problem description

Let G = (N,A) be a directed graph where N is the set of nodes and A is the set of arcs. Let I ⊂ N be the set of potential hubs. Each hub i ∈ I is given a fixed opening cost Fi. Let J ⊂ N be the set of clients. Each client j ∈ J is given a demand di. An homogeneous fleet of vehicles of capacity Q is available. They can be located at any open hub to deliver the clients. Each arc (i,j) ∈ A is given a travel cost cij. The Location Routing Problem (LRP) consists in selecting the hubs to open and in computing a set of routes to deliver the clients such that:
The LRP is NP-hard as it generalizes the CVRP. It combines the CVRP with the Facility Location Problem (FLP).


Three classic sets of instances are available:
We propose a new set of instances. Instances range from 16 to 341 nodes. Graphs are asymmetrical, vehicle fleet is homogeneous and depots are non-homogeneous. Besides, there is no correlation between distance and transportation time and between demand and service time. The set has be split in 3 classes: small, medium and large instances.