New hybrid heuristics for a location-routing problem

As pointed out by Nagy and Salhi in their recent survey [1], many variants of the location routing problem (LRP) are addressed in the literature. Generally speaking the LRP consists of determining locations for depots from which customers are served on routes with the objective of minimizing the overall cost. In this talk we consider the capacitated locationrouting problem (CLRP) which is defined as follows. Let G = (X, E) be an undirected graph where X is the vertex set and E the edge set. X = V ∪ W is composed of m vertices in V associated with potential location sites and of n vertices in W associated with customers. A cost matrix is defined on E and a fixed opening cost is associated with each vertex of V. Each customer i must be served a demand di from a depot. The total demand served from one depot must not exceed the depot capacity Q . To deliver the demand, a fleet of vehicles is available and with each vehicle is associated a maximal capacity Q. A solution of the CLRP is a set of location sites for the depots and a collection of routes where: (i) each customer is visited only once; (ii) the total demand for each route is at most Q; and (iii) the total demand delivered from each depot is at most Q . The CLRP aims to determine a minimal total cost solution. The total cost is the sum of the opening costs and of the routing costs.