An Operational Mixed-Integer Programming Model for Autonomous Electric Ride-Hailing Fleets

In this article, we consider an operator of an autonomous electric ride-hailing fleet who must decide, for every vehicle and period, whether to remain in place, travel empty to a rider, carry a rider, or charge at a station. The proposed mixed-integer programming model combines five operational features: deadhead travel to the rider, a tolerance window for pickup, an occupancy state, partial charging at capacitated stations, and energy bought at a time-of-use tariff. The objective combines travel cost, penalties for unserved requests, electricity purchased, and the value of energy left at the horizon end. In addition, we show that, provided the battery has spare capacity in every later period, charging is optimal if and only if this terminal value exceeds the tariff. Computational experiments on instances solved to proven optimality confirm this threshold at three price levels. The results show that the worth of a time-of-use tariff depends on when its cheap hours fall: over a six-hour shift the same revenue-neutral tariff lowers the electricity bill by 38.8% when the cheap hours coincide with the periods in which the fleet charges, and raises it by 16.8% when they do not, with no change in service in either case. Moreover, the terminal value captures this free charging at no cost in service, while a minimum state-of-charge floor is the cheaper way to reach a higher battery target.