Optimizing a bi‐objective vehicle routing problem that appears in industrial enterprises

Abstract

In this paper, a new solution method is implemented to solve a bi-objective variant of the vehicle routing problem that appears in industry and environmental enterprises. The solution involves designing a set of routes for each day in a period, in which the service frequency is a decision variable. The proposed algorithm, a muti-start multiobjective local search algorithm (MSMLS), minimizes total emissions produced by all vehicles and maximizes the service quality measured as the number of times that a customer is visited by a vehicle in order to be served. The MSMLS is a neighbourhood-based metaheuristic that obtains high-quality solutions and that is capable of achieving better performance than other competitive algorithms. Furthermore, the proposed algorithm is able to perform rapid movements thanks to the easy representation of the solutions.

A Review of Heuristics and Hybrid Methods for Green Vehicle Routing Problems considering Emissions

“…where the planning horizon is extended to a number of days or periods. +e research of López-Sánchez et al [50] dealt with the bi-objective periodic vehicle routing problem with service choice (Bi-PVRP-SC). +is problem aims to minimize total emissions and maximize the service quality by optimizing a set of vehicle routes for each day of a planning horizon for a fleet of vehicles that starts and ends at a single depot.…”

“…Both sets consider Cartesian coordinates and, just for the 20-customer set, there are four cases representing different demands, namely, the demands vary in dependency of each case, that is, case 1 presents demands equal to 1 unit, case 2 between 1 and 10 units, case 3 between 1 and 100, and case 4 from 1 to 1000. López-Sánchez et al [50] used these instances for the Bi-PVRP-SC. Gaskell [151] presented six cases of study for the CVRP.…”

“…Regarding the existing benchmark for PVRP, Chao-Golden-Wasil [146] presented a set of 19 instances (e.g., López-Sánchez et al [50] for Bi-PVRP-SC). +e locations of the customers and depot in this set take the form of a windmill (1-10) or a Star of David (11)(12)(13)(14)(15)(16)(17)(18)(19) with planning periods of 4 and 6 days, respectively.…”

“…In addition, there are three types of customers for each form depending on the number and frequency of visits required. Referring to the instances generated for MDVRP, the most frequently used one is that which is cited by Cordeau et al [144] named as • E-PCVRP, [125]; HeVRPMD, Eskandarpour et al [65]; WCP-MDP, Wei et al [120]; BSS-EV-LRP, Yang and Sun [67] Chao et al [146] • Bi-PVRP-SC, López-Sánchez et al [50] Taillard [147] • • Eco-WCVRP, Molina et al [123]; BSS-EV-LRP, Yang and Sun [67] Solomon [73] • 2E-VRPSyn, Anderluh et al [46]; mixed-fleet logistics distribution problem under CO 2 emission cap, Islam and Gajpal [101]; HHC with synchronized visits and carbon emissions, Luo et al [102]; MTHVRP-PCIC, Lyu and He [41]; B-MFGVRPTW, Ren et al [104]; G-VRPTW, Yu et al [108]; cold chain logistics path optimization, Zhao et al [100]; G-VRPTW, Sanchez et al [103]; PRP, FCVRP, EMVRP, Kramer et al [53]; G-VRPTW, Küçükoglu et al [117]; PRP, Demir et al [51] • Bi-PVRP-SC, López-Sánchez et al [50] Christofides and Eilon [150] • GVRP, Dewi and Utama [22]; 2E-CVRPSC, Mühlbauer and Fontaine [47]; E-PCVRP, Trachanatzi et al [125]; WCP-MDP, Wei et al [120]; GVRP, de Oliveira da Costa et al [18] Gaskell [151] • GVRP, Dewi and Utama [22] Cordeau instances. +e authors presented a set of 23 instances based the sets from Christofides et al [148] (instances 1-7), Gillett and Johnson [152] (instances 8-11), and Chao et al [146] (12)(13)…”