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/ .

Abstract This article introduces formulations and an exact algorithm for the workforce scheduling and routing problem with park‐and‐loop. This problem extends the standard workforce scheduling and routing problem by allowing the use of walking subtours in the routes. We introduce a compact arc‐based formulation as well as a path‐based formulation with an exponential number of variables. To efficiently solve the latter, we propose a branch‐price‐and‐cut algorithm that leverages state‐of‐the‐art techniques, including a tailored version of the pulse algorithm to solve the pricing problem and the separation of subset row inequalities to strengthen the lower bound. We report on computational experiments carried out on a set of instances with up to 75 tasks adapted from the literature. The results show that our method systematically outperforms a standard MIP solver, proving optimality for 241 out of 324 instances. We also report experiments on the closely‐related service technician routing and scheduling problem, where our method delivered 12 new best solutions on a 54‐instance testbed from the literature.

Electric vehicles offer a pathway to more sustainable transportation, but their adoption entails new challenges not faced by their petroleum-based counterparts. A difficult task in vehicle routing problems addressing these challenges is determining how to make good charging decisions for an electric vehicle traveling a given route. This is known as the fixed route vehicle charging problem. An exact and efficient algorithm for this task exists, but its implementation is sufficiently complex to deter researchers from adopting it. In this work we introduce frvcpy, an open-source Python package implementing this algorithm. Our aim with the package is to make it easier for researchers to solve electric vehicle routing problems, facilitating the development of optimization tools that may ultimately enable the mass adoption of electric vehicles. Summary of Contribution: This work describes a novel software tool for the vehicle routing community. The tool, frvcpy, addresses one of the primary challenges faced by the vehicle routing community when considering problems involving the adoption of electric vehicles (EVs): how to make optimal charging decisions. The state-of-the-art algorithm for solving these problems is sufficiently complex to deter researchers from using it, leading them to adopt less robust methods. frvcpy offers an easy-to-use, lightweight implementation of this algorithm, providing optimal solutions in low (∼5 ms) runtime. It is designed to be easily embedded in larger solution schemes for general EV routing problems, requiring minimal input, offering compatibility with the community standard file types, and offering access both through the command line and a Python API. The tool has thus far proven adaptable, having been used by researchers studying EV routing problems with novel constraints. Our aim with frvcpy is to make it easier for researchers to solve EV routing problems, facilitating the development of optimization tools that may contribute toward the mass adoption of electric vehicles.