Competitive inventory models

This paper deals with the question of optimal inventory sizes in a competitive environment in which the demand for a product at a vendor depends on the inventory level of the product at that vendor relative to the inventories of the same product held by other competing vendors. The total demand for the product at all vendors is assumed to be fixed. This question is examined for two different replenishment policies: base stock policy where the vendors keep a constant level of inventory by ordering the product at the same rate as the observed demand; and continuous review policy where all vendors replenish their inventories periodically when the inventory level drops to a predetermined level.