中文摘要：

提出了规模经济条件下的协同运输路线优化问题,引入了分段线性凹成本函数表示协同运输成本的规模经济特征,构造了该问题的混合整数规划模型和求解算法,展开了算法测试,并取得了非常好的计算绩效,同时给出了模型与算法在我国中枢航线网络设计中的应用过程。考虑到协同运输容易因合并运输而延长了路线,扩展了模型与算法,增加了总出行距离的限制。

英文摘要：

This paper presents the route optimization problem of collaborative transportation with economies of scale, while the flow cost is defined by piece-wise linear concave function. We formulate a mixed-integer programming model for the problem and provide heuristics based on LP relaxed model. The computational experiments show the algorithm works well. We also applied the algorithm to Chinese hub-and-spoke airline network design. At last, we discuss the extension problem by adding the constraint of route distance to the model and algorithm, because collaborative transportation may increase the route distance when merging flows.