Two-stage production scheduling with an option of outsourcing from a remote supplier

This paper studies a two-stage production system with n job orders where each job needs two sequential operations. In addition to the two in-house production facilities, the manufacturer has another option of outsourcing some stage-one operations to a remote outside supplier. The jobs with their stage-one operations outsourced are subject to a batch transportation delay from the outside supplier before their respective stage-two operations can be started in-house. The problem is to design an integrated schedule 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 an optimal algorithm and a heuristic algorithm to solve the problem, and conducted computational experiments to validate our model and algorithms. Our modeling and algorithm framework can be extended to handle other more general cases such as when the outside supplier has a production facility with a different processing efficiency and when there are many outside suppliers on a spot market.