In today’s competitive economy , increasing environmental and social awareness, and rising energy and material costs lead to implement more efficient efforts to deal with environmental green house gas emissions’ new laws and regulations. In the field of logistics and traortation, these efforts have been concentrated on minimizing vehicle pollution and have resulted in the emergence of a new concept called Green Logistics . There are several approaches to reach the goal of this concept and achieve a green supply chain. Vehicle Routing Problem (VRP) is the core of these approaches. Green VRP aims to integrate economic and environmental costs and applies efficient and effective methods in order to manage environmental concerns and achieve economic goals. In a distribution system, replacing conventional vehicles that use fossil fuels with emission free vehicles that are more compatible with the environment is an effective approach in Green VRPs. Hybrid electric vehicles are one of green vehicles that use a combination of an electric engine and an internal combustion engine. In this research, we study a hybrid electric VRP. We consider different practical modes of these vehicles and model their different operational constraints using basic assumptions of VRP. We propose a multi-mode hybrid electric VRP with time windows and present a mixed-integer model for this problem. The objective of this model is minimizing total costs of traveled distances in the distribution system. Due to NP-hardness of the problem, we propose a new parallel mathematical-heuristic algorithm to solve the problem. We compare the performance of our algorithm with the results of CPLEX software in the small scale problems. For large scale problems, we first develop two improved versions of Variable Neighborhood Search algorithm. Then, we compare our proposed algorithm with these two ones. Computational results denote the outperformance of the proposed algorithm.
