Permutation flowshops in group scheduling with sequence-dependent setup times

This paper focuses on the flow shop sequence dependent group scheduling (FSDGS) problem with minimisation of total completion time as the criterion (Fm|f(mls), prmu, S-plk|Sigma C-j). The research problem is formulated in form of two different mixed integer linear programming (MILP) models. Comparing with the latest MILP model for the proposed problem in the literature, the complexity size of the proposed models are significantly reduced. One of the proposed mathematical models is so effective that even medium-sized instances (problems up to 60 jobs in all groups) are solved to optimality in a reasonable amount of time. Moreover, a metaheuristic hybridising genetic and simulated annealing algorithm, called GSA, is proposed to solve the problems heuristically. All the results and analyses show the high performance of the proposed mathematical models as well as the proposed metaheuristic algorithm compared to the available ones in literature.