Modifying the service patterns of public transport vehicles to account for the COVID-19 capacity

As public transport operators try to resume their services, they have to operate under reduced capacities due to COVID-19. Because demand can exceed capacity at different areas and across different times of the day, drivers have to refuse passenger boardings at specific stops. Towards this goal, many public transport operators have modified their service routes by avoiding to serve stops with high passenger demand at specific times of the day. Given the urgent need to develop decision support tools that can prevent the overcrowding of vehicles, this study introduces a dynamic integer nonlinear program that proposes service patterns to individual vehicles that are ready to be dispatched. In addition to the objective of satisfying the imposed vehicle capacity due to COVID-19, the proposed service pattern model caters for the waiting time of passengers. Our model is tested in a bus line connecting the university of Twente with its surrounding cities demonstrating the improvement in terms of vehicle overcrowding, and analyzing the potential negative effects related to unserved passenger demand and excessive waiting times

Public Transport Optimization

This textbook provides a comprehensive step-by-step guide for new public transport modelers. It includes an introduction to mathematical modeling, continuous and discrete optimization, numerical optimization, computational complexity analysis, metaheuristics, and multi-objective optimization. These tools help engineers and modelers to use better existing public transport models and also develop new models that can address future challenges. By reading this book, the reader will gain the ability to translate a future problem description into a mathematical model and solve it using an appropriate solution method. The textbook provides the knowledge needed to develop highly accurate mathematical models that can serve as decision support tools at the strategic, tactical, and operational planning levels of public transport services. Its detailed description of exact optimization methods, metaheuristics, bi-level, and multi-objective optimization approaches together with the detailed description of implementing these approaches in classic public transport problems with the use of open source tools is unique and will be highly useful to students and transport professionals.</p

The multi-vehicle dial-a-ride problem with interchange and perceived passenger travel times

The Dial-a-Ride Problem (DARP) introduced in the early 1980s is the NP-Hard optimization problem of developing the most cost-efficient vehicle schedules for a number of available vehicles that have to start from a depot, pick up and deliver a set of passengers, and return back to the same depot. DARP has been used in many modern applications, including the scheduling of demand-responsive transit and car pooling. This study departs from the original definition of DARP and it extends it by considering an interchange point where vehicles can exchange their picked-up passengers with other vehicles in order to shorten their delivery routes and reduce their running times. In addition to that, this study introduces the concept of generalized passenger travel times in the DARP formulation which translates the increased in-vehicle crowdedness to increased perceived passenger travel times. This addresses a key issue because the perceived in-vehicle travel times of passengers might increase when the vehicle becomes more crowded (i.e., passengers might feel that their travel time is higher when they are not able to find a seat or they are too close to each other increasing the risk of virus transmission or accidents). Given these considerations, this study introduces the Dial-a-Ride Problem with interchange and perceived travel times (DARPi) and models it as a nonlinear programming problem. DARPi is then reformulated to a MILP with the use of linearizations and its search space is tightened with the addition of valid inequalities that are employed when solving the problem to global optimality with Branch-and-Cut. For large problem instances, this study introduces a tabu search-based metaheuristic and performs experiments in benchmark instances used in past literature demonstrating the computation times and solution stability of our approach. The effect of the perceived passenger travel times to the vehicle running costs is also explored in extensive numerical experiments.</p