scheduling on flexible flow shop with cost-related objective function considering outsourcing options

This study considers outsourcing decisions in a flexible flow shop scheduling problem, in which each job can be processed by either an in-house production line or outsourced. the selected objective function aims to minimize the weighted sum of tardiness costs, in-house production costs, and outsourcing costs with respect to the jobs due date. the purpose of the problem is to select the jobs that must be processed inhouse, schedule processing of the jobs inhouse, and finally select and assign other jobs to the subcontractors. we develop a mixed-integer linear programming (milp) model for the research problem. regarding the complexity of the research problem, the milp model cannot be used for large-scale problems. therefore, four metaheuristic algorithms, including sa, ga, pso, hybrid pso-sa, are proposed to solve the problem. furthermore, some random test problems with different sizes are generated to evaluate the effectiveness of the proposed milp model and solution approaches. the obtained results demonstrate that the ga can obtain better solutions in comparison to the other algorithms.