Capacity allocation and coordination issues for the timely processing of outsourced operations

We consider dynamic capacity booking problems faced by multiple manufacturers each outsourcing certain operations to a common third-party firm. Each manufacturer, upon observing the current state of the third-party schedule, books capacity with the objective to jointly minimize holding costs that result from early deliveries, tardiness penalties due to late deliveries, and third-party capacity booking costs. When making a reservation, each manufacturer evaluates two alternative courses of action: (i) reserving capacity not yet utilized by other manufactures who booked earlier; or (ii) forming a coalition with a subset or all of other manufacturers to achieve a schedule minimizing coalition costs, i.e., a centralized schedule for that coalition. The latter practice surely benefits the coalition as a whole; however, some manufacturers may incur higher costs if their operations are either pushed back too much, or delivered too early. For this reason, a cost allocation scheme making each manufacturer no worse than they would be when acting differently (i.e., participating in a smaller coalition or acting on their own behalf,) must accompany centralized scheduling for the coalition. We model this relationship among the manufacturers as a cooperative game with transferable utility, and present optimal and/or heuristic algorithms to attain individually and coalitionally optimal schedules as well as a linear program formulation to find a core allocation of the manufacturers’ costs.