Risk-Pooling Along a Fixed Delivery Route Using a Dynamic Inventory-Allocation Policy

This paper examines static and dynamic policies for replenishing and allocating inventories amongst N retailers located along a fixed delivery route. Each retailer faces independent, normally-distributed period demand and incurs a proportional holding or backorder cost on end-of-period net-inventory. A warehouse places a system-replenishment order every m periods which is received after a fixed leadtime of T periods. Immediately upon receipt, a delivery vehicle leaves the warehouse with the system-replenishment quantity and travels to the retailers along a fixed route with fixed leadtimes between successive retailers. The warehouse holds no inventory. Under the "static" policy, allocations are determined for all retailers simultaneously at the moment the delivery vehicle leaves the warehouse. Under the "dynamic" policy, allocations are determined sequentially upon arrival of the delivery vehicle at each retailer. Our major analytical results, under appropriate dynamic (static) allocation assumptions, are: (1) optimal allocations under each policy involve bringing each retailer's "normalized-inventory" to a corresponing "normalized" system inventory; (2) optimal system replenishments are base-stock policies; (3) the minimum expected cost per cycle of dynamic (static) policy can be derived from an equivalent dynamic (static) composite retailer. Given this, we prove that the "risk-pooling incentive"---a simple measure of the benefit from adopting dynamic allocation policies---is always positive. Our simulation tests confirm that dynamic allocation policies yield lower costs than static policies, regardless of whether or not their respective allocation assumptions are valid. However, the magnitude of the cost savings is very sensitive to some system parameters.