A Mixed Integer Programming Model for Location-Routing Problem of Electric Vehicles: A Case Study

Location-routing problem is one of the most studied topics to minimize logistic costs among researchers due to its essential role in the success of companies. Nowadays, since companies also try to minimize the consumption of products that have adverse effects on global warming, electric vehicles are efficient tools to reduce carbon emissions. The usage of EVs raises a new problem in determining the location of charging stations while creating routes due to their low range compared to fossil fuel vehicles. In this paper, a mixed integer programming model is developed to simultaneously determine the number and location of charging stations, the number of electric vehicles, and their routes with time windows within a unified decision-making framework, while accounting for vehicle capacity, battery range, charging duration, and return-time requirements and preventing subtours through time-windowconstraints rather than explicit subtour-elimination constraints. The model is tested on 15 instances derived from the operations of a cargo company with one depot and 29 distribution centers in Bursa, Türkiye, under vehicle-range scenarios of 100 and 150 km. Feasible solutions are obtained for all instances within the specified time limit.