A mathematical model for integrating lot-sizing and scheduling problem in capacitated flow shop environments

In this paper, a multiproduct multiperiod capacitated production system that has been organized as a flow shop is considered. The main novelty of the paper is proposing a more efficient mathematical model for the problem of integrating lot sizing and scheduling with sequence-dependent setups. In comparison to the former model, because of fewer continuous and binary decision variables and constraints in the proposed model, this model is very easier to solve. Comparison between two models proves the superiority of the proposed model. Two mixed integer programming-based approaches with rolling horizon framework have been used to solve this model. To evaluate the performance of the proposed model and solution method, problems of different scales have been studied. The used algorithms search the solution space for both lot-sizing and scheduling problems and find a combination of production planning and scheduling that is feasible and close to optimum.

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