Optimization of Fare Structure and Service Frequency for Maximum Profitability of Transit Systems

Abstract

Providing efficient public transportation has been recognized as a potential way of alleviating congestion, improving mobility, mitigating air pollution, and reducing energy consumption. Many people use public transportation systems for their daily commute, while others use different transportation modes (e.g. cars, taxis, carpools, etc.). Inexpensive fares with good transit service encourages ridership, and the resulting revenue may be used to provide better service. Optimization of transit service frequency and its associated fare structure is desirable in order to increase revenue at reasonable transit operating expenditure. The objective of the study reported here is to maximize profit subject to service capacity constraint, while elastic demand is considered. The solution methodology is developed and applied to solve the profit maximization problem in a case study based on Newark, NJ, USA. Numerical results, including optimal solutions and sensitivity analyses, are presented. It is found that an optimal temporal headway and differential fare structure that maximizes total profit for the studied subway system can be efficiently solved.     

Optimal stop spacing and headway of congested transit system considering realistic wait times

Abstract

This paper revisits the classical transit scheduling problem and investigates the relationship between stop spacing and headway, considering realistic wait time and operable transit capacity. Headway and stop spacing are important determinants for planning a transit system, which influence the service level as well as the cost of operation. A mathematical model is developed, and the objective function is user travel time which is minimized by the optimized stop spacing and headway, subject to the constraints of operable fleet size and route capacity. Optimal stop spacing and headway solutions are obtained in a numerical example. Sensitivity analysis is conducted, and the effect of model parameters on user travel time is explored.     

Multi-objective re-synchronizing of bus timetable: Model,complexity and solution

This work is originally motived by the re-planning of a bus network timetable. The existing timetable with even headways for the network is generated using line by line timetabling approach without considering the interactions between lines. Decision-makers (i.e., schedulers) intend to synchronize vehicle timetable of lines at transfer nodes to facilitate passenger transfers while being concerned with the impacts of re-designed timetable on the regularity of existing timetable and the accustomed trip plans of passengers. Regarding this situation, we investigate a multi-objective re-synchronizing of bus timetable (MSBT) problem, which is characterized by headway-sensitive passenger demand, uneven headways, service regularity, flexible synchronization and involvement of existing bus timetable. A multi-objective optimization model for the MSBT is proposed to make a trade-off between the total number of passengers benefited by smooth transfers and the maximal deviation from the departure times of the existing timetable. By clarifying the mathematical properties and solution space of the model, we prove that the MSBT problem is NP-hard, and its Pareto-optimal front is non-convex. Therefore, we design a non-dominated sorting genetic (NSGA-II) based algorithm to solve this problem. Numerical experiments show that the designed algorithm, compared with enumeration method, can generate high-quality Pareto solutions within reasonable times. We also find that the timetable allowing larger flexibility of headways can obtain more and better Pareto-optimal solutions, which can provide decision-makers more choice.     

A methodology for choosing between fixed‐route and flex‐route policies for transit services

Flex‐route transit brings together the low cost operability of fixed‐route transit with the flexibility of demand responsive transit, and in recent years, it has become the most popular type of flexible transit service. In this paper, a methodology is proposed to help planners make better decisions regarding the choice between a conventional fixed‐route and a flex‐route policy for a specific transit system with a varying passenger demand. A service quality function is developed to measure the performance of transit systems, and analytical modeling and simulations are used to reproduce transit operation under the two policies. To be closer to reality, two criteria are proposed depending on the processing of rejected requests in the assessment of the service quality function for flex‐route services. In various scenarios, critical demand densities, which represent the switching points between the two competing policies, are derived in a real‐world transit service according to the two criteria. Copyright © 2014 John Wiley & Sons, Ltd.     

Integrated operations planning and revenue management for rail freight transportation

In the rail industry, profit maximization relies heavily on the integration of logistics activities with an improved management of revenues. The operational policies chosen by the carrier have an important impact on the network yield and thus on global profitability. This paper bridges the gap between railroad operations planning and revenue management. We propose a new bilevel mathematical formulation which encompasses pricing decisions and network planning policies such as car blocking and routing as well as train make-up and scheduling. An exact solution approach based on a mixed integer formulation adapted to the problem structure is presented, and computational results are reported on randomly generated instances.     

Welfare maximization for bus transit systems with timed transfers and financial constraints

Conventional and flexible bus services may be combined to better serve regions with a wide range of characteristics. If demand densities and resulting service frequencies are low, the coordination of bus arrivals at transfer stations may significantly reduce passenger transfer times. A method is proposed for integrating, coordinating, and optimizing bus services while considering many‐to‐many travel patterns, demand elasticity, financial constraints, and appropriate service type for various regions. The objective is to maximize welfare, that is, the sum of producer and consumer surplus. The problem is solved with a hybrid optimization method, in which a genetic algorithm with bounded integer variables is selected for solving one of the subproblems. The service types, fares, headways, and service zone sizes are jointly optimized. Sensitivity analyses explore how the choice among conventional and flexible busses depends on the demand, subsidy, and demand elasticity parameters. The results also show that welfare can increase due to coordination, and these increases are found to be higher in cases with high demand or low subsidy. Copyright © 2015 John Wiley & Sons, Ltd.     

An eigenmodel for iterative line planning,timetabling and vehicle scheduling in public transportation

Planning a public transportation system is a multi-objective problem which includes among others line planning, timetabling, and vehicle scheduling. For each of these planning stages, models are known and advanced solution techniques exist. Some of the models focus on costs, others on passengers’ convenience. Setting up a transportation system is usually done by optimizing each of these stages sequentially.In this paper we argue that instead of optimizing each single step further and further it would be more beneficial to consider the whole process in an integrated way. To this end, we develop and discuss a generic, bi-objective model for integrating line planning, timetabling, and vehicle scheduling. We furthermore propose an eigenmodel which we apply for these three planning stages and show how it can be used for the design of iterative algorithms as heuristics for the integrated problem. The convergence of the resulting iterative approaches is analyzed from a theoretical point of view. Moreover, we propose an agenda for further research in this field.