Excerpt from Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem
Our system model has one warehouse and one capacitated vehicle; hence, we effectively assume that the higher level decisions have been made to assign a single warehouse and a. Single vehicle to serve all retailers in a particular region. An ample amount of inventory is available at the warehouse, and the cost of holding this inventory is not included in the model. Retailer demand and vehicle travel times are random, unsatisfied demand is backordered, and the objective is to minimize costs due to holding and backordering inventory (cost rates may differ by retailer) and operating the vehicle. One of the crucial decisions in our problem is the vehicle idling policy: when the vehicle is at the warehouse, the controller can either send the vehicle out with a full load or let the vehicle sit idle; because we employ a long run average cost criterion, if the vehicle does not idle and the traffic intensity of the system is less than one, then an infinite amount of retailer inventory will build up over the long run.
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