6th IFAC Conference on Management and Control of Production

and Logistics
The International Federation of Automatic Control
September 11-13, 2013. Fortaleza, Brazil

Efficiency of Urban Public Transport:

Case Study of Brazilian Cities
Suguiy, T.* , Carvalho, M. F.**, Nithack e Silva, D. L.***

*CTI – Renato Archer – Campinas - Brazil (takao@cti.gov.br)

** PUC - Campinas – Brazil ( marcius@puc-campinas.edu.br)
***EMDEC – Campinas, Brazil (daniel@emdec.com.br)

Abstract: Urban population growth and new habits motivated by technological advances, such as electronic
commerce and home office use, have important consequences for mobility and urban transport in cities. Accordingly,
it is essential to define indices for monitoring the results of actions taken by municipalities in order to guide new
policies. Using the Competitiveness Indicators of Campinas (ICC) as a reference, this paper evaluates urban public
transport in Brazilian cities. The Data Envelopment Analysis (DEA) method is used to evaluate three different cases:
infrastructure efficiency, service level of public transport quality, and cities efficiency score. The results show the
conflict among different objects and emphasize the responsibility of the public sector to balance public policies to
meet the basic needs of the population.

strategic policies, the Campinas municipality created the

1. INTRODUCTION
research project ICC with the participation of 49
According to Castells (1972) the urban space is not merely a municipalities, which include more than 300,000 inhabitants.
distinct area of countryside around the city, but a political Four public areas were included in this research project:
space that provides residence for members of the workforce. social protection, social promotion and opportunity
The urban population is growing rapidly. In 2007, the urban generation, promotion and guaranty of rights and urban social
population exceeded the rural population, and the portion of economic infrastructure. The project encompasses systematic
individuals in the urban population is expected to reach 59% monitoring of the behavior of the cities surveyed in the last
in 2030 and 69% in 2050 (Kiwitt, 2010, 98). This growth has six years to identify successful municipal policies that could
resulted from new habits motivated by technological guide actions for improving quality of life in the municipality
advances, such as e-commerce and home office use, causing and for creating a municipal management intelligent network
important changes to both mobility and urban transport in (Oliveira et al., 2011). The availability of these indices allows
cities. Research by the São Paulo State Government notes the results of the actions undertaken in the surveyed cities to
that the number of motorized travel has grown from 20.6 be monitored. Although the ICC constitutes a work of great
million/day in 1997 to 25.3 million/day in 2007, while the importance, the data need to be treated to evaluate the urban
population grew 16% in the same period (Romero and Bruna, transport of a municipality in relation to the other
2010). The same trend of higher urban growth has been municipalities researched.
confirmed in most Brazilian cities (Sellitto, 2010). In
DEA is a methodology for comparing the performance of
particular, in the city of Campinas, a survey by Empresa
organizations with multiple indicators. In recent years, DEA
Municipal de Desenvolvimento de Campinas S.A (EMDEC)
has been utilized to evaluate various contexts. Some
shows that the average transport speed decreases 1.5% per
applications of DEA in the area of logistics include Karlaftis
year because of the increase in the current transportation fleet
(2004); Karlaftis & Tsamboulas (2012); Ozbek et al. (2009);
(Costa, 2012). Because individuals within urban populations
Carvalho, Carvalho and Lima (2010); Novaes (2001); and
are often far from food sources, raw materials, supplies, jobs
Tamagawa, Taniguchi & Yamada (2010), among others.
and leisure, an efficient urban public transport is needed.
The urban transportation is a dynamic system composed of This article evaluates urban public transportation using the
subsystems that evolve over time by the provision of data available from the ICC for three different cases:
alternative modals as a result of changes in technology and infrastructure efficiency, service level, and cities efficiency
lifestyle. Passenger transport is highly complex, with random score. This paper is organized as follows: the next section
behaviors and nonlinearities that influence and that are reviews the concept of DEA; section three presents the
influenced by the environment, providing benefits and methodology for the study; section four evaluates urban
consequences for the population (Khisty, Arslan, 2005). public transport in 21 cities for the three proposed cases; and
Public authorities must balance these benefits and the last section presents the final considerations.
consequences with public policies that meet the basic needs
of the population. The scarcity of resources forces the public 2. DEA OPERATIONAL EFFICIENCY
sector to strive to make more effective investments, achieve In his classic work, Farrell (1957) highlighted the importance
higher productivity and improve service level. of measuring production efficiency for both economic
The question is how to measure the productivity and service theorists (to evaluate the relative efficiency between
level in urban public transport. To evaluate and formulate industries) and economic policy making (to formulate

