The Inventory Routing Problem: A Survey

The inventory routing problem addresses the coordination of inventory replenishment and transportation. Specifically, it is concerned with the problem of determining strategies for the distribution of a single product from a single supplier to multiple customers. For this purpose, the supplier operates a fleet of vehicles. It is assumed that product usage at the customers is known (or that the probability distributions of customer usage are known). The supplier makes decisions regarding which customers' inventories to replenish, how much to deliver at each customer, and how to combine customers into vehicle routes. Such a decision is called an itinerary. The set of feasible itineraries is determined by constraints on the travel times and work hours of vehicles and drivers, delivery time windows at the customers, the storage capacities and current inventory levels of customers, and other constraints dictated by the application. It may be feasible for a vehicle to perform more than one route per day. The objective is to maximize the profit over a given planning horizon (or the expected discounted profit over an infinite horizon), incorporating sales revenues, production costs, transportation costs, inventory holding costs, and shortage penalties. In this presentation, we will identify and discuss the complexities of the inventory routing problem and we will review and explain algorithmic approaches proposed for the design cost-effective distribution strategies.