Measuring the Efficiency of Public Transport Lines in Albania using
DEA Model
MARIANA NIKOLLA1, JONA MULLIRI1, ARTUR RIBAJ2*, ALBA TEMA3
1Department of Mathematics and Informatics, Faculty of Economics and Agribusiness,
Agricultural University of Tirana,
Tirana,
ALBANIA
2Faculty of Economics,
LOGOS University College, University of Tirana,
Tirana,
ALBANIA
3Faculty of Economics and Agribusiness,
Agricultural University of Tirana,
Tirana,
ALBANIA
*Corresponding Author
Abstract - Public transport is considered important to reduce air pollution. For this reason, it is very important
to have efficient public transport lines. The purpose is to analyze 15 public transport lines in Albania by using
the DEA model. The analysis is based on information about citizens' perceptions of five attributes (frequency,
cleanliness, possibility to find a seat, punctuality, and ticket price) of public transport lines. The information is
provided by conducting a survey of 120 users of public transport lines. The results indicate that it's important to
improve some attributes to increase the use of public transport.
Key-words: DEA Model, public transport, efficiency, input, output
Received: October 5, 2022. Revised: February 12, 2023. Accepted: March 8, 2023. Published: April 10, 2023.
1 Introduction
Environmental pollution is one of the critical issues
the world is facing nowadays. Albania is one of the
countries with the highest levels of pollution, where
air pollution is present and very concerning.
According to the polluted countries map published
by the World Health Organization (2022), Albania
has the highest level of pollution among the Western
Balkan Countries. Also, according to, [1], air quality
in Albania didn’t meet World Health.
Fig. 1: Death rate from air pollution, Albania, 1990
to 2019. Death rates are given as the number of
attributed deaths from pollution per 100,000
populations.
Source: IHME, Global burden of disease [2019]
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The full dataset used in Fig. 1 is at the Appendix
section. These rates are age-standardized, meaning
they assume a constant age structure of the
population: this allows for comparison between
countries and over time.
Organization guidelines for acceptable PM2.5
exposures. The observed average of PM2.5
exposures in Albania for the present year is 15.4
μg/m3 while the acceptable annual average
according to WHO should not exceed 10 μg/m3. Air
pollution is the result of many factors such, as the
reduction of urban green spaces, non-efficient waste
management, or the use of non-conventional fuel.
However, the main reason for air pollution in
Albania seems to be vehicle emissions, where old
diesel vehicles remain problematic. Different ways
have been explored to reduce air pollution,
especially in urban areas. One of these ways is
encouraging citizens to use public transport, [2].
However, in Albania and especially in the capital
city of Tirana. There is a very high level of use of
private cars. In 2020, Tirana is ranked first, among
the European capital with the most polluted air, [3].
This is also confirmed by the measurements of NO2
concentration. The main purpose article analyzes the
efficiency of 15 public transport lines and identifies
the factors that would improve their performance.
The efficiency analysis is conducted by using the
DEA mathematical model, which consists of the
results of the relative efficiency of similar units that
use some inputs and produce some inputs, [4]. To
estimate the pollution from public transportation, we
will use the Statistics in Tirana’s SDS indicate that
36% of residents are active users of public transport;
27% use their private cars; and the rest are classified
as using alternatives, such as bicycles, motorcycle,
and walking, [5]. The actual public transport fleet
consists of 305 buses, out of which only 65 buses
comply with Euro-V/VI standards on combustion
emissions. According to data provided by the
Municipality of Tirana, the combined public
transport capacity (seats and standing volume) is
30,365 passengers, with only 31% of this capacity
consisting.
