Optimal Fare Research Articles

The Combined Zone And Fare Planning Problem

This paper looks at the problem of planning an integrated transit system from the viewpoint of optimal fares and zone design. More succinctly, the matter is how to plan an integrated fare system that allows each passenger to travel within different zones with a single zone-based ticket. A 2-level model is given, which is both quite near to real operation practices and makes the planner able to consider various transit firms operating within the same context. The main problem is divided into 2 distinct subproblems: one for the fare problem, and the other for the zone problem, solved sequentially. The fare problem leads to the minimization of an aggregated cost function that is mainly related both to the budget needs of each transit agency, and changing in fare levels for the patronage. The zone problem is solved by a heuristic method which was set up to randomly search for the optimal zone configuration reflecting a given fare policy. Computational test results of the proposed model applied on a real database gathered in the metropolitan area of Florence are also reported.

Travel distance and optimal transport policy

A theoretical model is adopted in order to discuss optimal fare and optimal quality of supply schemes for a transport operator. The analysis shows how fare and quality of supply are related to travel distance and to the transport operator's emphasis on profit versus consumer surplus. Under reasonable assumptions imposed on the actual functions we find that the more weight the operator attaches to profit, the higher the fare level and the higher the generalised travel costs. How the operator's objectives influence the quality of transport and perhaps more surprisingly how travelling distance influences fares, quality of transport and generalised travel costs, are ambiguous with relation to the starting restrictions placed on the actual functions. The paper then discusses the special case in which the quality of transport is exogenous to the transport operator. One important result is that higher demands set to the transport operator regarding the quality of the transport supply do not necessarily reduce the transport users' generalised travel costs. Some of the model's results are commented in the light of empirical studies from Norway.

On the optimal fare policies in urban transportation

This paper focuses on welfare optimal transport policies in a public transport market where positive externalities from the route supplier to the travellers as well as negative externalities within group of consumers exist. Additionally, there might be capacity constraints of two types. Firstly, the actual numbers of travellers in a period cannot be above the actual seat capacity supplied by the operator. Secondly, the number of seats supplied by the operator cannot exceed the maximum seat capacity given by the fleet of vehicles the operator controls in the period. Among other things, the paper shows that in the case where there is excess seat and route capacity, the fares should be equal to sum of the short run marginal operational costs and the costs an additional passenger is causing on the other travellers. In the long run, however, fares should be equal to sum of the long run marginal operational costs and the costs an additional passenger is causing on other travellers minus the gain in reduced time costs for all of the passengers that the final unit of supply brings.

Value-of-time distributions and competitive bus services

Abstract The effect of value-of-time (VOT) distributions on price and quality competition among differentiated bus services in a simple corridor is investigated. Three travel modes are considered: private car; higher-quality, higher-fare minibuses; and lower-fare, lower-quality conventional buses. With a given continuous distribution of VOT, users are assumed to minimize individual generalized trip cost and divide themselves among the three travel modes that are differentiated in travel time and monetary cost. Competitive equilibrium is established in terms of each bus firm's optimal frequency and optimal fare; also, the profitability of the two types of bus service is examined.

Optimal Fare Structure for Transit Networks with Elastic Demand

A bilevel model is presented to optimize the fare structure for transit networks with elastic demand under the assumption of fixed transit service frequency. It is known that the transit fare structure has significant effects on passengers' demand and route choice behavior. The transit operator therefore should predict passengers' response to changing fare charges. A bilevel programming method is developed to determine the optimal fare structure for the transit operator while taking passengers' response into account. The upper-level problem seeks to maximize the operator’s revenue, whereas the lower-level problem is a stochastic user equilibrium transit assignment model with capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Finally, a numerical example is given together with some useful discussion.

