Performance Benchmarking in Public Transport Sector. The Data Envelopment Analysis (DEA) method

Seminar Paper, 2015

21 Pages, Grade: 1,3


Table of Content

List of Abbreviations

List of Figure

List of Table

1 Introduction
1.1 Motivation
1.2 Objectives and Outline

2 Performance Benchmarking
2.1 Overview
2.2 Basic DEA Models

3 Performance Benchmarking in Public Transport
3.1 Structure of the Public Transportation Sector
3.2 Different Views
3.3 Classification of the Performance Criteria
3.3.1 Input Variables
3.3.2 Output Variables
3.3.3 External Variables
3.4 Features of DEA Models

4 Conclusion and Outlook

5 Bibliography

List of Abbreviations

illustration not visible in this excerpt

List of Figure

Figure 2-1: Return to scale CRS vs. VRS

List of Table

Table 3-1: Evaluation aspects and different viewpoint

Table 3-2: Exemplary selection of input and output in public transport

Table 3-3: Input factors

Table 3-4: Output factors

Table 3-5: External factors

Table 3-6: Exemplary features of DEA models

1 Introduction

1.1 Motivation

In the most industrialized countries, urban traffic remains a significant transport mode for the community. In the area of public transport, in addition to municipal companies, there are private companies. Both public and private companies make use of a varie- ty of vehicles, such as buses, trams, light rail, ferries, and metros, in a highly regulat- ed environment. Government intervention in the public transport sector is wide- spread. The traffic policy of some industrialized countries, such as Germany or Nor- way, tries to increase the quality and efficiency of public transport to save expendi- ture. Furthermore, the European Union (EU) as a semi intergovernmental institution tries to dissolve the dominance of the municipal bus enterprises by establishing vari- ous competitive tendering procedures1. In addition, there are growing funding con- straints in many governments’ budgets that lower the States’ subventions for traffic companies. The expenditure of public money by public agencies is justified both in terms of welfare efficiency and equity goals. Therefore, an intensive pressure by the governments and communities to make a lasting improvement for efficiency is placed on the service providers and policy makers. Consequently, public agencies have to overcome the future increase in competition and the demands of economical offers.2

In every branch of industries, such as in public transport, the benchmarking studies present an important aid for decision-making. For instance, in strategy decisions or in decision of mergers this method can be used. Moreover, the knowledge about the competition situations of the public transport seems to be essential for transport policy.3 Conversely, in public transport, there are some environmental factors that impact the decisions of policy makers municipal and private urban traffic providers. Therefore, global agreements to decrease environmental CO2-emissions, oil reserves, and the population in larger cities also motivate the development of performance benchmarking measurement models for public transportation systems.

1.2 Objectives and Outline

The non-parametric approach is a common method for measuring the relative effi- ciency in the area of performance benchmarking and operations research. This ap- proach does not require the a priori specification of a function.4 The estimation of the frontier of the production set only requires that the production set satisfies some properties, such as input and output factors. The Data Envelopment Analysis (DEA) method is a non-parametric approach that uses mathematical programming to esti- mate production frontiers and calculus efficiency scores. The above technical expla- nation is necessary, as the present seminar paper deals with the application of the DEA approach in the field of the public transport. The objective of this paper is to re- view the state of the art in performance benchmarking in terms of different DEA- based framework and criteria to measure efficiency in the environments of public transport. To contribute to this goal, the ambition is to provide a systematic analysis of the performance criteria of the DEA models. Consequently, the main focus of this paper is to examine and classify the performance criteria.

In addressing the above, this paper, in the second chapter, describes the theoretical background of performance measurement and the basic DEA models. Therefore, the first section of chapter two presents the general idea and methodology of efficiency measurement as an overview while the second section deals with some background information and the most important models of DEA that apply in most studies. In the third chapter, different DEA-based frameworks, various viewpoints, and performance criteria to measure efficiency in the field of public transportation environments are examined. In the first section of chapter three, the characteristic of the public transport sector and the main issues for performance benchmarking in this sector are analysed. The second section addresses the different evaluation perspectives while the third section analyses and classifies the performance criteria. In the last section of the third chapter, the features of DEA models are examined. The last chapter pro- vides a conclusion with a summary and an outlook on further research opportunities.

