This paper considers the vehicle routing problem of a fleet operator to serve a set of transportation requests with flexible time windows. That is, the operator presents discounted transportation costs to customers to exchange the time flexibility of pickup or delivery. A win-win routing schedule can be achieved via such a process. Different from previous research, we propose a novel bi-level optimization framework, to fully characterize the interaction and negotiation between the fleet operator and customers. In addition, by utilizing the property of strong duality, and the KKT optimality condition of customer optimization problem, the bi-level vehicle routing problem can be equivalently reformulated as a mixed integer nonlinear programming (MINLP) problem. Besides, an efficient algorithm combining the merits of Lagrangian dual decomposition method and Benders decomposition method, is devised to solve the resultant MINLP problem. Finally, extensive numerical experiments are conducted, which validates the effectiveness of proposed bi-level model on the operation cost saving, and the efficacy of proposed solution algorithm on computation speed.
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