A pickup and delivery problem under the assumption of stochastic battery depletion of electric vehicles

Logistics activities play a critical role in the supply chain, in terms of on-time product delivery and successful implementation of production/service processes. Electric vehicles, rather than fossil fuel vehicles, can be used in freight transportation activities in urban areas to lower the carbon footprint of logistic operations. However, there are considerable infrastructure gaps in electric vehicle battery swap/charging facilities. As a result, optimizing electric vehicle travel routes has become increasingly complicated and essential. There are some concerns regarding the use of electric vehicles in transport activities. Vehicle speed might fluctuate based on traffic density at different times of the day, particularly in urban transportation operations. Uncertainty in vehicle speed can have an impact on energy consumption. Therefore, it is significant to address speed and energy consumption uncertainty while planning logistics operations. Furthermore, the risk of vehicles running out of batteries before completing the planned route elevates drivers' range anxiety and may result in increased penalty costs for businesses. In this study, a many-to-many pickup and delivery problem, which is a variant of a vehicle routing problem, is addressed. Unlike previous attempts in the literature on the same type of problem, here, electric vehicles are employed for delivery operations and the energy consumption of vehicles is not known in advance. From this point of view, in this study, a Quadratic Chance Constraint Mixed-Integer Programming model and a heuristic solution approach are proposed for the many-to-many pickup and delivery problem using electric vehicles. The numerical analyses highlight the importance of estimating energy consumption in detail and addressing the uncertainty in energy consumption. According to the findings, it has been revealed that the uncertainty of energy consumption affects the distribution plans and the amount of energy consumed by the vehicles along the route. Considering the uncertainty of energy consumption reduces drivers' range anxiety and avoids unexpected costs such as vehicle downtime and inability to deliver products on time.