# An optimization model for line planning and timetabling in automated urban metro subway networks

## TL;DR

This paper introduces a mixed integer nonlinear programming model for optimizing line planning and timetabling in automated urban metro networks, considering cost, passenger demand, and technical constraints.

## Contribution

It presents a novel integrated optimization model and a Math-Heuristic solution approach for complex metro network planning problems.

## Key findings

- Model effectively incorporates demand, technical features, and operational decisions.
- The Math-Heuristic provides practical solutions for real-world networks.
- Computational experiments demonstrate the model's applicability and efficiency.

## Abstract

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation systems from both, a cost-oriented and a passenger-oriented perspective, as time-dependent demands, interchange stations, short-turns and technical features of the trains in use. The incoming flows of passengers are modeled by means of piecewise linear demand functions which are parameterized in terms of arrival rates and bulk arrivals. Decisions about frequencies, train capacities, short-turning and timetables for a given planning horizon are jointly integrated to be optimized in our model. Finally, a novel Math-Heuristic approach is proposed to solve the problem. The results of extensive computational experiments are reported to show its applicability and effectiveness to handle real-world subway networks