Integer programming formulations for the time-dependent elementary shortest path problem with resource constraints

GONZALO LERA ROMERO; JUAN JOSÉ MIRANDA BRONT

Ciudad Autónoma de Buenos Aires

Workshop; MIPAR 2018; 2018

Departamento de Computación, FCEyN, UBA

The impact of congestion in transportation has become one of the main concerns regarding urban planing in large cities. Time-Dependent Vehicle Routing Problems (TDVRPs) is the name given to a broad family of VRPs that explicitly incorporate the congestion by considering variable travel times. In this paper we study the Time-Dependent Elementary Shortest Path Problem with Resource Constraints (TDESPPRC), that appears as the pricing sub-problem in column generation-based approaches for TDVRPs. We consider two integer programming formulations which exploit the characteristics of the time-dependent travel time function and are evaluated on benchmark instances. On preliminary computational experiments, the approach is able to effectively solve instances with up to 25 vertices in reasonable times, showing its potential to be used within a Branch and Price algorithm.