The Electric Vehicle Routing and Overnight Charging Scheduling Problem on a Multigraph

In the electric vehicle (EV) routing and overnight charging scheduling problem, a fleet of EVs must serve the demand of a set of customers with time windows. The problem consists in finding a set of minimum cost routes and determining an overnight EV charging schedule that ensures the routes’ feasibility. Because (i) travel time and energy consumption are conflicting resources, (ii) the overnight charging operations take considerable time, and (iii) the charging infrastructure at the depot is limited, we model the problem on a multigraph where each arc between two vertices represents a path with a different resource consumption trade-off. To solve the problem, we design a branch-price-and-cut algorithm that implements state-of-the-art techniques, including the ng-path relaxation, subset-row inequalities, and a specialized labeling algorithm. We report computational results showing that the method solves to optimality instances with up to 50 customers. We also present experiments evaluating the benefits of modeling the problem on a multigraph rather than on the more classical 1-graph representation. History: Accepted by Andra Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada through the Discovery grants [Grant RGPIN-2023-03791]. It was also partially funded by HEC Montréal through the research professorship on Clean Transportation Analytics. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0404 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0404 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .