Abstract: In this paper, we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor. The manufacturer needs to determine which jobs should be produced in-house and which jobs should be subcontracted. Furthermore, it needs to determine a  production schedule for jobs to be produced in-house. We discuss five classical scheduling objectives as production costs. For each problem with different objective functions, we give optimality conditions and propose dynamic programming algorithms.

Key words: scheduling, subcontracting, dynamic programming, parallel machines