Externalities, Tangible Externalities, and Queue Disciplines
Management Science
A General Framework for the Study of Decentralized Distribution Systems
Manufacturing & Service Operations Management
A Two-Location Inventory Model with Transshipment and Local Decision Making
Management Science
A Three-Stage Model for a Decentralized Distribution System of Retailers
Operations Research
Shipment Consolidation: Who Pays for It and How Much?
Management Science
Cooperation Between Multiple Newsvendors with Warehouses
Manufacturing & Service Operations Management
Cost Allocation for Joint Replenishment Models
Operations Research
The Aumann-Shapley price mechanism for allocating congestion costs
Operations Research Letters
Cost sharing of cooperating queues in a Jackson network
Queueing Systems: Theory and Applications
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We consider a number of servers that may improve the efficiency of the system by pooling their service capacities to serve the union of the individual streams of customers. This economies-of-scope phenomenon is due to the reduction in the steady-state mean total number of customers in the system. The question we pose is how the servers should split among themselves the cost of the pooled system. When the individual incoming streams of customers form Poisson processes and individual service times are exponential, we define a transferable utility cooperative game in which the cost of a coalition is the mean number of customers (or jobs) in the pooled system. We show that, despite the characteristic function is neither monotone nor concave, the game and its subgames possess nonempty cores. In other words, for any subset of servers there exist cost-sharing allocations under which no partial subset can take advantage by breaking away and forming a separate coalition. We give an explicit expression for all (infinitely many) nonnegative core cost allocations of this game. Finally, we show that, except for the case where all individual servers have the same cost, there exist infinitely many core allocations with negative entries, and we show how to construct a convex subset of the core where at least one server is being paid to join the grand coalition.