Optimal Intercity Transportation Services with Heterogeneous Demand and Variable Fuel Price

Abstract

In this thesis we examine how fuel price variation affects the optimal mix of services in intercity transportation. Towards this end, we make two main contributions. The first is the development of an analytic total logistics cost model of intercity transportation, which is sensitive to fuel price and incorporates multiple classes of vehicles serving passengers with differentiated values of time. The second is an empirical investigation of the cost relationship between fuel price and operating cost for intercity transportation vehicles. The analytic total logistics cost models are combined with the empirical models to gain insights into the impact of fuel price on optimal service mixes in representative corridors. We consider a scheduled intercity transportation corridor on which different classes of intercity transportation vehicles serve passengers with differentiated values of time. In determining optimal service mix, we consider a central planner choosing the vehicles and service frequencies that provide the minimum total logistics cost for an intercity transportation corridor. The total logistics cost is the sum of the two main intercity transportation cost components: vehicle operator cost and passenger cost. In considering operating and passenger costs together, we balance cost efficiency and level of service of alternative vehicles with different cost structures and service attributes. In developing the total logistics cost model, we seek both analytic insights and numerical examples. To keep the model analytically tractable while at the same time incorporating multiple objectives, including fuel cost, operating cost, schedule delay, and line-haul time, we incorporate the continuum approximation method from logistics. In employing the continuum approximation, discrete variables are considered continuous, leading to analytic functions from which we can evaluate qualitatively the relationships among fuel price, service level, and comparative vehicle cost. An investigation of the analytic model suggests that, while a fuel price increase would increase costs for any corridor, the rate of cost increase for a corridor served by a mix of vehicle technologies diminishes more rapidly with fuel price. We also find that an increase in fuel price causes vehicles to become more differentiated with respect to the value of time of the passengers they serve. In other words, under high fuel prices the total logistics cost can be minimized by effectively segregating passengers on different types of vehicles according to their values of time. We complement the analytic findings with an empirical investigation of the cost relationship between fuel price and operating cost for different classes of intercity transportation vehicles. We perform this analysis for a subset of intercity transportation vehicles for which data is readily available: jet and turboprop aircraft. In developing a translog operating cost model for jet aircraft, we estimate a flexible functional form that provides a detailed representation of the empirical relationship between fuel cost and operating cost, allowing for substitution, scale, aircraft age, and other effects – including interactions – to be captured. The function reveals that as fuel price increases, airlines will take steps to use fuel more efficiently by leveraging other inputs; however, the potential for this supplier input substitution for fuel is rather modest. This finding reinforces the formulation of the analytic total logistics cost model, in which the only actions available to a central planner to reduce costs are changing technologies and service frequencies. It also proves that empirical models with simpler functional forms are able to accurately predict operating costs, despite the lack of variable interactions. Using linear empirical operating cost models, we estimate operating cost and total logistics costs for intercity transportation corridors served by single vehicle fleets of three different aircraft classes. We find that a specific turboprop aircraft model, with a relatively low fuel consumption rate, provides intercity transportation service with the minimum operating cost compared with a jet with smaller seating capacity over all fuel prices considered and medium-capacity jets for some fuel prices. However, this is no longer the case when total logistics cost is considered, due to the lower quality of passenger service turboprops provide. At a given intercity transportation corridor distance, the fuel price for which the total logistics cost per passenger is equal across turboprops and low-capacity jets is in the fuel price range experienced from 2004 and expected through 2020. For this fuel price range, the total logistics cost per passenger for the medium-capacity jet is generally lower than the turboprop and always lower the lowcapacity jet. This suggests that a mix of services between intercity transportation vehicles could minimize cost for this range of fuel price. To investigate the possibility of mixing services to reduce costs further, we combine the analytic total logistics cost model with the empirical models. In addition to a jet and turboprop aircraft model, we build a high speed rail cost model and consider high speed rail as an additional intercity transportation technology. We find the minimum cost vehicle combination to be sensitive to fuel price in a small transition zone within which the cost ordering of vehicle combinations changes significantly, whereas outside this zone the orderings are stable. As the transition area is in the range of fuel prices forecasted between the years 2010-2035, the results indicate fuel price changes between 2010 and 2035 may dramatically alter the most cost-effective ways to provide intercity passenger transport. We find that high speed rail is a part of a mixed vehicle service that can reduce total logistics cost, suggesting that an integrated air and rail strategy could be an effective tool to manage costs and fuel consumption for an intercity transportation system.