Two-stage supply chain scheduling with an option of outsourcing in stage one

This paper studies a two-stage supply chain scheduling problem with n job orders where each job needs two sequential operations. In addition to the two in-house machines each for one operation, the manufacturer has another option of outsourcing some stage-one operations to an outside subcontractor. The jobs with their stage-one operation outsourced are subject to a single batch delivery from the subcontractor before their respective stage-two operations can be started in-house. The problem is to design an integrated scheduling that considers both the in-house production and the outsourcing with the aim of optimally balancing the outsourcing cost and the makespan. The problem is NP-hard. We have developed a heuristic algorithm to solve the problem, and conducted computational experiments to validate our model and algorithm.