A quantitative approach for the long-term assessment of Railway Rapid Transit network construction or expansion projects

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.