  In this paper, we study the cooperative operation problem between the fleet
operator and incentive-aware customers in an on-demand delivery system.
Specifically, the fleet operator offers discounts on transportation costs in
exchange of the delivery time flexibility of customers. In order to capture the
interaction between the fleet operator and customers, a novel bi-level
optimization framework is proposed. By exploiting the strong duality, and the
KKT optimality condition of customer optimization problems, we can reformulate
the bi-level optimization problem as a mixed integer nonlinear programming
problem. Considering the inherent difficulties of MINLP, a computationally
efficient algorithm, which combines the merits of Lagrangian dual decomposition
and Benders decomposition, is devised to solve the resulting MINLP problem in a
distributed manner. Finally, extensive numerical experiments demonstrate that
the proposed cooperation scheme can decrease the delivery fees for the
customers, and reduce the operation cost of the fleet operator at the same
time, thus leading to a win-win situation for both sides.
