Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem

We analyze three queuing control problems that model a dynamic stochastic distribution system, where a single capacitated vehicle serves a finite number of retailers in a make-to-stock fashion. The objective in each of these vehicle routing and inventory problems is to minimize the long run average inventory (holding and backordering) and transportation cost. In all three problems, the controller dynamically specifies whether a vehicle at the warehouse should idle or embark with a full load. In the first problem, the vehicle must travel along a prespecified (TSP) tour of all retailers, and the controller dynamically decides how many units to deliver to each retailer. In the second problem, the vehicle delivers an entire load to one retailer (direct shipping) and the controller decides which retailer to visit next. The third problem allows the additional dynamic choice between the TSP and direct shipping options.