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economic policy for a specific industry). He noted that outputs (sales volume and returns). The determination of
generating a satisfactory measure of efficiency for multiple which variables should be included in the study is a relevant
input systems was a challenge. Twenty years after the point of research and will be examined later in this article.
seminal work of Farrell, Charnes et al. (1978) introduced a
methodology for evaluating the relative efficiency of This classic approach treats each DMU as a black box, and
production units with multiple inputs and multiple outputs. by considering only the inputs and the outputs produced, the
efficient and inefficient units are identified through linear
The methodologies, later called Data Envelopment Analysis programming. Moreover, the relative inefficiency of a given
(DEA), with the concept of decision making unit (DMU) unit can be identified, which supports strategic decisions for
allow one to measure the efficiency of each unit in a multiple the improvement of that DMU. However, this approach does
input and output system (Cook and Seiford, 2009). Efficiency not indicate which is the best DMU in the analyzed set and
means that the organization uses its resources productively does not provide ways to classify them. To introduce
and cost effectively, produces more with less resources, or discriminatory power, Foroughi (2011) proposed a model of
even rationalizes its inputs. Efficiency can be defined as extreme efficiency that is considered to be more stable with
follows: respect to efficiency where it is necessary to solve a single
model for the identification of the best DMU, which is
Output advantageous in comparison with the model of Andersen and
Efficiency = (1) Petersen (1993). This model can be written as follows:
Input
Maximize (d) (3)
With DEA, it is possible to identify the best practice for a Subject to:
unit of a set of comparable organizations (DMUs). From the s m
knowledge of the input (resources) and output (products)
variables for each DMU, DEA establishes an efficient r 1
U r Yrj  V X
i 1
i ij  tj  d 0 j  1, 2 ,... n; r  1,... s; i  1...m)

frontier (efficient border) defined by the identification of a set s m

of efficient units. Figure 1 shows a comparison of relatively   U r Yrj   Vi X ij  t j  1 j  1, 2 ,...n; r  1,...s; i  1...m)
efficient DMUs. The line defines the better efficiency data r 1 i 1
solutions border, and organizations below this line (Ox and m

Oy) must improve their performance to achieve efficiency by V X

i 1
i ij 1 j  1, 2 ,... n;
seeking a new position situated on the line.
n

t j 1 j  1, 2 ,...n;
Output Efficient frontier j 1

t j  {0,1}, j  1,2,...n,
Ox {vi }  V ; {u r }  U .
Oy

According to Foroughi (2011), the DMU obtained from the

model above is extremely efficient (Thrall, 1996).

Input 3. METHODOLOGY
Figure 1. The concept of a Data Envelopment line For implementing DEA, Golany and Roll (1989) proposed a
model with three phases: the first phase defines the DMUs
That is, an inefficient DMU should undertake actions that that are included in the analysis; the second phase elects the
make it efficient by applying efforts to reach any point on the relevant and appropriate variables (inputs and outputs) that
border efficiency line. The efficiency E0 of DMU0, in a belong in the study of efficiency of the selected DMUs; and
system with multiple inputs and multiple outputs, can be the third phase is related to the application of DEA model.
determined as follows (Charles, Cooper and Rhodes, 1978): Dyson et al. (2001) and Ozbek (2009) extended the previous
e0  max U
r
r Yr 0 work to include six phases. This work is based on the Ozbek
(2009) methodology and defines the following six phases.
Subject to: v xi
i io 1 (2)

