Coordination of Outsourced Operations at a Third-Party Facility Subject to Booking, Overtime, and Tardiness Costs

We consider an outsourcing problem where a group of manufacturers outsource jobs to a single third party who owns a specialized facility needed to process these jobs. The third party announces the time slots available on her facility, and the associated prices. Manufacturers reserve, on a first-come-first-book basis, time slots that they desire to utilize. Booking of overtime is possible, at a higher cost. A job completed after its due date incurs a tardiness cost. Each manufacturer books chunks of facility time and sequences his jobs over the time slots booked to minimize his booking, overtime, and tardiness costs. This model captures the main features of outsourcing operations in industries such as semiconductor manufacturing, biotechnology, and drug R&D. In current practice, the third party executes all outsourced jobs without performing optimization and coordination. We investigate the issue of the third party serving as a coordinator to create a win--win solution for all. We propose a model based on a cooperative game as follows: (i) Upon receiving the booking requests from the manufacturers, the third party derives an optimal solution if manufacturers cooperate, and computes the savings achieved. (ii) She devises a savings sharing scheme so that, in monetary terms, every manufacturer is better off to coordinate than to act independently or coalesce with a subgroup of manufacturers. (iii) For her work, the third party withholds a portion (rho) of the booking revenue paid by the manufacturers for time slots that are released after coordination. We further design a truth-telling mechanism that can prevent any self-interested manufacturer from purposely reporting false job data to take advantage of the coordination scheme. Finally, we perform a computational experiment to assess the value of coordination to the various parties involved.