Summary: Cooperation in stochastic inventory models
with continuous review
Richard J. Boucherie
May 27, 2010
Consider multiple companies that continuously review their inventories and face
Poisson demand. We study cooperation strategies for these companies and analyse
if there exist allocations of the joint cost such that any company has lower costs
than on its own; such allocations are called stable cost allocations. We start with
two companies that jointly place an order for replenishment if their joint inventory
position reaches a certain reorder level. This strategy leads to a simple expression of
the joint costs. However, these costs exceed the costs for non-cooperating companies.
Therefore, we examine another cooperation strategy. Namely, the companies reorder
as soon as one of them reaches its reorder level. This latter strategy has lower costs
than for non-cooperating companies. Numerical experiments show that the game-
theoretical distribution rule -- a cost allocation in which the companies share the
procurement cost and each pays its own holding cost -- is a stable cost allocation.
These results also hold for situations with multiple companies.