3.1 Objective
U Y  V X
r
r rj
i
i ij 0  j for all r, i
The objective is to identify how efficient an organization or
{vi }V; {ur }U . Decision Making Unit is in relation its peers. For urban
passenger transport, there are two points of view regarding
where U and V are the sets of all acceptable weights. performance, the supplier’s and the users'. Providers may
measure performance differently from service users. In the
This is known as the CCR (Charles, Cooper and Rhodes) public sector, both views of performance should be
model. A production process uses multiple inputs (hours measured.
worked, materials and dimensions) and several relevant

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3.2 DMUs definition and selection of variables that exceed the definition above, some
variables can be aggregated using, for example,
DEA is a method that measures the relative efficiency regression analysis (Ozbek, 2009).
among comparable units. DMUs should be selected for iii. Analysis of the results – The resulting variables and
inclusion in a study with caution because DEA is sensitive to DMUs from the above items are considered in the DEA
extreme values (Dyson et al., 2001). DEA takes into account model. However, those variables that present small
the best practices, but inaccurate data can lead to deviations weights can be removed from the list because they have
in the analyses, so accounting for some characteristics may less impact on the indices.
be important in determining which DMUs are included in the
study. According to Dyson (2001), the set of DMUs to be 3.4 Model formalization and selection
analyzed must be homogeneous: each DMU should perform
the same activity with similar objectives; the set of input data The basic models of DEA can be grouped into (1) models for
and outputs should be common to all the units under review; DMUs with constant returns to scale (Models CCR) and
and the DMUs must operate in a similar external environment models with variable returns to scale (BCC) and (2) input-
and have similar technologies because these factors impact oriented models or output-oriented models. According to
the performance of a unit. Given these considerations, Dyson Ozbek (2009), two orienting questions must be answered in
et al. (2008) noted that "the selected units should produce the selecting an appropriate model: Does the set of DMUs have
same goods and services, using the same inputs.” The above constant returns to scale? Are the DMUs more interested in
considerations seek to ensure that the indicators related to the working its input (to minimize) or its output (to maximize)?
DMUs are reliable and that any extreme variations are, in
fact, concrete situations, not errors of measurement. For this 3.5 Model validation
reason, prior to an application of the methodology, an
exploratory data analysis is required. For selecting DMUs, The construction of a model is an iterative process whose
Ozbek et al. (2009) suggests using two steps: (1) DMUs results must be validated so that the model is reliable. The
representing different units or organizations and (2) those DEA modeling process starts with a set of DMUs and
representing different periods of DMUs to the same unit or variables, but there is no guarantee that the initial choice is
organization. In the latter case, the analysis is based on time. well-suited for analysis. According to Ramanathan (2003), a
There are no standards to define the number of participant sensitivity analysis can occur (1) by removing any efficient
units, but the minimum value is related to the number of DMU or (2) by removing some variables of the model. Thus,
variables, as explained below. items 3.1 to 3.3 should be revisited with the generation of
new results through the inclusion or exclusion of DMUs and
3.3 The input and output variable selection input or output variables. Then, a sensitivity analysis of the
results for each of these studies should be performed.
DEA and its applications are heavily dependent on the input
data. The input data are used to identify the DMUs and select 3.6 Case generation and results analysis
the variables to include in the analysis. For a greater number
of units, there is a greater probability of finding DMUs that DEA does not directly identify the causes of inefficiency, but
will form an efficient border, but when more DMUs are it reveals the reasons why a DMU is classified as inefficient
considered, there are greater difficulties in identifying and points to directions for improvement. These directions
homogeneity within the final set of data. To define the for improvement can be taken as strict or as input for a more
number of DMUs and variables to be considered by the DEA comprehensive decision process. These decisions should be
model, three requirements must be met (Sarkis, 2007): (a) the tested to evaluate the new position of the DMU. Therefore,
number of DMUs has to be at least twice the number of when using DEA, it is necessary to analyze the various
variables; (b) the inputs and outputs with correlated data must scenarios and each one’s adequacy for the proposed problem.
be removed; and (c) the data should be normalized. An in- The number of scenarios to be analyzed depends on the
depth discussion of variable selection models is available in purpose of the study and the characteristics of the system as
Wagner and Shimshak (2007). However, the three most discussed in the application of this study.
important points are as follows:
4. URBAN PUBLIC TRANSPORTATION SYSTEM
i. Qualitative analysis – A critical analysis of the variables EVALUATION
is performed by experts with the ability to define how
crucial a variable is based on the following guiding
questions: How many production goals is the variable The reference document for this study is the Campinas
related to? Does the variable contain relevant information Competitiveness Indicators (ICC), which were developed
that is not included in other variables? Are the data from 27,000 statistical data points for 49 municipalities of
needed for the variable available and reliable? Brazil, which include more than 300,000 inhabitants. The
fifty-six indicators in this document relate to protection,
ii. Quantitative method – In DEA, a greater number of
social promotion and opportunity generation and were
variables included in the analysis produces a lower level
classified into nine themes: citizenship and social assistance,
of discrimination. One suggested rule is that the DMU
health and culture, education, sport, work and income, public
number = 2*m*t, where m is the number of inputs and t
safety, public finances, basic sanitation, transport and transit.
is the number of outputs. When there are a large number

