Outsourcing and scheduling for a two-machine flow shop with release times

This article addresses a two-machine flow shop scheduling problem where jobs are released intermittently and outsourcing is allowed. The first operations of outsourced jobs are processed by the first subcontractor, they are transported in batches to the second subcontractor for processing their second operations, and finally they are transported back to the manufacturer. The objective is to select a subset of jobs to be outsourced, to schedule both the in-house and the outsourced jobs, and to determine a transportation plan for the outsourced jobs so as to minimize the sum of the makespan and the outsourcing and transportation costs. Two mathematical models of the problem and several necessary optimality conditions are presented. A solution approach is then proposed by incorporating the dominance properties with an ant colony algorithm. Finally, computational experiments are conducted to evaluate the performance of the models and solution approach.