Production Scheduling considering Outsourcing Options and Carrier Costs

We consider a single-machine scheduling problem with outsourcing options in an environment where the cost information of the downstream is available via some information sharing technologies. The due date is assigned to the position differently from the traditional due date. Each job can be processed in-house or outsourced. Note that, for cost saving, as many due dates as the number of outsourced jobs should be canceled. An in-house job incurs a stepwise penalty cost for tardiness, and an outsourced job incurs an outsourcing cost. Thus, the objective is to minimize the total penalty and outsourcing cost minus the total profit from cost savings. We show that the problem is weakly NP-hard and investigate some polynomially solvable cases. Due to the high complexity of the dynamic programming, we developed heuristics and verified their performance through numerical experiments.