On a competitive inventory model with a customer's choice probability

In this paper we consider a model in which a customer chooses one of two retailers with a choice probability depending on the distance from the customer's position to the retailer's position over a line segment market. We study an optimal strategy for two retailers in a competitive inventory model by using an equilibrium point in the context of the game theory. We find an equilibrium point concerned with the optimal ordering quantity to minimize the total cost.