One of the main issues to address in the analysis of a public railway rapid transit network construction project is the assessment of expected revenue and cost. On a network topology already defined, the problem considered in this paper consists on finding the construction schedule that maximizes the project long-term net profit, not only deciding on the construction schedule and the network operation but also determining the subsidy to compensate the service operator along the considered long-term planning horizon. Aiming at early attending the demand of citizens, partial pieces of the constructed lines are put into service as soon as they were finished. Hence, in order to determine a subsidy to compensate service operators from a possible non-profitable network operation, it is necessary to measure the variable operation costs that emerge along with the progressive enlargement of a connected network. Further, the problem can be viewed as a particular case of a multiple resource-constrained scheduling problem, where both, the budget and the construction equipment availability act as limiting resources. We propose a non-linear mixed integer programming model which is fully linearized and solved by using a two-phase branch-and-cut procedure. We illustrate the proposed methodology within a real case, the Metro network project of the city of Seville.

在分析公共铁路快速运输网络建设项目时要解决的主要问题之一是对预期收入和成本的评估。在已经定义的网络拓扑上，本文考虑的问题在于找到使项目长期净利润最大化的施工进度，不仅要决定施工进度和网络运营，还要确定补贴以补偿服务运营商沿长期规划的视野。为了尽早满足市民的需求，部分建成的线路一建成便投入使用。因此，为了确定补贴以补偿服务运营商可能的非盈利网络运营，有必要测量随着连接网络的逐步扩大而出现的可变运营成本。此外，该问题可以看作是多资源受限的调度问题的一种特殊情况，其中预算和建筑设备的可用性两者都是限制资源。我们提出了一种非线性混合整数规划模型，该模型可以完全线性化并通过使用两阶段分支切分法来求解。我们在实际案例中说明了所建议的方法，即塞维利亚市的地铁网络项目。我们提出了一种非线性混合整数规划模型，该模型可以完全线性化并通过使用两阶段分支切分法来求解。我们在实际案例中说明了所建议的方法，即塞维利亚市的地铁网络项目。我们提出了一种非线性混合整数规划模型，该模型可以完全线性化并通过使用两阶段分支切分法来求解。我们在实际案例中说明了所建议的方法，即塞维利亚市的地铁网络项目。