Coordination of outsourced operations to minimize weighted flow time and capacity booking costs

A set of manufacturers outsources certain operations to a single third party following the announcement of a booking price for each available day of production. Knowing these costs, manufacturers book available production days in a first-come-first-serve order to optimize their individual cost. The cost for each manufacturer consists of booking and work-in-progress costs, as expressed by the weighted flow time. When window booking is completed, the third party identifies a schedule that minimizes the total cost incurred by all manufacturers. This coordination reduces the total cost but may result in higher costs for a subset of manufacturers. For this reason, the third party devises a savings sharing scheme with which the monetary benefit for each manufacturer is greater. In this article we present algorithms for the problem considered, as well as savings-sharing schemes that make coordination a better alternative for all parties. The highlight of our experiments is that the costs of the production chain can be reduced by an average of 32% if one-third of the members let the third party cover their increased work-in-progress cost in exchange for 38%–53% of the total savings.