We consider multi-echelon supply chains, typically consisting of retailer, distributor, manufacturer, etc. The inventory of each actor is subject to its own delay in delivery time, and each chooses its own inventory replenishment strategy. We model this interaction with a system of linear differential delay equations. When put in matrix form the system is triangular and we derive an exact solut...

This paper is concerned with the coordination of inventory control in divergent multiechelon inventory systems under periodic review and decentralized control. All the installations track echelon inventories. Under decentralized control the installations will decide upon replenishment policies that minimize their individual inventory costs. In general these policies do not coincide with the opt...

We consider a distribution system with a central warehouse and multiple retailers. The warehouse orders from an outside supplier and replenishes the retailers which in turn satisfy customer demand. The retailers are nonidentical, and their demand processes are independent compound Poisson. There are economies of scale in inventory replenishment, which is controlled by an echelon-stock, batch-tr...

We study a multi-echelon joint inventory-location model that simultaneously determines the location of warehouses and inventory policies at the warehouses and retailers. The model is formulated as a nonlinear mixed-integer program, and is solved using a Lagrangian relaxation-based approach. The efficiency of the algorithm and benefits of integration are evaluated through a computational study.

W consider a two-echelon inventory system with a capacitated centralized production facility and several distribution centers (DCs). Both production and transportation times are stochastic with general distributions. Demand arrives at each DC according to an independent Poisson process and is backlogged if the DC is out of stock. We allow different holding and backlog costs at the different DCs...