Optimal replenishment order for uncertain demand in three layer supply chain

The authors study the well-known order quantity model in a three-player context, using a framework of newsboy problem. An expected average cost function of the chain by trading off inventory cost and shortage costs is formulated which is minimized to obtain optimal order sizes of the supplier, manufacturer and retailer. Our theoretical analysis of both cases; (i) when demand per unit time of each member of the chain is uncertain, (ii) when uncertain demand is distributed uniformly over finite time horizon; suggests the determining of optimal order sizes of the members so that the expected average channel cost is minimum. Numerical examples for different distributions are illustrated to justify our model.