Solving the Capacitated Location-Routing Problem by a Cooperative Lagrangean Relaxation-Granular Tabu Search Heuristic

Abstract

Most of the time in a distribution system, depot location and vehicle routing are interdependent, and recent studies have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location-routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a cooperative metaheuristic to solve the LRP with capacitated routes and depots. The principle is to alternate between a depot location phase and a routing phase, exchanging information on the most promising edges. In the first phase, the routes and their customers are aggregated into supercustomers, leading to a facility-location problem, which is then solved by a Lagrangean relaxation of the assignment constraints. In the second phase, the routes from the resulting multidepot vehicle-routing problem (VRP) are improved using a granular tabu search (GTS) heuristic. At the end of each global iteration, information about the edges most often used is recorded to be used in the following phases. The method is evaluated on three sets of randomly generated instances and compared with other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem and show that this metaheuristic outperforms other methods on various kinds of instances.

Location-Routing Problem with Simultaneous Home Delivery and Customer’s Pickup for City Distribution of Online Shopping Purchases

“…Moreover, considering the most recent and effective methods in the literature, the performance comparison is provided in Table 3 based on the CPU and Best Gap/BKR. The compared algorithms are GRASP in Prins et al [49], MAPM in Prins et al [39], LRGTS in Prins et al [50], GRASP+ELS in Duhamel et al [36], SALRP in Vincent et al [35], ALNS in reference [51], MACO in [32], GRASP+ILP in Contardo et al [52], GVTNS in Escobar et al [38] and Hybrid GA in Lopes et al [43]. Among those compared algorithms, GRASP+ILP is on average the most effective on this set of benchmark instances followed by ALNS, GVTNS, MACO and SALRP.…”

Green open location-routing problem considering economic and environmental costs

“…The method used to generate the Pareto front is the ò-constraint method, using Ψ2 as objective and Ψ1 as a constraint. Sixteen instances used by Prins et al (2007) are used in order to verify the efficacy of the proposed model and to confirm the observation that by increasing the number of vehicles the fuel consumption and hence total emission can be reduced, in the context of OLRP considering fuel consumption minimization.…”

“…In this study the test scenarios correspond to instances of the literature to the capacitated location-routing problem presented in (Prins et al, 2007), which include 20, 50, 100 and 200 customers and from 5 to 10 deposits. The calculation of consumption of the vehicle was taken from the report of University of Michigan: Transportation Research Institute (2014), in which it is established that the average fuel consumption of a vehicle with these characteristics is 1 gallon per 15.81 km traveled.…”

“…1. Pareto front and three representative optimal solutions for the instance 100_10_2b used by Prins et al (2007) Point B was selected according to the min-max criterion. This solution is characterized by an medium number of depots and vehicles with medium length paths.…”

“…Other solutions along the Pareto front represent different trade-off configurations between these two objectives. ,242 141,192.58 20,528 32,714 6,000 112,304.90 16,229.03 7 3 59,902 138,853.67 20,188 32,714 7,000 110,444.53 15,960.19 19 7 3 62,208 138,413.21 20,124 35,084 7,000 110,094.18 15,909.56 34 7 4 70,789 135,956.99 19,767 44,022 7,000 108,140.50 15,627.24 8 4 71,640 134,931.79 19,618 44,022 8,000 107,325.06 15,509.40 5 9 4 72,611 134,731.32 19,589 44,022 9,000 107,165.60 15,486.36 Table 1 Computational results for instances used by Prins et al (2007) Table 1 presents the results obtained with the proposed model in 16 instances. Columns 2-5 show information about the optimal solution in three different points on the Pareto front: number of routes, number of depots, value of objective function Ψ1, value of objective function Ψ2.…”