2 Performance Benchmarking

2.1 Overview

Relative performance measurement or benchmarking can be used to facilitate the decision-making with the help of learning processes, or the coordination and control of employees through motivation. In this context, benchmarking is a systematic com- parison of the performance of similar decision making units (DMUs). DMUs can be companies, organizations, divisions, or projects that transform the same type of re- sources to the same type of products and/or services. The homogeneity of the DMUs refers mainly to the existence of similar tasks, objectives, and uniform environmental conditions. Furthermore, it requires the use of identical input and output factors5. Benchmarking can be used a static or in a dynamic framework. Another possibility for benchmarking setting is the different view of the management system in a centralized and decentralized management system6. DMUs that are seen as a transformation of multiple resources into multiple products are influenced by external factors. The transformation can be affected by non-controllable factors, and non-ascertainable ability and efforts. Furthermore, exogenous factors as non-discretionary resources or products impact DMUs. In general, outputs are the desirable outcomes and inputs are the valuable resources.

The set of input-output combinations available to DMUs is the production possibility set (PPS). The best input-output combination forms the technology frontier. In this context, the technology frontier shows the largest possible output for a given input or the smallest possible input for a given output7. The ratio of outputs to inputs defines productivity. Efficiency is measured by comparing the actual productivity with the ide- al productivity. Therefore, the efficiency of a DMU depends on its level of productivity. There are two basic concepts of efficiency measurement, namely the output orienta- tion and the input orientation. Output-oriented efficiency occurs if a company produc- es as much output as possible from a specific quantity of input. Input-oriented effi- ciency is presented if a company produces a specific quantity of output by using as little input as possible. There are two types of modelling methods of relative perfor- mance measurement. One type of modelling is the parametric approach (e.g. by ap- plying stochastic frontier analysis) and the other is a non-parametric approach (e.g. by applying DEA). In general, the application procedure of the DEA method is struc- tured into three phases. The first phase concerns the definition and selection of ho- mogeneous units. In second phase, a set of inputs and outputs factors are deter- mined. Finally, in the third phase, an appropriate modelling method is applied.8

2.2 Basic DEA Models

The non-parametric approach does not require a specification of a production func- tion. The estimation of the frontier of the production set only requires that the produc- tion set satisfies some assumptions and properties. The DEA method is a non- parametric approach method of efficiency measurement. It was introduced by Farell in 1957 and later extended by Charnes, Cooper, and Rhodes in 1978. This approach uses mathematical programming to successively estimate an enveloping production frontiers and calculus efficiency scores. Based on the examined data and the defini- tion of various assumptions, the efficient DMU is estimated as the "best-practice pro- duction function" and serves as a basis for comparison of the DMUs.9 By applying the DEA method, the basic PPS is unknown. Therefore, it is necessary to construct the model based on real observations and some specific assumptions. In terms of properties satisfied by the environment under consideration, the PPS can be charac- terized precisely by applying desired mathematical axioms, such as non-emptiness, free disposability, convexity, ray unboundedness, or constant returns to scale (CRS). Non-emptiness, free disposability, convexity, and CRS together construct one of the standard PPSs in modern benchmarking.10

Among the DEA models, the following two basic models are the most widely used: the CCR (Charnes, Cooper and Rhodes) model and the BCC (Banker, Charnes and Cooper) model11. Both models can be used by the input-oriented and output-oriented approach, and in both, the efficiency frontier is constructed by the linear combination of unit in the PPS (see figure 2-1). The efficiency scores received from CCR model are known as technical efficiency. These efficiency scores reflect the radial distance from the efficiency frontier estimated at the units concerned. A lower score of the units amounts to inefficiency in the units. When the units has efficiency score less than 1, then there must be at least one other DMU in the PPS that is efficient. These efficient DMUs are called the reference set for the inefficient unit. The CCR model is based on the assumption of CRS. CRS means that output increases by that same proportional change as all inputs change; however, there is no economies or dise- conomies of scale presented (e.g., doubling all inputs will generally lead to a doubling in all outputs).

