A robust just-in-time flow shop scheduling problem with outsourcing option on subcontractors

Scheduling is known as a great part of production planning in manufacturing systems. Flow Shop Scheduling (FSS) problem deals with the determination of the optimal sequence of jobs processing on machines in a fixed order. This paper addresses a novel robust FSS problem with outsourcing option where jobs can be either scheduled for inside or outsourced to one of the available subcontractors. Capacity limitation for inside resource, just-in-time delivery policy and uncertain processing time are the key assumptions of the proposed model. The objective is to minimize the total-weighted time required to complete all jobs and the total cost of outsourcing. So, a Robust Mixed-Integer Linear Programming (RMILP) model is proposed to accommodate the problem with the real-world conditions. Finally, the obtained results show the effects of the robustness in optimizing the model under uncertainty condition. Moreover, the comparison analysis demonstrated the superiority of our proposed model against the previous Non-Linear Programming (NLP) model in the literature.