A General Framework for the Study of Decentralized Distribution Systems

Abstract

We develop a general framework for the analysis of decentralized distribution systems. We carry the analysis in terms of a simplified model which entails N retailers who face stochastic demands and hold stocks locally and/or at one or more central locations. An exogenously specified fraction of any unsatisfied demand (demand greater than locally available stock) at a retailer could be satisfied using excess stocks at other retailers and/or stocks held at a central location. We consider inventory ordering and allocation decisions. The operational decisions of inventory and allocation of stocks and the financial decision of allocation of revenues/costs must be made in a way consistent with the individual incentives of the various independent retailers. We develop a "coopetitive" framework for the sequential decisions of inventory and allocation. We introduce the notion of claims that allows us to separate the ownership (with decision rights) and the location of inventories in the system. For the cooperative shipping and allocation decision, we use the concept of core and develop sufficient conditions for the existence of the core. For the inventory decision, we develop conditions for the existence of a pure strategy Nash Equilibrium. For this decentralized system, we show that there exists an allocation mechanism that achieves the first-best solution for inventory deployment and allocation. We develop conditions under which the first-best equilibrium will be unique. Our model can be easily generalized to include complicated ownership structures such as "super dealers," partnerships, "inventory speculators," and situations in retail e-commerce settings such as "click-through arrangements," separation of "demand generators," and "fulfillment houses," etc. It can also be applied to situations involving capacity allocations and product substitutions.Decentralization, Distribution, Game Theory, Inventory, e-Business

Game Theory in Supply Chain Analysis

“…In the second (cooperative) stage retailers observe demand and decide how much inventory to transship among locations to better match supply and demand and how to appropriate the resulting additional profits. Anupindi et al (2001) conjecture that a characteristic form of this game has an empty core. However, the biform game has a non-empty core and they find the allocation of rents based on dual prices that is in the core.…”

“…Anupindi et al (2001) consider a game where multiple retailers stock at their own locations as well as at several centralized warehouses. In the first (non-cooperative) stage retailers make stocking decisions.…”

Cost Allocation for Joint Replenishment Models

“…Applications of game theory in analyzing cooperations among supply chain agents can be found in Anupindi et al [2], Granot and Sošić, [8], and Nagarajan and Sošić [15]. For an excellent comprehensive review, see Nagarajan and Sošić [16].…”

Game Theory in Supply Chain Analysis

“…Hence, NE seems to be the necessary condition for the prediction of any rational behavior by players. 2 While attractive, numerous criticisms of the NE concept exist. Two particularly vexing problems are the nonexistence of equilibrium and the multiplicity of equilibria.…”