The Inventory Routing Problem
An undirected complete graph describes the transportation network with costs associated with the edges. One vertex represents the depot and the other vertices the customers.
The IRP enlarges the set of decisions to be made with respect to the Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) adding the days of visit to the customers. The daily consumption (in volume or weight) of the customers is given, but the quantities to be delivered are not known.
The IRP is the problem of deciding, day by day:
the quantity to deliver to each customer
how to organize the routes.
The aim is to minimize the total cost (either routing cost or the sum of the inventory costs and the routing costs).