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4.1 Objective of the study The DEA model can be input-oriented if the desire is to
minimize the resources used in the operation without
The objective of the study is to evaluate the urban public reducing the level of output, or it can be output-oriented if the
transport systems of Brazilian municipalities using secondary desire is to maximize the output without reducing the level of
data from the reference document (ICC) under three input. The output-oriented model, CCR (or CRS), was
objectives: infrastructure efficiency, service level and city developed to analyze studies 1 and 2, as it provides an
efficiency score. Efficiency is defined as the relationship evaluation of larger entities and discriminates against the
between inputs and outputs, while service level is related to BCC model (or variable returns to scale – VRS). In case 3 we
an appropriate degree of user satisfaction with the service used the CCR (or CRS) and BCC (or VRS) output-oriented
provided. models. The normalization of the data showed results very
close to calculations performed with the raw data, which
4.2 DMU Definitions and selection minimizes the importance of the model selection and
formalization.
The cities (DMUs) were chosen from the ICC document
taking into account the availability of all the variables 4.5 Validation
considered in the final analysis. Each city is considered to be
one DMU, however no distinction was made regarding DEA is a method that measures the relative efficiency among
whether a city is part of a metropolitan region or whether it is comparable units, so it is sensitive to extreme values, and
a capital. As the topic is public transport in the urban thus, DMUs must be selected for inclusion in the study with
environment, the DMUs have similar objectives and operate caution (Dyson et al., 2001). The development of any model
in similar environments. In the analysis, because urban is an iterative process where the results must be validated so
transport was evaluated, the requirement of similarity of that the model is reliable. DEA starts from a set of DMUs and
technology was considered to have been met, as few cities a set of variables to be included in the model, and the results
have train or subway transportation. The data were collected are heavily based on the definitions of these sets. There is no
and analyzed over 6 years. guarantee that the initial choice of DMUs and variables is
ideal, and thus, different scenarios must be analyzed. There
4.3 Definitions and selection of the variables are different studies to support strategic, tactical and
operational decisions. In this paper, three studies to support
The variables that were selected for this study are as follows:
strategic decisions are presented: study 1 considers
i. Municipality inhabitants - IBGE data provide infrastructure efficiency, study 2 considers service level and
information on the population residing in the city. study 3 identifies more efficient cities through Forought´s
Theoretically, some individuals use the transport system. extreme efficiency model and compares the results with the
Possible distortion can occur in cities with various efficiency scale proposed by Cooper et al. (2007). Finally, the
attractions (trade, education, health, leisure, business, Andersen and Petersen (1993) proposal for ranking DMUs
etc.) that may bring in people from neighboring towns. was used. From the initial 49 DMUs, 21 were considered in
Inhabitants, as a decision variable, assist planners in accordance with the criteria in section 3.3. For these 21
selecting the most appropriate transportation modal. DMUs, the scenarios were tested, and it was verified that the
ii. Public transport fleet – This variable indicates the non-utilization of some input/output variables, including taxi
amount of vehicles that are available, i.e., this variable is fleet, total number of vehicles in the municipality and
a transport capacity indicator. The bus in the public inflations, did not change the result.
transport fleet should be adequate, reliable, comfortable,
clean and the service should be punctual in order to 4.6 Studies and results of analysis
attract user to adopt it as a means of transportation. .
iii. Average daily passengers carried – This valuable, which The ICC report (2011 version) ranks cities according to the
is reported by the surveyed cities, defines the average percentage of passengers/population carried by an urban
number of daily passengers carried by the public public transport fleet. It ranks Porto Alegre 1st, São Paulo
transport system. This indicator seeks to describe the 2nd and Vila Velha last of the 49 cities. However, analysis of
amount of passenger travel in the system (a person can multiple inputs and multiple outputs changes the municipality
make one or more trips per day). This number includes competitiveness rankings in relation to the ICC ranking.
passengers who passed through turnstiles or were
possibly counted. In some cities, many gratuities 4.6.1 Case 1 – Infrastructure efficiency
(elderly) do not pass through turnstiles, so they are not
included in this indicator. The inputs city population and public transport fleet and the
iv. Average gratuity – This variable is the number of trips output average daily passengers carried were considered. The
that were made by passengers who have the right to be results show that the cities of Porto Alegre and São Bernardo
transported without buying a ticket or pay a lower rate. do Campo have the highest infrastructure efficiency. This
Similar to the previous item, there are free trips that measure of infrastructure efficiency evaluates resource use,
cannot be included in this indicator. however, and does not indicate that these municipalities have
"perfect" transportation systems. Rather, the municipalities
4.4 Model selection and formalization are benchmarked with respect to use of the infrastructure
following a set of specified inputs and outputs.