2 Literature Review
To investigate the urban public route's efficiency
utilizing the "data envelopment analysis (DEA)"
technique. To analyze route performance, DEA is
using, and performance measures including route
design, cost, service, operation, and comfort
efficiency. Transit performance was studied by
many transportations, [6], showing that the DEA
application is very significant in the urban transport
area. Moreover, [7], applied a non-parametric DEA
procedure to estimate the productive efficiency of a
transit system. Furthermore, [8], used DEA to assess
the US transit systems' efficiency for five years;
they found the existence of positive relations
between efficiency and effectiveness Transit system
produces multiple outputs consuming multiple
inputs. There had been a debate about which of
those parameters defines the overall performance of
public transit. [9], used operation time, round-trip
distance, and the number of the bus stop as inputs to
measure operational efficiency whereas commuters
who use buses, population 65 and older, and persons
with disabilities were used as inputs to measure
spatial effectiveness. [10], used fuel consumption,
number of full-time workers, and number of
operating buses as the input variables. [11], used
average travel time per round trip, number of
vehicles, operators, and the total number of stops in
the round trip as input variables. Input variables can
be modified by the researchers as per the
requirements and scope of their study as long as
they include the major operating and maintenance
cost of the system. [12], used output variables: total
average number of passengers per day as an
effective measure and vehicle km per day as an
efficiency measure. The main purpose of this
article is to analyse the efficiency of 15 public
transport lines and to identify the factors that would
improve their performance. The efficiency analysis
is conducted by using the DEA mathematical model,
which consists of the results of the relative
efficiency of similar units that use some inputs and
produce some outputs. DEA can employ various
output variables as performance indicators as per the
scope of the study. Choosing the input and output
variables as being a critical state, special attention
should be given considering the direction of the
study. The model DEA not only enables us to
measure the performance of urban lines in the study,
but it also shows us the way to improve the
efficiency of the transport lines, which during the
study, resulted in relatively low performance. The
aim is of course to increase competition between
urban lines and encourage them to satisfy and fulfill
the needs and expectations of the population. The
results of the study serve as feedback to improve the
quality of public transport in the referred lines and
throughout the country.
3 Methodology
The DEA is a non-parametric method applied to
compare the efficiency measurement of several units
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with the same objectives using linear programming.
It gives an image of a general measure performance
of different units. Firstly, [13], introduced it, and
later, [14], extended this technique. A key advantage
of DEA was by handled multiple inputs and outputs;
this gives comprehensive consideration for analysis
units. The inputs and outputs of units depend on the
properties of the system analyzed. When the DEA
model is used, some limitations of the model must
be taken into account, which are: the number of
units must be at least twice the sum of the input and
output variables; it is a good method to compare a
unit with other similar units in the selection, not
compared to a "theoretical maximum". Some
features that make DEA a very popular and used
technique are:1. It enables the use of analyzes with
several inputs and several outputs; 2. It does not
require any assumption about the functional form
connecting inputs and outputs; 3. Units are directly
comparable to another unit or a combination of the
unit’s others; 4. Inputs and outputs can be measured
in different measurement units.
DEA is a linear programming problem as
formulated in the equation below to determine the
efficiency score.
4 Case Study
Albania Public Transport Lines (The
Number of Lines n = 15)
The Sample that is taken is 120 users of public
transport lines n =120. The information used to
conduct the analysis consists of primary data. This
information was provided through a questionnaire
focused on questions that tend to measure the above
attributes (on a scale of 1 to 10, where 1 is the
maximal satisfaction and 10 is the minimal level of
satisfaction) for 15 public transport lines. The
transport lines are
1
: These line are shown in Table 1.
1
1. Kombinat-Kinostudio, 2. Kruje-Tirana, 3. Kamez -
Center, 4. New Tirana, 5 Laprake-Tirane, 6 Tirane-Diber,
7 Fier-Tirane, 8 Fier- New Seman 9. Student City -
Jordan Misja, 10. Institute-Center, 11. Fushë Krujë -
Tirana 12. Krujë - Fushë Krujë, 13. Kashar - Yzberisht -
Center. 14. Porcelan Center, 15. Lac - Tirana
Table 1. The number of transport line
The majority of the respondents are young, which is
part of the population which uses more public
transport, but there are also respondents of different
ages. While in terms of gender, 66% of respondents
are female and 34% are male. Regarding
employment status 50.4% are employed and 28%
are students, while the rest are retirees and
unemployed.
Table 2. Variables used, definition, and measure
Input Variables
Output Variables
1. Frequency
Refers to the frequency of lines in
stations, [15].
On a scale of 1 to 10
1. Public transport
quality perception
Level of satisfaction of
citizens using public
transport, [17].
On a scale of 1 to 10
2. Punctuality
Refers to the opportunity to access
the service in the timetable, [16].
On a scale of 1 to 10
3. Cleanliness
Level of cleanliness and presence
of garbage in the busses, [16].
