, and data science, with a particular focus on scheduling and operations optimisation.Abida KerdaliAbida Kerdali received her PhD in National Higher School of Statistics and Applied Economics. She is a Lecturer at the same School in University center of Kola, Algeria. Her research area is operational research, with a focus on economic problems.Mourad BoudharMourad Boudhar received his PhD in mathematics at the University USTHB of Algiers. He is a professor at the Department of Operational Research, University USTHB. His research interests include issues related to operational research and optimisation, with a particular focus on scheduling problems with new constraints as transportation, conflict, recirculation, multi-agents, etc. He has published several research papers in national and international journals and conference proceedings.