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4.6.2 Case 2 - The given service level 22%, respectively.

The inputs the city's population and the average number of 4.6.3 Case 3 – Public transport efficiency evaluation
passengers carried per day and the output urban
transportation fleet were considered. This study seeks to This study identifies the most efficient city through the
identify the "comfort" that the public transportation system discriminatory power of the extreme efficiency model
offers to passengers in place of efficiency. The ICC (version (equation 3) proposed by Foroughi (2011). In case 2, the
2011) discloses the percentage of the population that is cities of Curitiba and Betim had the highest service level. The
carried by bus and ranks Curitiba 14th and Betim 36th for results of Foroughi´s extreme efficiency for the years 2006,
2009. However, based on the inputs and outputs in this study, 2007, 2008, and 2010 shows the city of Curitiba with highest
Curitiba and Betim rank highest in service level. This result rank. In 2009, São Paulo was the most efficient. We
indicates that the population opts for the public transport calculated the efficiency of scale (Cooper et al. 2007), and we
considering comfort, availability, occupation rates, price and again found that Curitiba is the most efficient, which is
ease of reaching the destination. consistent with the measure of extreme efficiency by
Foroughi (2011). Finally, using the proposal of Andersen and
Table 1 – Results for case 2 Petersen (1993), we calculated the average efficiency ranking
for the DMUs. Figure 2 shows the DMU rankings, and again,
Curitiba is the most efficient, followed by Betim, São Paulo
City/Year 2005 2006 2007 2008 2009 2010
Anapólis 53,06 92,69 84,09 84,31 79,07 75,60
and Vila Velha. Campinas is ranked ninth. These results
Belo Horizonte 90,97 85,29 86,36 85,23 84,39 95,00 confirm the applicability of DEA for this study.
Betim 91,25 100,00 100,00 100,00 100,00 100,00
Blumenau 74,32 68,90 74,36 70,55 68,59 69,80
Campinas 74,34 82,62 87,08 84,99 83,11 84,18
Campo Grande 81,08 77,57 78,75 69,68 67,89 69,99
Caruaru 78,34 77,51 74,33 78,64 75,60 83,69
Curitiba 100,00 100,00 100,00 100,00 100,00 100,00
Fortaleza 75,73 68,01 68,97 64,19 61,97 58,18
Guarulhos 100,00 85,36 83,70 82,65 73,56 95,74
Juiz de Fora 75,19 73,71 74,33 72,89 72,43 77,55
Mogi das Cruzes 68,23 69,11 62,24 60,47 54,09 54,03
Porto Alegre 82,06 79,34 80,79 80,05 80,40 84,75
Salvador 64,49 61,30 58,72 57,77 59,15 66,21
Santos 53,67 63,86 66,64 64,35 63,83 64,00
Serra 91,72 83,99 90,82 94,43 100,00 93,22
Sorocaba 75,06 69,98 68,89 69,42 69,48 69,85
São Bernardo do Campo 45,83 41,04 41,37 39,38 39,28 47,95
São Paulo 100,00 97,26 100,00 97,52 97,88 96,27
Uberlândia 75,93 72,62 67,00 71,19 65,91 65,39
