Price-Directed Cost Sharing and Demand Allocation among Service Providers with Multiple Demand Sources and Multiple Facilities

Problem definition: We consider capacity sharing through demand allocation among firms with multiple demand sources and multiple service facilities. Firms decide on the allocation of demand from different sources to different facilities to minimize delay costs and service-fulfillment costs possibly subject to service-level requirements. If firms decide to operate collectively as a coalition, they must also decide on a scheme for sharing the total cost. Academic/practical relevance: We study capacity sharing through demand allocation in service systems in the presence of service-fulfillment costs. Our problem is motivated by service collaboration in healthcare involving public–private partnerships. Methodology: We formulate the problem as a cooperative game and identify a cost allocation that is in the core. Results: The cost-allocation scheme we identify is price-directed, and the cost of each firm consists of three components: (1) the delay cost incurred within the firm; (2) a cost paid for the capacity used by the firm at facilities owned by other firms; and (3) a payment received for fulfilling demand of other firms at facilities owned by the firm. Interestingly, we show that the cost-allocation scheme is equivalent to a market equilibrium—that is, it can be implemented in a decentralized fashion. We extend our analysis to settings where the capacity of each facility is endogenously determined and to settings where a service-priority policy is deployed. Our results are robust to a variety of generalizations: partial sharing, partial transfer, facilities modeled as general queueing systems, and convex delay costs. Managerial implications: Our findings provide guidelines for and insights into how to carry out demand allocation and cost sharing among different firms in the presence of service-fulfillment costs to foster service collaboration. In particular, the equilibrium market prices can be viewed as the prices/subsidies for service collaboration in a public–private partnership.