Optimization models for the single delay management problem in public transportation

Passengers travelling in public transportation networks often have to use different lines to cover the trip from their origin to the desired destination. As a consequence, the reliability of connections between vehicles is a key issue for the attractiveness of the intermodal transportation network and it is strongly affected by some unpredicable events like breakdowns or vehicle delays. In such cases, a decision is required to determine if the connected vehicles should wait for the delayed ones or keep their schedule. The Delay Management Problem (DMP) consists in defining the wait/depart policy which minimizes the total delay on the network. In this work, we present two equivalent Mixed Integer Linear Programming models for the DMP with a single intial delay, able to reduce the number of variables with respect to the formulations proposed by literature. The two models are solved by a ∗The research is part of the project “Analysis and Optimization of Intermodal Public Transportation Networks in the Brussels Capital Region” funded by the Brussels-Capital Region in the context of the Prospective Research for Brussels program.