A Robust Just-in-Time Flow Shop Scheduling Problem with Outsourcing Option on Subcontractors
by: Alireza Goli, Erfan Babaee Tirkolaee, and Mehdi Soltani
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.
Keywords: Flow shop scheduling; outsourcing; just-in-time; due date; Robust optimization
Flow shop is a production system where all machines are organized based on operational jobs. Flow Shop Scheduling (FSS) problem involves determining an optimal schedule for jobs processing on machines and has been a research benchmark for many years. Optimization algorithms for two and three-machine flow shop problems have been developed in conjunction with different targets. As the majority of FSS problems are NP-hard; i.e., problems with non-polynomial run time, all of the exact, heuristic and meta-heuristic solution methods seek to minimize total completion time (makespan) (Chung, Flynn, & Kirca, 2006).