Fuzzy Mathematical Programming and Self-Adaptive Artificial Fish Swarm Algorithm for Just-in-Time Energy-Aware Flow Shop Scheduling Problem With Outsourcing Option

Flow shop scheduling (FSS) problem constitutes a major part of production planning in every manufacturing organization. It aims at determining the optimal sequence of processing jobs on available machines within a given customer order. In this article, a novel biobjective mixed-integer linear programming (MILP) model is proposed for FSS with an outsourcing option and just-in-time delivery in order to simultaneously minimize the total cost of the production system and total energy consumption. Each job is considered to be either scheduled in-house or to be outsourced to one of the possible subcontractors. To efficiently solve the problem, a hybrid technique is proposed based on an interactive fuzzy solution technique and a self-adaptive artificial fish swarm algorithm (SAAFSA). The proposedmodel is treated as a single objectiveMILP using a multiobjective fuzzy mathematical programming technique based on the e-constraint, and SAAFSA is then applied to provide Pareto optimal solutions. The obtained results demonstrate the usefulness of the suggested methodology and high efficiency of the algorithm in comparison with CPLEX solver in different problem instances. Finally, a sensitivity analysis is implemented on the main parameters to study the behavior of the objectives according to the real-world conditions.