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Joint Delay and Cost Optimization for Electric On-Demand Vehicles with In-Route Charging

On-Demand electric vehicle (EV) systems are expected to play a significantly increasing role in near future urban transportation systems, to cope with the massive increases in urban population and reduce global carbon emissions. One inconvenience in MoD-EV systems is the need of some customers to perform in-routing charging, which may cause delays in the trip time. Moreover, the customer choice of which station to charge at is an operational issue for the MoD-EV service operator due to the different pricing for the charging at different stations. Given a connected system linking these EVs and charging stations to the operator, we propose a routing scheme that aims to reduce these inconveniences for both the customers and the operator. By modeling the routing problem between multiple MoD-EV stations with in-route charging as a multi-server queuing system, we formulate the joint problem of minimizing the average overall trip time for all customers, relative to their actual trip time without in-route charging, and the average overall cost of charging as a dual-objective stochastic convex optimization problem. Optimal routing decisions are then derived analytically for any arbitrary weighting of the two problem objectives. Simulation results show the significant merits of our proposed solution as compared to shortest time and random routing decisions. They also illustrate the trade-offs between the delay experienced by the customer and the charging cost for the operator.