Journal of Optimization in Industrial Engineering Vol.13, Issue 2, Summer & Autumn 2020, 165-183 DOI:10.22094/JOIE.2020.1871922.1667 165 A New Mathematical Model for the Green Vehicle Routing Problem by Considering a Bi-Fuel Mixed Vehicle Fleet Neda Manavizadeh a,* , Hamed Farrokhi-Asl b , Stanley Frederick W.T. Lim d a Department of Industrial Engineering, KHATAM University, Tehran, Iran b School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran c Institute for Manufacturing, University of Cambridge, Cambridge, United Kingdom d W.P. Carey School of Business, Arizona State University, Tempe, United States Received 21 June 2019; Revised 09 December 2019; Accepted 23 February2020 Abstract This paper formulates a mathematical model for the Green Vehicle Routing Problem (GVRP), incorporating bi-fuel (natural gas and gasoline) pickup trucks in a mixed vehicle fleet. The objective is to minimize overall costs relating to service (earliness and tardiness), transportation (fixed, variable and fuel), and carbon emissions. To reflect a real-world situation, the study considers: (1) a comprehensive fuel consumption function with a soft time window, and (2) an en-route fuel refueling option to eliminate the constraint of driving range. A linear set of valid inequalities for computing fuel consumption were introduced. In order to validate the presented model, first, the model is solved for an illustrative example. Then each component of cost objective function is considered separately so as to investigate the effects of each part on the obtained solutions and the importance of vehicles speed on transportation strategies. Computational analysis shows that, despite the limitation of an appropriate service infrastructure, the proposed model demonstrated an average reduction of 44%, 6% and 5% in carbon emission costs, total distribution costs, and transportation costs respectively. Moreover, the study found paradoxical effects of average speed, suggesting the need to manage trade-offs: while higher speeds reduced service costs, they increased carbon emission costs. In the next stage, some experiments modified from the literature are solved. According to these experiments, in all instances greater objective function values for Gasoline vehicles are gained. The difference in the carbon emission objective is also significant, with an average of 44.23% increase. Finally, managerial and institutional implications are discussed. Keywords: Green vehicle routing; Carbon emission; Bi-fuel light truck; Soft time window; Green logistics 1. Introduction Transportation has various hazardous effects on the environment (Koҫ and Karaoglan, 2016), including toxic effects on ecosystems, noise pollution, acidification, depletion of the ozone layer, and the greenhouse effect (Knörr, 2011). Globally, road transportation contributes an estimated 21% of the overall carbon dioxide (CO 2 ) emissions (Jabali, Woensel, and de Kok 2012). Consequently, institutions are implementing freight regulations and carbon emission policies in order to regulate vehicle footprints and limit emissions by companies (Quak and Dekoster, 2007; Bynum et al. 2018). In response, firms are pressured to implement ―green logistics‖ initiatives in order to reduce their carbon footprint. A commonly adopted approach in the transportation industry, which utilizes analytical modeling to optimize vehicle routing and scheduling, in order to reduce the overall travelled distance and the corresponding carbon emissions. The study of vehicle routing problems (VRP) has evolved overtime since its inception in 1959 (Dantzig and Ramser, 1959), in an attempt to capture these emerging trends. This triggered the modifications to traditional VRPs, where environmental constraints were incorporated into the planning and management of vehicles (Rabbani et al., 2016; Rabbani et al. 2018; Farrokhi-Asl et al. 2018). These modifications have, amongst others, produced a new variant of VRP known as the Green VRP (GVRP) (Lin et al, 2014), with the objective of minimizing fuel consumption or CO 2 emissions and operating costs, concomitantly fulfilling customer demanded service levels (Bektaş and Laporte, 2011). While the extant literature has focused exclusively either on fossil fuel vehicles or alternative fuel vehicles (AFVs) in GVRP modeling, the benefits of hybridization (i.e. bi- fuel) to address the shortcoming of higher carbon emission intensity (Association, 2004) and price associated with fossil fuel or the lack of an appropriate service infrastructure and the constraint in driving range, associated with alternative fuel (e.g. compressed natural gas [CNG]), have promoted increasing adoptions in the transportation industry. Companies are gradually equipping their production lines with bi-fuel pickup trucks *Corresponding author Email address: n.manavi@khatam.ac.ir