A Parallel Machine Scheduling Problem with Outsourcing Options

This paper considers an integrated decision for scheduling and outsourcing(or, subcontracting) of a finite number of jobs(or, orders) in a time-sensitive make-to-order manufacturing environment. The jobs can be either processed in a parallel in-house facilities or outsourced to subcontractors. We should determine which jobs should be processed in-house and which jobs should be outsourced. And, we should determine the schedule for the jobs to be processed in-house. If a job is determined to be processed in-house, then the scheduling cost(the completion time of the Job) is imposed. Otherwise(if the job should be outsourced), then an additional outsourcing cost is imposed. The objective is to minimize the linear combination of scheduling and outsourcing costs under a budget constraint for the total available outsourcing cost. In the problem analysis, we first characterize some solution properties and then derive dynamic programming and branch-and- bound algorithms. An efficient heuristic is also developed. The performances of the proposed algorithms are evaluated through various numerical experiments.

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