Branch-and-cut-and-price for the Electric Vehicle Routing Problem with Time Windows, Piecewise-Linear Recharging and Capacitated Recharging Stations

The Electric Vehicle Routing Problem with Time Windows, Piecewise-Linear Recharging and Capacitated Recharging Stations aims to design minimum-cost routes for a fleet of electric vehicles subject to intra-route and inter-route constraints. Every vehicle is equipped with a rechargeable battery that depletes while it transports goods along its route. A vehicle must detour to a recharging station to recharge before draining its battery. To approximate a real recharging process, the amount of energy restored is modeled as a piecewise-linear function of the time spent recharging. Furthermore, each station has a small number of chargers, and hence, when and where a vehicle can recharge must be scheduled around the availability of a charger. This interaction between vehicles does not appear in classical vehicle routing problems and motivates the development of new methods that can exploit the joint routing and scheduling structure. This paper proposes a branch-and-cut-and-price algorithm that designates the routing to integer programming using Dantzig-Wolfe decomposition and the scheduling to constraint programming using logic-based Benders decomposition. Experimental results indicate that this hybrid method solves 34% of the instances with 100 customers.