A bi-objective MILP model for blocking hybrid flexible flow shop scheduling problem: robust possibilistic programming approach

One of the important issues in scheduling due to the frequent use of it in manufacturing industries and factories is the hybrid flow shop (HFS) scheduling problem. In this paper, a bi-objective mixed integer linear programming (MILP) model for the problem is presented in which blocking constraint is also considered. The first objective function tries to minimize the makespan and the second one tries to minimize the total costs of machine allocation at each stage. In fact, in this model, the number and the type of machines at each stage are determined by the model according to the processing and setup times and cost of machines. Because most issues in the real world are uncertain, in this study, processing times, sequence-dependent setup times, and costs are considered as uncertain parameters. The robust possibilistic programming (RPP) approach is used to cope with the uncertainty. In this paper, the realistic and the hard worst-case robust approaches are used. The realistic and the soft worst-case robust models became the same because we are only concerned about the robustness of the makespan. Comparing the results between fuzzy and robust fuzzy models shows that the realistic model is more suitable than fuzzy and hard worst-case models in terms of mean and standard deviation.