Formulation and exact algorithms for electric vehicle production routing problem

•A mathematical formulation for electric vehicle production routing problem.•Homogeneous and heterogeneous fleets of electric vehicles.•Two exact solution methods based on logic-based Benders decomposition.•Numerical experiments to verify the effectiveness of the proposed algorithms. Advanced decision-making models have been recently developed to integrate various aspects of a supply chain, i.e., production, distribution, shipping, and routing. These have resulted in higher productivity and significant cost saving. On the other side, regulations, and incentives to operate Electric Vehicles (EVs) are growing to address the environmental impacts of a supply chain. In this study, we present an Electric Vehicle Production Routing Problem (EVPRP) to achieve optimal decisions. In the proposed problem the limitation of battery capacity and charging facilities is incorporated. In addition, to address the issue of long charging, the option of partial charging is considered using both Heterogeneous (HT) and Homogeneous (HM) fleets. We propose a mixed-integer linear programming model for the EVPRP, which is mathematically validated by solving (via CPLEX) the new instances generated compatible with the EVPRP. Due to the NP-hardness of the EVPRP model, which cannot solve large-scale instances by a commercial solver, we develop two types of exact algorithms named, Logic-Based Benders Decomposition (LBBD) algorithms. The first one is based on each vehicle in each period (LBBDvt), and the second algorithm is applied for each period (LBBDt). The performance of the proposed model and LBBD algorithms is validated through the computational experiments on the HM and HT EVPRP data sets. The computational results show that the proposed exact algorithms clearly outperform the MIP formulation solved by Cplex as well as demonstrate the efficiency of both algorithms in finding high-quality solutions.