Vila Velha 97,70 95,37 85,01 100,00 77,83 100,00
Figure 2 – Average Ranking of DMUs
Table 1 presents the change in the municipality index over
time for the peers, showing no change in the index for some 5. FINAL CONSIDERATIONS
municipalities and improvement for others. Local strategic
influences significantly affect the index. An action by the city Transportation is essential to people’s daily lives, and its
of Betim created the Regional Commissions of Transport and transportation planning should prioritize the needs of citizens,
Traffic (CRTT), which is composed of community members having as a main actors and the ultimate goal .The
and helps shape public policies regarding public contribution of the DEA tool is quite significant in this study
transportation in the city. The slogan "we are working to because it provides clear results while avoiding evaluators
offer the best possible service" and the statement by the interference through the assignment of weights to indicators
President and CEO of Transbetim, Eduardo Lucas, that they according to their own criteria. The modeling process is
have "Made changes in schedules and itineraries by listening neither complex nor laborious with the availability of several
the people" (http://redejpnews. blogspot.com/2010/05/nova- software tools.
red-de-transport-publico-EM. html) certainly contributed to
its high municipality index. In 1974, Curitiba implemented a In this study, the DEA results obtained with the raw data
high capacity bus system, BRT (Bus Rapid Transit), with 20 extracted directly from the database showed little difference
miles of exclusive bus route for urban transport. Significant when compared with the normalized data. Using different
improvements in infrastructure, vehicles and operational input and output variables significantly influences the results.
measures contributed to a higher quality of service (Lerner, This study considers three cases, each with a set of inputs and
2009), as demonstrated by the leading position of Curitiba outputs.
throughout the years analyzed. Moreover, for Campinas to The use of different objectives allows the municipalities to be
improve its service level given its number of inhabitants, it compared in terms of different aspects of efficacy and
should have increased the fleet by 34%, 21%, 14% and 18% performance.
in the years 2005, 2006, 2007 and 2008, respectively, and in For example, Porto Alegre and São Bernardo have the
2009 and 2010, it should have increased the fleet by 20% and highest infrastructure efficiency but low service level. In
18% and decreased the passengers transported by 17% and contrast, Curitiba and Betim have high service level but not

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