This paper studies an intermodal container terminal (IMT) location and design problem, where the IMT operator wants to locate a set of open-access IMTs and design their capacity levels to maximize its profit. Following the IMT operator’s decisions, network users, responsible for container transportation, will independently choose their routes and may procure intermodal services from the IMT operator. Since only limited information is available before the existence of the network, we employ the entropy maximization principle as a least-biased approach to estimate the flow distribution resulting from the network users’ route choices. This enables the IMT operator to predict profit and evaluate the quality of its network design decisions. We formulate the problem as a mixed-integer bilevel nonlinear program, automatically embedding a decentralized flow estimation scheme into the optimization of IMT location and capacity design. By exploring the rationale behind the entropy maximization principle, our problem can also be interpreted as a leader–follower game, in which the IMT operator (as the leader) aims to maximize its profit and the network users (as the follower) maximize their welfare. Due to the bilevel structure and the nonlinear entropy function, the problem is extremely changeling. To support its application in real-world contexts, we propose both exact and approximation algorithms. Finally, we conduct a real-world case study on Sydney Greater Metropolitan Area and draw managerial implications.

中文翻译：

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多式联运集装箱码头位置和容量设计，采用分散式流量估算


本文研究了多式联运集装箱码头 （IMT） 的位置和设计问题，其中 IMT 运营商希望找到一组开放式 IMT 并设计其容量水平以最大化其利润。根据 IMT 运营商的决定，负责集装箱运输的网络用户将独立选择其路线，并可以从 IMT 运营商处购买多式联运服务。由于在网络存在之前只有有限的信息可用，因此我们采用熵最大化原则作为最小偏差方法来估计网络用户路由选择产生的流量分布。这使 IMT 运营商能够预测利润并评估其网络设计决策的质量。我们将问题表述为混合整数双层非线性规划，自动将分散式流量估计方案嵌入到 IMT 位置和容量设计的优化中。通过探索熵最大化原则背后的基本原理，我们的问题也可以解释为领导者-追随者博弈，其中 IMT 运营商（作为领导者）旨在最大化其利润，而网络用户（作为追随者）最大化他们的福利。由于双层结构和非线性熵函数，这个问题非常多变。为了支持其在实际环境中的应用，我们提出了精确和近似算法。最后，我们对悉尼大都会区进行了真实案例研究，并得出了管理意义。