An extended rolling stock problem with empty trains timetabling through a heuristic approach

In this article, we address a variant of the rolling stock (RS) problem in dense railway systems within a metropolitan context. It consists in determining every train composition and scheduling empty trains to efficiently fit the demand. By empty trains we refer to scheduled trips where trains travel along the system without carrying passengers. A heuristic is presented to generate eligible slots for empty trains.Two objective functions are considered: minimizing the amount of RS and minimizing its usage (number of kilometres). An illustrative case study corresponding to the C5 line of a Spanish railway is presented.