Setting services in public transit lines in short time periods under time-varying demand

:This paper focuses on a mathematical programming based model for setting the schedule of a given number of services on a public transportation network. The structure of the model is that of a time-expanded or diachronic network, where origin to destination flows vary dynamically over a short time horizon (several hours) and are assumed to be known deterministically. The model basically aims to minimize the total travel time of passengers during the time horizon by properly setting the lag times between services on the lines and thereby accommodating conveniently the schedules of the services on different lines in order to enhance transfers. Two different types of diachronic networks are considered, in which three basic algorithmic alternatives have been tested: a heuristic method based on the classical projected gradient, Benders decomposition, and a combination of both. Among other applications, the model can potentially be applied in operational aspects for disruption recovery in Rail-Rapid Transit and Suburban Railway systems by using bus shuttles or auxiliary bus lines. The computational viability of the model, in terms of adequate response time, is shown using test networks of auxiliary bus lines. Its computational performance in readjusting schedules for larger suburban rail systems is also evaluated.