Dynamic Routing , Inventory Allocation , and Replenishment in a Distribution System with One Warehouse and N Symmetric Retailers

This paper examines “distribution policies” — that is, combined system inventoryreplenishment, vehicle routing and inventory-allocation policies — designed to minimize total expected purchasing and inventory-management (i.e., inventory-holding and backordering) costs/period for a one-warehouse N-retailer “symmetric” distribution system managed under a periodic-review policy. With respect to dynamic routing, we prove that an optimal distribution policy incorporates routing the vehicle to the retailer with the least inventory first (LIF). With respect to allocation and replenishment, we prove that under the “allocation assumption”, myopic replenishment and allocation policies are optimal. Using a numerical study, we demonstrate that optimal LIF routing and allocation policies can significantly reduce the inventory-management costs associated with fixed routing and dynamic allocation in "medium-to-large" customer demand-variance scenarios. We also demonstrate that one of two intuitively-appealing heuristics can yield inventory-management costs quite close to optimum. Next, we establish a necessary condition for optimal system replenishment, which allows for its numerical determination. Finally, a numerical study demonstrates the effectiveness of the following heuristic distribution policy: replenish the system and allocate inventory as if routing were fixed, but, in fact, use LIF routing,