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以港口为节点的区域物流与其所在地区的区域经济相互影响、协调发展. 本文研究了二级港口物流网络问题，即港口之间的海上航线系统以及各个港口与其经济腹地之间的集疏运系统的二级网络. 在动态腹地条件下，构建以区域港口群总运输成本为上层优化目标，以个体港口的经济效益为下层目标的双层规划模型. 模型反映了港口竞争力、腹地划分以及运力配备的动态性，因此更接近港口实际. 为有效求解模型，利用Kuhn-Tucker理论将双层规划问题转化成单层规划模型，并且应用算例对模型和算法的有效性进行验证，最后通过Matlab对模型进行了求解. 数值结果表明，双层规划模型及求解方法具有可行性.

Optimization of Two-Stage Port Logistics Network of Dynamic Hinterland Based on Bi-level Programming Model

The regional logistics based on port and its regional economic react on each other and develop in unison. This paper studies the two-stage port logistics network, the first one is the sea routes system between any two ports, and the second one is the network of the transportation system between each port and its economic hinterland. Based on the conditions of dynamic hinterland, the study proposes a bi-level programming model with the upper objective of the total transportation cost in the regional port cluster and the lower objective of the economic benefits for individual port. The competitiveness of the port, the demarcation of the hinterland, and the traffic capacity are reflected dynamically in the model, which is closer to the real system. The model is transformed into a single-programming model based on the Kuhn-Tucker theory to solve the model. Numerical tests are provided to illustrate the validity of the model and algorithm. Finally, the example is solved by Matlab. The results show that the bi-level model and the algorithm are feasible.