General bounds for the optimal value of retailers' reorder point in a two-level inventory control system with and without information sharing

摘要

In this study, an inventory system consisting of a single product, one supplier, and multiple identical retailers is considered. Each retailer replenishes inventory from the supplier according to the well known (R,Q) policy. Transit times are constant and retailers face independent Poisson demand. The supplier utilizing the retailers' information in decision making for replenishment policy with a given order size starts with m initial batches (of size Q) and places an order in a batch of size Q to an outside source when a new order is placed. In this inventory system, excess demand is backordered, delayed orders are satisfied on a first-come first-serve basis, and no partial shipment is allowed. By partitioning the cost function of this system, general upper and lower bounds for the optimal value of R are determined. Based on several numerical examples, it is shown that these bounds (especially the lower bound) allow the optimal reorder point to be found more effectively with a shorter solving time.