On a scale of 1 to 10
4. Ticket price
Structure of the prices of different
ticket types, [15].
On a scale of 1 to 10
5. Possibility to find a seat
The possibility of the passengers
taking a seat on the bus, [19].
On a scale of 1 to 10
*Note: Table 2 created by the authors
Transport Lines
Kombinat-Kinostudio
Kruje-Tirane
Kamez- Qender
New Tirana
Laprake-Tirane
Tirane-Diber
Fier-Tirane
Fier- New Seman
Qyteti Studentit-Jordan Misja
Institut Qender
Fushe Kruje-Tirane
Kruje-Fushe Kruje
Kashar -Yzberisht Qender
Porcelan Qender
Lac-Tiranë
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To measure the efficiency of public transport lines is
used the input-oriented DEA model (Table 2).
DEA calculates the efficiency of a unit compared to
all units in analysis, choosing the best possible
alternative. Technical efficiency in DEA in the
presence of some inputs and outputs is determined
as the weighted sum of outputs divided by the
weighted sum of inputs. The set of weights for a
unit should be solved in a way that gives the greatest
possible value of technical efficiency information
for that unit, meanwhile, the values of the efficiency
indicator of other units, for the same set of weights
are between 0 and 1. Efficient units have a technical
efficiency indicator value of 1, while units that have
an indicator value of less than 1 are inefficient, [19],
[20]. The efficiency of the unit assessed () using
DEA, is given by the formula:
󰇛 󰇜  





(1)
Then is set objective function
 
 (2)
With necessary constraints for each analyzed unit:
1.

 
2.


3.
  and (3)
If this coefficient is equal to 1, the analyzed unit is
considered efficient, while if it is smaller than 1,
then the analyzed unit is considered relatively
inefficient, [19], [20].
4.1 Data Analysis of Case Study
The linear Programming problem for the study unit
is as follows:
Max: 5 output per unit weight of 1.
Conditions:
The problem is solved using the computer program
Excel (Data, Solver Solution), [18], [19], [20], [21].
Table 3 are presented the results of the DEA
analysis of efficiency for unit 1 and other units.
Based on this solution we identify the efficient
transport lines, which are Kombinat-Kinostudio,
Krujё-Tirana, Kamёz-Center, Fier-New Seman,
Qyteti Studentit-Jordan Misja, Fush Krujё-Center,
Lac-Tirana, and Porcelan- Center, while other
transport lines have resulted inefficient. Problem-
solving is done by a
Table 3. The results of the DEA analysis for the
study units
*Note: Table 3 created by the authors, n=15
The results of the DEA analysis for the study units
are presented in Table 3. Also, the model provides
the opportunity to improve efficiency for inefficient
transport lines, showing the best combination of
inputs that increase the level of satisfaction of public
transport users. To apply this, we will take into
analysis 12 units that have resulted inefficient.
Firstly, we have applied for the DEA for the Krujё-
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Fush Krujё transport line. Unit 12, Krujё-Fush
Krujё resulted from less efficiency than other units
of the group, respectively 󰇛 󰇜. Then
we select the option Sensitivity Report in the Solver
Results dialog box. In the results of the Sensitivity
Report, the absolute value of shadow prices in the
column "Difference", are weights of the composed
unit.
Table 4. The results of DEA analysis for the Krujё-
Fushe Krujё transport line.
*Note: Table 4 created by the authors
The results of DEA analysis for the Krujё-Fushe
Krujё transport line is presented in Table 4. The
hypothetical unit produces output equivalent to the
output of the unit under study seeking smaller
amounts or equivalent to those used by inefficient
units.
Table 5. The results of the sensitivity of unit 12
*Note: Table 5 created by the authors
Table 6 is presented the best combination of inputs
that make unit 12 efficient by DEA.
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Table 6. The Composite unit values for unit 12.
*Note: Table 6 created by the authors
The improved DEA efficiency for unit 12 is shown
in Table 7. As we see, it is very important to
improve attributes such as punctuality, ticket price,
cleanliness, or frequency.
Table 7. Improved DEA efficiency for unit 12
*Note: Table 7 created by the authors
5 Conclusion and Recommendations
Environmental issues, especially air pollution is one
of the most concerning issues in Albania.
