Cooperative Operation of the Fleet Operator and Incentive-Aware Customers in an On-Demand Delivery System: A Bilevel Approach

In this article, 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 customers’ delivery time flexibility. In order to capture the interaction between the fleet operator and customers, a novel bilevel optimization framework is proposed. By exploiting the strong duality, and the Karush–Kuhn–Tucker (KKT) optimality condition of customer optimization problems, we can reformulate the bilevel optimization problem as a mixed-integer nonlinear programming (MINLP) 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.