Transit network design and frequency setting with elastic demand: a mixed-integer linear programming approach

This work introduces a new single-level mixed-integer linear programming framework for the Transit Network Design and Frequency Setting Problem that successfully integrates discrete choice models into a linear formulation. The model aims to capture demand by taking into consideration the travellers’ preferences and activates or deactivates routes at a certain frequency accordingly, from a given pool of possible routes. This work was applied both to an illustrative example and to a case study of the existing bus and Bus Rapid Transit network in an area of the Barcelona Metropolitan Area, comprising 9 lines and 319 origin-destination pairs. For each origin-destination pair, each possible itinerary within the network is pre-computed and is compared against the best itinerary of each of the competing modes of transport, which are obtained using Google Maps. For each itinerary in the network, it is computed its probability of being chosen, based on its utility, using a multinomial logit model, that takes into consideration the access, waiting and travel times, cost, and number of transfers. The coefficients were calibrated using a Stated Preferences Survey. The goal is to maximise the total network demand by tuning the active routes and frequencies, activating the itineraries with the highest probability of being chosen, allocating most or a pre-determined percentage of the demand to them, constrained by number and capacities of buses. The formulation allows for different assumptions on traveller assignment and coverage. The models are solved with exact methods within reasonable computational time and low optimality gaps.