Mathematical formulations for the bimodal bus-pedestrian social welfare network design problem

Abstract We face the problem of designing a bus transit network, locating the most convenient bus stops and defining the set of bus lines without considering an a priori set of candidate lines. In order to model the problem, we consider a bimodal network composed of two layers, each one corresponding to a different transportation mode: pedestrian and bus. We propose two exact formulations and compare them by means of the ϵ -constraint method, thus obtaining a set of efficient solutions that simultaneously consider the total user travel time (composed of in-bus travel time, waiting time, walking time and transfer time) and service operator objectives. Finally, the best formulation is tested in a real case scenario.