A Multi-Objective Solution of Green Vehicle Routing Problem

Abstract

Distribution is one of the major sources of carbon emissions and this issue has been addressed by Green Vehicle Routing Problem (GVRP). This problem aims to fulfill the demand of a set of customers using a homogeneous fleet of Alternative Fuel Vehicles (AFV) originating from a single depot. The problem also includes a set of Alternative Fuel Stations (AFS) that can serve the AFVs. Since AFVs started to operate very recently, Alternative Fuel Stations servicing them are very few. Therefore, the driving span of the AFVs is very limited. This makes the routing decisions of AFVs more difficult. In this study, we formulated a multi-objective optimization model of Green Vehicle Routing Problem with two conflicting objective functions. While the first objective of our GVRP formulation aims to minimize total CO2 emission, which is proportional to the distance, the second aims to minimize the maximum traveling time of all routes. To solve this multi-objective problem, we used ɛ-constraint method, a multi-objective optimization technique, and found the Pareto optimal solutions. The problem is formulated as a Mixed-Integer Linear Programming (MILP) model in IBM OPL CPLEX. To test our proposed method, we generated two hypothetical but realistic distribution cases in Izmir, Turkey. The first case study focuses on an inner-city distribution in Izmir, and the second case study involves a regional distribution in the Aegean Region of Turkey. We presented the Pareto optimal solutions and showed that there is a tradeoff between the maximum distribution time and carbon emissions. The results showed that routes become shorter, the number of generated routes (and therefore, vehicles) increases and vehicles visit a lower number of fuel stations as the maximum traveling time decreases. We also showed that as maximum traveling time decreases, the solution time significantly decreases.

Karbon salınımını azaltan ve hizmet kalitesini arttıran iki amaçlı yeşil araç rotalama problemi

“…Kabadurmuş vd. [26]'nin çalışmalarında, Erdogan ve Hooks [2]'un Yeşil Araç Rotalama Problemi iki amaçlı hale getirilmiştir. Problemde, karbon salınımı ve maksimum rota süresi en aza indirgenmiştir.…”

“…Kabadurmuş vd. [26] ve Demir vd. [28], bu çalışmadaki çözüm yöntemine benzer şekilde, εkısıtı yöntemini kullanmışlardır.…”

Heterogeneous Fleet Green Vehicle Routing Problem: A Literature Review

“…On the other hand, since AFVs started to operate recently, the AFSs are still very few. Therefore, this condition makes routing decisions for AFVs getting more difficult to do [9].…”

“…There are some researchers who develop GVRP with multiobjective using exact methods. The examples of this method are -Constraint [9,86], mathematical model and try to solve model by using CPLEX software [83], mix integer programming [84], and MILP [85]. For heuristic method, existing researches used Clarke and Wright Savings Heuristic Algorithm (CWSHA) and Sweep Algoritm (SwA) [28], multi-objective evolutionary algorithm (MOEA) [88], planning algorithm and using MOBILE5 software to help in calculating emission [14].…”

“…The purposes were to minimize carbon emission used in the routing [5,6], minimize total travel distance [7,8], and minimize total cost [6]. In order to achieve its environmental purposes, GVRP includes alternative fuel vehicles (AFVs) concept [9]. AFVs is one of the techniques that can be used to reduce the carbon which is one of the important aspects in GVRP theory.…”