Sequence-based MILP modeling for flexible job shop scheduling

In this paper, a novel mixed integer linear programming formulation is developed for the Flexible Job Shop Scheduling Problem. The theoretical foundation of the proposed MILP model takes its root from the sequence-based modeling paradigm for production scheduling, which was initially propounded by Alan. S. Manne. The proposed MILP model is capable of solving scheduling problems associated with both totally- And partially-flexible job shops. The developed MILP model consists of fewer numbers of continuous variables and is capable of solving larger size instances of the problem. In order to demonstrate the effectiveness of the model, it is applied to standard benchmarks from literature. In order to investigate the combined impact of possessing fewer numbers of continuous decision variables on the performance of the proposed MILP model, three other different performance measures: computational time, size dimensionality and quality of generated schedules are utilized. Finally, the proposed MILP is compared vis-à-vis the best-performing MILP in the literature. The obtained results simply corroborate the superiority of our developed MILP model in all the aforementioned performance measures.