On the Interactions Between Routing and Inventory-Management Policies in a One-Warehouse N-Retailer Distribution System

This paper examines the interactions between routing and inventory-management decisions in a two-level supply chain consisting of a cross-docking warehouse and N retailers. Retailer demand is normally distributed and independent across retailers and over time. Travel times are fixed between pairs of system sites. Every m time periods, system inventory is replenished at the warehouse, whereupon an uncapacitated vehicle departs on a route that visits each retailer once and only once, allocating all of its inventory based on the status of inventory at the retailers who have not yet received allocations. The retailers experience newsvendor-type inventory-holding and backorder-penalty costs each period; the vehicle experiences in-transit inventory-holding costs each period. Our goal is to determine a combined system inventory-replenishment, routing, and inventory-allocation policy that minimizes the total expected cost/period of the system over an infinite time horizon. Our analysis begins by examining the determination of the optimal static route, i.e., the best route if the vehicle must travel the same route every replenishment-allocation cycle. Here we demonstrate that the optimal static route is not the shortest-total-distance (TSP) route, but depends on the variance of customer demands, and, if in-transit inventory-holding costs are charged, also on mean customer demands. We then examine dynamic-routing policies, i.e., policies that can change the route from one system-replenishment-allocation cycle to another, based on the status of the retailers' inventories. Here we argue that in the absence of transportation-related cost, the optimal dynamic-routing policy should be viewed as balancing management's ability to respond to system uncertainties (by changing routes) against system uncertainties that are induced by changing routes. We then examine the performance of a change-revert heuristic policy. Although its routing decisions are not fully dynamic, but determined and fixed for a given cycle at the time of each system replenishment, simulation tests with N = 2 and N = 6 retailers indicate that its use can substantially reduce system inventory-related costs even if most of the time the chosen route is the optimal static route.