Strengthened Formulations and Valid Inequalities for Single Delay Management in Public Transportation

Abstract

The delay management problem arises in public transportation networks, often characterized by the necessity of connections between different vehicles. The attractiveness of public transportation networks is strongly related to the reliability of connections, which can be missed when delays or other unpredictable events occur. Given a single initial delay at one node of the network, the delay management problem is to determine which vehicles have to wait for the delayed ones, with the aim of minimizing the dissatisfaction of the passengers. In this paper, we present strengthened mixed integer linear programming formulations and new families of valid inequalities. The implementation of branch-and-cut methods and tests on a benchmark of instances taken from real networks show the potential of the proposed formulations and cuts.

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“…[21] propose two classes of valid inequalities for P based on mixedinteger rounding and lifting function, namely, the continuous cover and continuous packing (reversed cover) inequalities. We follow a similar idea to strengthen the formulation for LCIM, with moderate modification as P ⊂ P. Applications of continuous cover and continuous packing inequalities for P can be seen in delay management for public transportation [22], job scheduling with uncertain multiple resources [23], discrete lot sizing [24] and single-item capacitated lot sizing [25]. They can also be extended to solve general mixed-integer optimization that contains mixed 0-1 knapsack set with bounded continuous variables, see [26,27,28].…”