A geometric model for an effective rescheduling after reducing service in public transportation systems

Railway systems in metropolitan areas carry a high density of traffic daily, heterogeneously distributed, and exposed to the negative consequences derived from service disruptions. An interesting topic in the literature is to obtain performance protocols in the presence of contingencies which can affect the system operation, avoiding the propagation of perturbation and minimizing its consequences. The objective of this paper is to assess the decision of rescheduling the train service, reducing the current supply along one transportation line in order to reinforce the service of another line, exploited by the same public operator, which has suffered an incidence or emergency. A methodology, based on a geometric representation of solutions which allows the use of discrete optimization techniques, is developed in order to attend to the underlying demand with efficiency criteria in this context of unexpected incidents.