Joint order (1, T) policy for a two-echelon, single-item, multi-retailer inventory system with Poisson demand

This study considers a two-echelon inventory system with one central warehouse and a number of non-identical retailers with Poisson demands, constant lead times, and lost sales for a single item. The warehouse works as a cross-docking terminal with no inventory and coordinates shipments to retailers. We apply the Joint order (1, T) policy in such an inventory system. In the standard (1, T) policy, the warehouse sends one unit of the item to each retailer in a fixed cycle time, which is calculated by considering each retailer separately. In the joint order (1, T) policy, the warehouse decides to replenish one unit of the item for each retailer in a cycle time which is adjusted to be an integer multiple of a base cycle time. Thus, under such an ordering policy, the warehouse can better adjust shipments to retailers so that they can be batched with other retailers' orders, which results in overall savings in ordering, shipping and stock out costs for the entire system on average. We calculate the total cost of the system, and present a procedure to obtain near optimal values of the base cycle time and the integer multiples of the base cycle in which retailers should be served.