Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie A model for capacitated green vehicle routing problem with the time- varying vehicle speed and soft time windows Zhitao Xu a , Adel Elomri b , Shaligram Pokharel c, ⁎ , Fatih Mutlu d a College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 29 Jiangjun Avenue, Nanjing 211106, China b Division of Engineering Management and Decision Sciences, College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar c Department of Mechanical and Industrial Engineering, Qatar University, Doha, Qatar d ICRON Technologies, Istanbul, Turkey ARTICLE INFO Keywords: Green logistics Capacitated vehicle routing problem Time-varying speed Fuel consumption Traveling salesman problem ABSTRACT This paper investigates the capacitated green vehicle routing problem (GVRP) with time-varying vehicle speed and soft time windows. The GVRP is developed as a multi-objective mixed integer nonlinear programming (MINLP) model that incorporates a fuel consumption calculation algorithm. The proposed model considers the vehicle load and capacity as well as time-varying speed in order to account for trafc congestion. An improved non-dominated sorting genetic algorithm (NSGA-II) with adaptive strategies and greedy strategies is developed to solve the GVRP. The results of numerical experiments show that the consumption of fuel in a supply chain can be decreased sharply without any signifcant loss in customer satisfaction. The proposed NSGA-II has a better capability and efciency than the original NSGA-II. Our experiments also indicate that the proposed model outperforms most of the best-known solutions obtained from the traditional modeling approaches. 1. Introduction There is a worldwide consensus that global warming and emission of greenhouse gases (GHGs) are the challenges of the century. Logistics, particularly the freight transportation is considered as one of the major contributors to these emissions (Sureeyatanapas, Poophiukhok, & Pathumnakul, 2018). For instance, transportation accounts for about 21% of global carbon emissions (Bühler & Jochem, 2008; Jabali, Woensel, & de Kok, 2012). The importance of greening supply chains is also emphasized in a recent review by Xu, Elomri, Pokharel, and Mutlu (2019). Thus, not only the cost optimization but also the sustainability of logistic networks has become important (Poonthalir & Nadarajan, 2018). Researchers have extended the vehicle routing problems (VRPs) to consider environmental impacts. The well-known VRP (Huang, Blazquez, Huang, Paredes-Belmar, & Latorre-Nuñez, 2019; Rezgui, Chaouachi Siala, Aggoune-Mtalaa, & Bouziri, 2019) primarily focus on the economic impact of vehicle routes in distribution networks. The extension of these models to consider environmental impact is a recent phenomenon. This type of extended VRPs is named as the Green Vehicle Routing Problem (GVRP) by various authors (such as Koç & Karaoglan, 2016; Poonthalir & Nadarajan, 2018; Tiwari & Chang, 2015; Yin & Chuang, 2016). The GVRP is characterized by the objective of harmonizing the environmental and economic costs. This is to be achieved through the design of efective routes to meet both the ecological and fnancial concerns under a variety of other constraints imposed by diferent models (such as vehicle capacity and time window). For the GVRP, the carrier frms and their customers have diferent concerns. The carrier frms focus on the design of vehicle routes to reduce carbon emissions. Xu et al. (2017a, 2017b) mention that this type of concern can be due to the emissions constraints or carbon policies faced by the frm. Speed factor is one of the important considerations for vehicle routes as the road speed changes due to various reasons including congestion, thus leading to a higher level of emissions (Franceschetti et al., 2017). Therefore, the GVRP should consider the time-of-the-day dependent travel times to cover a particular distance (Jabali et al., 2012). From the customers’ point of view, the product needs to be received within the specifed time windows (Pérez-Rodríguez & Hernández-Aguirre, 2019; Poonthalir & Nadarajan, 2018; Pradenas, Oportus, & Parada, 2013; Qian & Eglese, 2016). Therefore, delivery outside the time windows may require the carrier to pay penalties (Afshar-Bakeshloo, Mehrabi, Safari, Maleki, & Jolai, 2016; Taş, Dellaert, Van Woensel, & De Kok, 2013; Taş, Gendreau, Dellaert, van Woensel, & de Kok, 2014). Recent research on minimizing emissions in models related to the GVRP can be divided into two main categories. In the frst category, the https://doi.org/10.1016/j.cie.2019.106011 Received 16 August 2018; Received in revised form 7 June 2019; Accepted 6 August 2019 ⁎ Corresponding author. E-mail address: shaligram@qu.edu.qa (S. Pokharel). Computers & Industrial Engineering 137 (2019) 106011 Available online 09 August 2019 0360-8352/ © 2019 Elsevier Ltd. All rights reserved. T