  Fixed pickup and delivery times can strongly limit the performance of freight
transportation. Against this backdrop, fleet operators can use compensation
mechanisms such as monetary incentives to buy delay time from their customers,
in order to improve the fleet efficiency and ultimately minimize the costs of
operation. To make the most of such an operational model, the fleet activities
and the incentives should be jointly optimized accounting for the customers'
reactions. Against this backdrop, this paper presents an incentive-aware
electric vehicle routing scheme in which the fleet operator actively provides
incentives to the customers in exchange of pickup or delivery time flexibility.
Specifically, we first devise a bi-level model whereby the fleet operator
optimizes the routes and charging schedules of the fleet jointly with an
incentive rate to reimburse the delivery delays experienced by the customers.
At the same time, the customers choose the admissible delays by minimizing a
monetarily-weighted combination of the delays minus the reimbursement offered
by the operator. Second, we tackle the complexity resulting from the bi-level
and nonlinear problem structure with an equivalent transformation method,
reformulating the problem as a single-level optimization problem that can be
solved with standard mixed-integer linear programming algorithms. We
demonstrate the effectiveness of our framework via extensive numerical
experiments using VRP-REP data from Belgium. Our results show that by jointly
optimizing routes and incentives subject to the customers' preferences, the
operational costs can be reduced by up to 5%, whilst customers can save more
than 30% in total delivery fees.
