This paper addresses a single-stage scheduling problem with outsourcing allowed where each job can be either scheduled for in-house production or outsourced to one of the outside subcontractors available. The manufacturer has an unrelated parallel machine system, and each subcontractor has its own single machine. Subcontractors are capable to process all the jobs. Unlike most of past research, our study considers the joint scheduling of both in-house and outsourced jobs simultaneously. The objective is to minimize sum of the total weighted completion time and total outsourcing cost. An integer programming formulation is presented and then improved through an optimality property on job orders. A heuristic algorithm is also introduced to decompose the problem into smaller and easier subproblems and solve them to optimality.