Comparison of Subsidized Fixed- and Flexible-Route Bus Systems

A comparison of subsidized fixed-route and flexible-route feeder bus systems is presented. Mathematical models are formulated to maximize welfare for the two feeder bus systems, subject to a subsidy constraint. Service-zone size, headway, and fare are the decision variables in the analyses. For subsidy operation it is demonstrated that the equilibrium demands for the two systems are different because of their specific service attributes, and that the optimal fare for a flexible-route system is generally higher than for a fixed-route system. The differences in welfare and fares between the two systems under different levels of subsidy for and different route length, service area, and travel speed are identified. Additional studies on integration or permitted competition for the two bus systems are also suggested.

Comparison of Subsidized Fixed- and Flexible-Route Bus Systems

A comparison of subsidized fixed-route and flexible-route feeder bus systems is presented. Mathematical models are formulated to maximize welfare for the two feeder bus systems, subject to a subsidy constraint. Service-zone size, headway, and fare are the decision variables in the analyses. For subsidy operation it is demonstrated that the equilibrium demands for the two systems are different because of their specific service attributes, and that the optimal fare for a flexible-route system is generally higher than for a fixed-route system. The differences in welfare and fares between the two systems under different levels of subsidy for and different route length, service area, and travel speed are identified. Additional studies on integration or permitted competition for the two bus systems are also suggested.

Market expansion, cannibalization, and international airline pricing strategy

We analyze market response and pricing of air travel on the Paris-Abidjan, Ivory Coast route operated by a French airline, Union des Transports Aeriens (UTA). We measure the impact of price on the overall size of the market, and examine the nature, pattern, and extent of cannibalization using a set of econometric models for overall passenger volume and for each fare class share. Our analysis shows that (1) only one class of fares expands the market; (2) cannibalization is very significant and highly asymmetric; (3) even small deviations from optimal prices substantially reduce profit. Based on these estimated models, we forecast demand for air travel and calculate optimal fares. We discuss how these models and results were used by UTA and the impact they had on pricing strategy.

Management's role in U.S. rail passenger decline, 1920–1941

Opinions vary as to whether the decline of American railroad passenger service can be attributed primarily to consumer choice or partly to structural impedances to the supply. Results are reported from testing the hypothesis that railroad management supplied service inappropriate in the new motor era: that management catered to a small, high-priced market, whereas it should have catered to a mass, low-priced market. An aggregate demand model with non-linear elasticity characteristics is estimated on railroad traffic between a sample of American cities for 1933. The model is sensitive to speed, fare and headway variables under the control of railroad management and reveals that there was a unique fare for a service of a given speed that maximized gross revenues. The observed fare for most of the 187 cases in the study was near or below the optimal fare, showing that rail managers judged their markets well, at least in the short run.

Air deregulation revisited: Choice of aircraft, load factors, and marginal-cost fares for domestic air travel

If airline deregulation is working as predicted, then fares should fall to marginal costs. This paper computes such optimal fares, allowing for a wide variation in point-to-point distance, traffic, and available aircraft type. It is shown that marginal-cost fares are exceeded by average carrier costs. This implies an unpleasant dilemma: either the industry is naturally destructive (if the returns are internal to firms) or else the sustainable industry configuration is less than welfare-optimal. In the latter case, the possibility of a Pareto-improvement with a judicious form of re-regulation cannot be ruled out. In light of this, a certain amount of caution about the results of deregulation is suggested.

An Approach to the Determination of Optimal Airline Fares: Some Useful Insights on Price Elasticities, Monopoly Power and Competitive Factors in the Airline Industry

Within the airline industry, demand curves can be derived externally by survey methods and cost curves can be generated internally by astute accounting procedures. The tradi tional tools of microeconomic analysis can be used in a practical way to arrive at profit maximizing fares. The optimizing procedures are not sensitive to the sampling ration in the survey and are therefore generally applicable. An empirical case study provides some useful insights on the competitive factors in the airline industry that help determine market segmentability, price elasticities of demand, and monopoly power.

A Simple Analysis of Optimal Fares on Scheduled Transport Services

A Simple Analysis of Optimal Fares on Scheduled Transport Services