Nicole Adler

Review of ranking methods in the data envelopment analysis context

Abstract Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to improve the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical techniques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA approach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking.

Evaluation of deregulated airline networks using data envelopment analysis combined with principal component analysis with an application to Western Europe

Abstract US experience shows that deregulation of the airline industry leads to the formation of hub-and-spoke (HS) airline networks. Viewing potential HS networks as decision-making units, we use data envelopment analysis (DEA) to select the most efficient networks configurations from the many that are possible in the deregulated European Union airline market. To overcome the difficulties that DEA encounters when there is an excessive number of inputs or outputs, we employ principal component analysis (PCA) to aggregate certain, clustered data, whilst ensuring very similar results to those achieved under the original DEA model. The DEA–PCA formulation is then illustrated with real-world data gathered from the West European air transportation industry.

High-speed rail and air transport competition: Game engineering as tool for cost-benefit analysis

This research develops a methodology to assess infrastructure investments and their effects on transport equilibria taking into account competition between multiple privatized transport operator types. The operators, including high-speed rail, hub-and-spoke legacy airlines and regional low-cost carriers, maximize best response functions via prices, frequency and train/plane sizes, given infrastructure provision, cost functions and environmental charges. The methodology is subsequently applied to all 27 European Union countries, specifically analyzing four of the prioritized Trans-European networks. The general conclusions suggest that the European Union, if interested in maximizing overall social welfare, should encourage the development of the high-speed rail network across Europe.

Improving discrimination in data envelopment analysis: PCA-DEA or variable reduction

Within the data envelopment analysis context, problems of discrimination between efficient and inefficient decision-making units often arise, particularly if there are a relatively large number of variables with respect to observations. This paper applies Monte Carlo simulation to generalize and compare two discrimination improving methods; principal component analysis applied to data envelopment analysis (PCA-DEA) and variable reduction based on partial covariance (VR). Performance criteria are based on the percentage of observations incorrectly classified; efficient decision-making units mistakenly defined as inefficient and inefficient units defined as efficient. A trade-off was observed with both methods improving discrimination by reducing the probability of the latter error at the expense of a small increase in the probability of the former error. A comparison of the methodologies demonstrates that PCA-DEA provides a more powerful tool than VR with consistently more accurate results. PCA-DEA is applied to all basic DEA models and guidelines for its application are presented in order to minimize misclassification and prove particularly useful when analyzing relatively small datasets, removing the need for additional preference information.

Competition in a deregulated air transportation market

Abstract Under deregulation, airlines developed hub-and-spoke (HS) networks enabling them to aggregate demand, increase frequency, reduce airfares and prevent entry into the marketplace. This research evaluates airline profit based on micro-economic theory of behaviour under deregulation. Through a two-stage Nash best-response game, equilibria in the air transportation industry is sought to evaluate the most profitable HS network for an airline to survive in a deregulated environment. In the first stage of the game, an integer linear program aids in generating potential networks. In the second stage, a nonlinear mathematical program maximizes profits for each airline, based on the networks chosen by all participants. The variables of the mathematical program include frequency, plane size and airfares. In an illustrative example, both monopoly and duopoly solutions are attainable as a function of demand.

Including principal component weights to improve discrimination in data envelopment analysis

This research further develops the combined use of principal component analysis (PCA) and data envelopment analysis (DEA). The aim is to reduce the curse of dimensionality that occurs in DEA when there is an excessive number of inputs and outputs in relation to the number of decision-making units. Three separate PCA–DEA formulations are developed in the paper utilising the results of PCA to develop objective, assurance region type constraints on the DEA weights. The first model applies PCA to grouped data representing similar themes, such as quality or environmental measures. The second model, if needed, applies PCA to all inputs and separately to all outputs, thus further strengthening the discrimination power of DEA. The third formulation searches for a single set of global weights with which to fully rank all observations. In summary, it is clear that the use of principal components can noticeably improve the strength of DEA models.

Hub-Spoke Network Choice Under Competition with an Application to Western Europe

The aim of this paper is to present a model structure that analyzes the hub-spoke network design issue within a competitive framework. Under deregulation, airlines have developed hub-and-spoke networks, enabling them to increase frequency by aggregating demand and to prevent entry into the marketplace by reducing airfares. While liberalization in the United States and Europe was undertaken to increase competition, the results in this direction are unclear. This research evaluates airline profits based on a microeconomic theory of airline behavior under deregulation and the effect on hub-and-spoke networks. Through a two-stage, Nash best-response game, we search for equilibria in the air transportation industry. The game is applied to Western Europe, where profitable hubs and monopolistic equilibria are clearly identifiable, and duopolistic equilibria are potentially viable, given sufficient demand.

Evaluating optimal multi-hub networks in a deregulated aviation market with an application to Western Europe

This paper develops, evaluates and ultimately aids in the choosing of an optimal, single allocation, hub-and-spoke network for an airline working in a deregulated market. An integer linear program evaluates potential hub network combinations, whose profits are then determined using a non-linear mathematical program. International gateway airports and regional hubs, profit, frequency and aircraft size are the decision variables. An adapted, conjugate-gradient projection algorithm is developed and the models are subsequently applied to Western Europe.

Strategies for managing risk in a changing aviation environment

Abstract Given the increasing volatility in the economic performance of airlines, partially reflecting the dynamics of demand for air transport and the fixed costs associated with the industry, all stakeholders need to consider appropriate strategies for better managing the risks. Many risks were identified in the literature previously, some even decades ago, however most have yet to be satisfactorily addressed. Urgency is growing. Removal of the remaining barriers to competition at all levels, congestion management, open skies policies across continents, computer-centric air traffic management systems and increased research and development into the processes and technology needed to reduce environmental externalities remain among the top challenges for the next decade.

Accounting for externalities and disposability: A directional economic environmental distance function

The existence of positive and negative externalities ought to be considered in a productivity analysis in order to obtain unbiased measures of efficiency. In this research we present an additive style, data envelopment analysis model that considers the production of both negative and positive externalities and permits a limited increase in input utilisation where relevant. The directional economic environmental distance (DEED) function is a unified approach based on a linear program that evaluates the relative inefficiency of the units under examination with respect to a unique reference technology. We discuss the impact of disposability assumptions in depth and demonstrate how different versions of the DEED model improve on models presented in the literature to date.