| Inventory analysis studies a system consisting of a group of participants (stores) who combine ordering and managing items. Minimizing the cost of an inventory system by choosing decision variables appropriately is the first objective. It is just as important to pass on the benefits of centralizing inventory management to the participants in a way that does not disrupt the combination. In this work cooperative game theory is used as a framework to study methods of allocating inventory costs and benefits. A cost game and a benefit game are associated with the inventory model.;For a single-item stochastic demand continuous review (Q,r) model, many allocation techniques do not provide an allocation of costs to participants which is in the core of the game. Such allocations are not stable, in the sense that come subset of the participants could form their own inventory system using the same model and reduce their cost. Furthermore, an allocation for the cost game could be in core whereas that for the benefit game is not. A refinement of the stability requirement is suggested; the allocation method must be justifiable, providing a core allocation for both cost and benefit games.;A single period stochastic inventory model with normally distributed individual demands is investigated in detail. Demands may be correlated between participants. The cooperative games associated with these centralization cost functions have a representation in a finite dimensional vector space. The games are monotonic (centralization is cheaper); and are concave when demands are uncorrelated; but when correlations are nonzero, the region of concavity is not simply defined. For three participants, equations defining the concavity region are presented. A theorem that all models of this class, for any number of participants, induce cooperative games whose core is not empty, is proved.;Now fix the individual distribution parameters of the participants. Management searches for that combination of correlations which yields the lowest cost, a target management will try for. An allocation method is found which produces justifiable core allocations for the game whose correlations is presented. For three participants, it converges with rate at worst linear; and the allocations also converge. |
