Production scheduling problem with assembly flow shop systems: mathematical optimisation models

This work presents four mixed integer linear programming (MILP) models for the assembly flow shop problem in order to minimize the makespan. This production environment has two stages: production and assembly. The first stage consists of different machines designed to manufacture parts of a product. The second stage is intended for a final assembly. The performance measure considered is highly essential for industries from different segments, as it focuses on the best use of the time available for production. Statistical analysis with different tools was used to assess the performance and efficiency of mathematical models, emphasizing the analysis of performance profiles. Results showed that mathematical models are efficient, and the position-based model presented the best results for small and large instances during computational experimentation. All mathematical models can be used as direct tools in decision-making for the production sequencing problem in the approached environment.