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 stochastic; i.e., 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, “dynamically allocating” its inventory along the way (i.e., allocating its inventory depending of the status of inventory at the retailers who have not yet received allocations). 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. If total vehicle travel time or cost is the only cost considered, then, of course, the optimal static route is the TSP (traveling-salesman problem) route. However, as we demonstrate, if inventory-holding and backorder-penalty costs are also considered, then the optimal static route also depends on the variances of customer demand, and, if inventory-holding costs are incurred on the vehicle, also on the means of customer demand. As a consequence, the optimal static route can be quite different from the TSP route. We then examine “dynamic” routing policies; i.e., policies that may change the route from one systemreplenishment-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 heuristic policy for deciding, in any given cycle, whether to use the optimal static route or to switch to one of the ( ! 1) N − alternative routes. Simulation tests of this “change-revert” heuristic for systems with N = 2 and N = 6 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.