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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... 

The vendor-managed inventory (VMI) is a common policy in supply chain management (SCM) to reduce bullwhip effects. Although different applications of VMI have been proposed in the literature, the multi-vendor multi-retailer single-warehouse (MV-MR-SW) case has not been investigated yet. This paper develops a constrained MV-MR-SW supply chain, in which both the space and the annual number of orders of the central warehouse are limited. The goal is to find the order quantities along with the number of shipments received by retailers and vendors such that the total inventory cost of the chain is minimized. Since the problem is formulated into an integer nonlinear programming model, the...