Equilibrium replenishment in a supply chain with a single distributor and multiple retailers

This paper addresses a problem encountered by a large-scale health service supply chain operating in a periodic review mode. Due to the vital nature of the products it provides, the number and timing of urgent orders are not limited. As a result, increasingly high transportation costs are incurred and the problem is to select an inventory replenishment (review) period that minimizes the transportation cost. Moreover, the supply chain involves multiple retailers which inevitably and independently respond to any change in replenishment policy since it may affect their inventory costs. Such a relationship results in a game between a distribution centre and retailers. Since the problem is intractable due to its scale and stochastic nature, we combine a game theoretic approach with an empirical analysis. We show that this system is predictable using equilibria and that the current replenishment equilibrium of the health service supply chain is close to the Nash solution. Numerical analysis shows that the transportation costs are cut if the distribution centre implements in reality its formal (Stackelberg) leadership by reducing the replenishment period. However, this does not coordinate the supply chain and greater system-wide savings are possible by increasing the replenishment period if the supply chain is vertically integrated or the parties cooperate.