A framework for decentralized multi-echelon inventory control

We provide a cost structure that can be used for decentralized control of a multi-echelon inventory system with a central warehouse and a number of retailers. This cost structure means that the warehouse, in addition to its local costs, pays a penalty cost for a delay at the warehouse to the retailer facing the delay. A basic assumption is that each installation starts with an initial policy concerning e.g., inventory control and transportation. The installations then play a Stackelberg game with the warehouse being the leader. By minimizing its local costs according to the suggested cost structure, an installation can reduce its costs. The total system costs are then reduced by the same amount. No installation needs to face higher costs due to policy changes at other installations, since the cost structure satisfies a rationality constraint. If an installation applies its initial policy the local costs are the same as in the initial state, even if the other installations change their policies. If the game is played repeatedly the system will approach a Nash equilibrium but not necessarily the centralized optimal solution. As an example we consider a system with one-for-one ordering retailers.