It is considered important to use public transport
as a way to reduce the high level of emissions of
private cars. We have taken in to analyze the
efficiency of 15 public transport lines. To conduct
the analysis, we have used the input-oriented DEA
model, which calculates the efficiency of a unit
compared to all units in the analysis, choosing the
best possible alternative. The analysis resulted in
some efficient transport lines such as Kombinat-
Kinostudio, Kruje-Tirana, Kamez-Qender, Fier-
New Semani, Qyteti Studentit-Jordan Misja, Fushe
Kruje-Qender, Lac-Tirana, and Porcelan-Qender.
We used Solver to improve the efficiency of the
Kruje-Fushe Kruje transport line.
For inefficient units exists a linear combination
of efficient units that results in a composite unit,
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which produces at least the same output using the
same or fewer inputs than the inefficient unit as in
the case of unit 12.
From the efficiency analysis (referring to the
result of the sensitivity report), the absolute value of
the shadow prices (Shadow Prices), are the weights
of the composite unit, which is more efficient than
the unit under study 12.
The average of the weights is approximately
40% for unit 15 (Lac-Tirana with 1 efficiency
result) and 16% for unit 14 Porcelan-Center with 1
efficiency result) from the composite unit
(assumed). This hypothetical unit resulted in the
same output as the output of unit 12 but reduced the
input perceptions.
6 Recommendation
A recommendation for future research could be the
increase of included attributes in the study. Also, a
larger sample and extension in other lines could
provide an in-depth understanding of the public
transport efficiency in Albania.
This study can be used to increase the performance
of transport lines to increase the use of public
transport.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflict of interest to declare
that is relevant to the content of this article.
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APPEDIX
These rates are age-standardized, meaning they
assume a constant age structure of the population:
this allows for comparison between countries and
over time.
Entity Code Year
Deaths - Cause: All causes - Risk: Household air pollution from solid fuels - Sex: Both - Age: Age-standardized (Rate)
Deaths - Cause: All causes - Risk: Ambient particulate matter pollution - Sex: Both - Age: Age-standardized (Rate)
Deaths - Cause: All causes - Risk: Air pollution - Sex: Both - Age: Age-standardized (Rate)
Deaths - Cause: All causes - Risk: Ambient ozone pollution - Sex: Both - Age: Age-standardized (Rate)
Albania ALB 1990 97.25 46.45 146.67 4.79
Albania ALB 1991 98.11 46.05 147.35 4.36
Albania ALB 1992 93.29 43.29 139.73 4.07
Albania ALB 1993 88.01 40.64 131.59 3.9
Albania ALB 1994 81.51 37.55 121.62 3.67
Albania ALB 1995 81.76 37.77 121.65 3.42
Albania ALB 1996 80.92 38.59 121.18 3.08
Albania ALB 1997 76.98 39.24 117.78 3.02
Albania ALB 1998 72.16 40.06 113.53 2.6
Albania ALB 1999 68.41 41.24 110.85 2.2
Albania ALB 2000 63.7 41.54 106.44 1.8
Albania ALB 2001 57.58 40 98.9 1.7
Albania ALB 2002 56.16 41.6 99.31 1.99
Albania ALB 2003 55.71 44.2 101.61 2.26
Albania ALB 2004 51.97 44.43 98.06 2.29
Albania ALB 2005 47.44 43.65 92.59 2.08
Albania ALB 2006 41.52 41.61 84.49 1.8
Albania ALB 2007 36.13 40.09 77.55 1.7
Albania ALB 2008 33.03 40.89 75.18 1.56
Albania ALB 2009 29.49 40.45 71.06 1.4
Albania ALB 2010 27.01 40.05 67.93 1.14
Albania ALB 2011 25.55 40.04 66.38 1.08
Albania ALB 2012 24.11 39.41 64.31 1.09
Albania ALB 2013 22.96 38.89 62.67 1.08
Albania ALB 2014 22.1 38.83 61.76 1.06
Albania ALB 2015 21.27 38.83 60.8 0.87
Albania ALB 2016 20.2 38.32 59.14 0.78
Albania ALB 2017 19.24 37.83 57.63 0.69
Albania ALB 2018 18.35 37.36 56.23 0.64
Albania ALB 2019 17.54 36.93 54.94 0.57
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