New formulation for scheduling flexible flow shop problems

This research extends the constrained vehicle routing problem concept to solve flexible flow shop scheduling problems. Mixed-integer linear programming and constraint programming formulations are developed for a flow shop problem with no-wait, time lags and release time restrictions to minimize the makespan in both permutation and non-permutation schedules. The comparative analysis of various models reveals that constraint programming models have superior computational performance than mixed-integer linear programming models. However, the mixed-integer linear programming models are also timely-efficient. Moreover, the efficiency of developed models is also represented in comparison with several benchmark datasets. Based on the findings, while the objective function values of the mixed-integer linear programming and constraint programming models in non-permutation schedules exhibit lower values than their respective equivalents in permutation schedules, both models demonstrate longer runtime in non-permutation schedules. Results represent that the proposed constraint programming and mixed-integer linear programming models are among the top three models of the benchmark datasets in terms of the number of decision variables and computational performance. One of the limitations of the research is that there is no comprehensive dataset in the literature considering all the restrictions in permutation and non-permutation schedules.