The green location-routing problem

This paper introduces the Green Location-Routing Problem (GLRP), a combination of the classical Location-Routing Problem (LRP) and the Pollution-Routing Problem (PRP). The GLRP consists of (i) locating depots on a subset of a discrete set of points, from where vehicles of limited capacity will be dispatched to serve a number of customers with service requirements, (ii) routing the vehicles by determining the order of customers served by each vehicle and (iii) setting the speed on each leg of the journey such that customers are served within their respective time windows. The objective of the GLRP is to minimize a cost function comprising the fixed cost of operating depots, as well as the costs of the fuel and CO2 emissions. The amount of fuel consumption and emissions is measured by a widely used comprehensive modal emission model. The paper presents a mixed integer programming formulation and a set of preprocessing rules and valid inequalities to strengthen the formulation. Two solution approaches; an integer programming based algorithm and an iterated local search algorithm are also presented. Computational analyses are carried out using adaptations of literature instances to the GLRP in order to analyze the effects of a number parameters on location and routing decisions in terms of cost, fuel consumption and emission. The performance of the heuristic algorithms are also evaluated.