If size can influence the ability to produce output efficiently, it is more appropriate to use a PPS under variable returns to scale (VRS). The BCC model is based on the assumption of VRS. Figure 2-1 illustrates what will happen if DMU is rescaled. In Figure 2-1, moving along the efficient frontier (VRS) from smaller to larger input, first the returns to scale is increasing (IRS), then constant (CRS), and finally decreasing (DRS). In the BCC model, the efficiency frontier is generated by the convex board of the units in the dataset. Efficiency scores of this model are known as pure technical efficiency12. Only the information of pure technical efficiency of a unit indicates if the DMU is operating at the optimal scale. Scale efficiency ratio is determined by dividing the technical efficiency by pure technical efficiency in either orientation. In this con- text, a DMU scale is efficient if the scale efficiency is equal to one. A scale efficiency ratio smaller than one indicate that the DMU is not scale efficient.13

illustration not visible in this excerpt

Figure 2-1: Return to scale CRS vs. VRS

3 Performance Benchmarking in Public Transport

3.1 Structure of the Public Transportation Sector

Mobility is seen as a key element for the prosperity of our society. The demand for mobility is satisfied by both individual transport and public transport. Through techno- logical progress and tariff enhancements, public transport has a unique role in in- creasing mobility. Public transport even has positive side-effects on individual transport through avoiding congestion on roads and parking spaces. Public transport can be classified into long-distance passenger transport (served by aircrafts, buses, ferries, and railways) and local public transport (served by buses, ferries, railways, taxis, and all types of aerial cableways, light railways, subway, and tramways).14

Policy makers play a major role in public transport. Public service obligations, regula- tory approval, and the peculiarities associated with certain types of infrastructure are all subject to public debate. The provision of public transport services serves as a social right for the sector’s existence. However, transport services are often not as cost-efficient as possible. In the last three decades, industrialized countries have de- veloped unique, complex, and capacious local public transport systems. Consequent- ly, there are some characteristic differences among countries. These differences, at times, result from regulation, ownership, or market structure. For example, the United Kingdom is a popular subject for liberalization and deregulation studies, while Swe- den has long been at the forefront of competitive tendering. Moreover, Italy similar to many other countries faces financial pressure on losses occurring in local public transport. From a welfare economic viewpoint, the public sector attends to four main goals: efficiency, equity, financial balance, and macroeconomic stabilisation.15

A crucial question in relation of performance benchmarking is “which type of operat- ing and regulatory environment is best suited to stimulate productivity growth and efficiency in the public transport sector?” Efficiency has played a prominent role in political and academic arguments guiding recent privatization and deregulation poli- cies. This result in the following issues in the area of public transport: effect of alter- native regulatory regimes, public versus private ownership, economies of density (scope and scale), and efficiency/productivity evaluation.


1 see Hartwig and Scheffler (2009), p. 4.

2 see Farsi et al. (2007), p. 346.

3 see Henning et al. (2013), p. 11.

4 see et al. Cooper (2006), p. 1.

5 see Coelli et al. (2005), p. 135.

6 see Scheel (2000), p. 13.

7 see Joro and Korhonen (2015), p. 27.

8 see Zhu (2015), p. 324.

9 see Cooper et al. (2006), p. 2.

10 see Scheel (2000), p. 40.

11 see Coelli et al. (2005), p. 162.

12 see Joro and Korhonen (2015), p.18.

13 see Cooper et al. (2006), p. 21.

14 see Roumboutsos (2015), p. 112.

15 see et al. Verhoest (2013), p. 4.

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Performance Benchmarking in Public Transport Sector. The Data Envelopment Analysis (DEA) method
Performance Benchmarking and Operations Research
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Performance Benchmarking, Operations Research, Data Envelopment Analysis, Public Transport, öfftentlicher Verkehr, Leistungsmessung, Effizienzmessung, Kennzahlen
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Andreas Davidek (Author), 2015, Performance Benchmarking in Public Transport Sector. The Data Envelopment Analysis (DEA) method, Munich, GRIN Verlag,


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