On time-indexed formulations for the parallel machine scheduling problem with a common server

AbstractThis article studies the problem of scheduling independent jobs on parallel machines with a common server, the objective of which is to minimize the makespan. In this case, the common server is responsible for performing the setup operations and, therefore, there must be no conflicts while conducting them. Four alternative time-indexed formulations for the problem are considered and evaluated computationally. Moreover, two algorithms are presented that can significantly improve the performance of the best time-indexed formulation. The results obtained on two benchmark datasets involving up to 100 jobs suggest that the proposed improved algorithms are substantially better than existing approaches.Keywords: Schedulingparallel machinescommon servertime-indexed formulationsinteger programming Disclosure statementThe authors declare that they have no conflict of interest.Data availability statementThe authors confirm that the data supporting the findings of this study are available within the article.Additional informationFundingThis research was partially supported by Comissão de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) [Grant Finance Code 001]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [Grants 428549/2016-0, 307843/2018-1 and 313601/2018-6]; Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (Faperj) [Grant E-26/202.887/2017]; [CAPES PrInt UFF No 88881].