Noncooperative Games for Subcontracting Operations

Consider a set of manufacturers, all of which can subcontract part of their workload to a third party. For simplicity, we assume that every manufacturer as well as the third party each possess a single production facility. Each manufacturer has to decide the amount of workload to be subcontracted so as to minimize the completion time of his in-house and subcontracted workloads. In an effort to provide good service to all, the third party gives priority to manufacturers whose subcontracted workload is small. This incentive scheme forces manufacturers to compete for position in the third-party processing sequence. We develop pure Nash equilibria schedules under three distinct protocols for production.