Polyhedral study for the delay management problem in public transportation

The Delay Management Problem for Public Transportation (DMP) arises in the context of the operational management of an intermodal public transportation network and has the aim of increasing the attractiveness of the network itself. Many passengers often have to use different lines to cover the trip from their origin to the desired destination and the attractiveness of the network is strongly related to the reliability of connections between vehicles. As a consequence, operational decisions are required to protect connections against some unpredictable events like breakdowns or vehicle delays. In such cases, operators have to determine if the connected vehicles should wait for the delayed ones or keep their schedule. The DMP consists of defining the wait/depart policy which minimizes the total delay on the network. In this work, we present a polyhedral study of the DMP. In particular, some new valid inequalities are presented, based on the 0-1 knapsack problem with a single continuous variable. We show that they represent facets for the convex-hull of some special cases of the DMP. The same inequalities are valid for the general case and they can be integrated in a Branch and Cut procedure.