A “Locate First - Route Second” Heuristic for a Combined Location-Routeing Problem

Abstract

We consider a two-stage facility location problem where on the second distribution stage, delivery vehicles operate on routes. The objective is to find the number, size and locations of the depots, together with the allocation of customers and the product flow from the plants to the depots, which minimize the sum of the trunking costs, variable and fixed depot costs and delivery costs, subject to the supply and demand constraints, depot capacities and vehicle capacity constraints.

To solve the problem, we present an iterative heuristic which - starting with the solution of the location part - ping-pongs between a facility location and a vehicle routeing problem until consistency between the solutions of the two subproblems is reached.

To get an initial estimate of the delivery costs, we use a approach based on hierarchical agglomerative clustering methods. The location subproblem is solved using a Lagrangean heuristic, which is based on the relaxation of the supply and capacity constraints. To solve the routeing subproblem, we use conventional tour construction heuristics together with some tour improvement procedures, which are also applied to the multiple depot routeing problem defined by the set of open depots.