iBusiness, 2013, 5, 154-160
Published Online December 2013 (http://www.scirp.org/journal/ib)
Open Access IB
Technical Efficiency in the Container Terminals in Mexico,
1982-2010: Through Data Envelopment Analysis (DEA)
Odette V. Delfín-Ortega, César L. Navarro-Chávez
Institute of Economic and Business Research, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, México.
Email: odettedelfin@hotmail.com, cesar126@hotmail.com
Received October 28th, 2013; revised November 18th, 2013; accepted December 2nd, 2013
Copyright © 2013 Odette V. Delfín-Ortega, César L. Navarro-Chávez. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original
work is properly cited.
The paper shows an analysis of the global technical efficiency of container terminals of the main ports of Mexico in the
period 1982-2010, through Data Envelopment Analysis (DEA). This methodology allows us to measure each decision
unit evaluated in relation to other homogeneous units. The aim of the study is to determine the importance of global
technical efficiency, pure technical efficiency and scale efficiency in the ports of México. For this purpose, quay length
and number of employees are used as input and as output of the number of containers. The results show that the Mexi-
can ports in general have a low technical global efficiency and only the ports showed that technical global efficiency,
technical pure efficiency and scale efficiency were Veracruz and Tuxpan in th e year 1982, and Manzanillo and Lazaro
Cárdenas in the year 2010. For that reason, it requires better operability which means greater mobility of TEUs.
Keywords: Technical Efficiency; Data Envelopment Analysis; Mexico Ports
1. Introduction
The ports are a very important part in the development of
a country, allowing a more efficient transport system.
The efficient operation of any of the activities taking
place within the port is important for products using
shipping to reach the end consumer markets at minimum
cost and in the shortest time possible.
In the specific case of container terminals, the market
for container services of maneuvers comprises different
services that are used to move a container between the
boat and land transpor tation. Additionally, shipping com-
panies, as users, demand high productivity services, so
that, to the extent that is greater, the time spent on the
boat will be lower, as well as the costs for the use of port
infrastructure [1].
Developing efficient port operations can significantly
improve the export competitiveness of a nation and the
availability of imported products.
The aim of this investigation is to determine the im-
portance of global technical efficiency, technical pure
efficiency and scale efficiency in the ports of México and
we consider the hypoth esis that the container terminals in
Mexico have a low global technical efficiency because
they have not achieved significant improvements in the
scale of production.
2. Literature Review
Efficiency is defined as “the degree of optimization of
the results obtaine d in relation to the resources u sed” [2].
Another definition that nicely illustrates the efficiency is
“the relationship between the goods and services con-
sumed and goods and services produced, or what is the
same, for services rendered (outputs) in relation to the
resources used for this purpose (inputs)” [3].
Data Envelopment Analysis model (DEA) is a non-
parametric technique that facilitates the construction of
an envelope surface or efficient frontier from the avail-
able data set under study entities known as DMU (Deci-
sion Making Unit) [4]. Technical efficiency has its origin
in the early years of the decade of the 50’s with Koop-
mans [5] and the first measure of technical efficiency is
proposed by Debreu [6] and Shephard [7], although with
different orientation (output and input, respectively).
Despite the theoretical relevance of these works, in any
efficiency quantified, this task is performed by Farrell [8],
which is considered the precursor to the extent of techni-
Technical Efficiency in the Container Terminals in Mexico, 1982-2010: Through Data Envelopment Analysis (DEA) 155
cal efficiency.
The scheme proposed by him, with the following
components, technical, allocative and overall efficiency.
In this sense, a particular production process is techni-
cally efficient when starting from a certain inputs and
assuming a fixed production technology, it achieves the
highest possible level of output. Allocative efficiency is
achieved, on the other hand, when knowing the prices of
inputs and assuming that there may be changes in pro-
duction technology, their combination allows to achieve
a given level of output at the lowest cost.
DEA models can be classified according to:
• The type of efficiency measure that provide: radial
and non-radial models.
• The orientation of the model: input-oriented, output-
oriented or input-output ori ented.
• The types of returns to scale production technology
characterized understood as the way in which the factors
of production can be characterized by the existence of
returns to scale: constan t or variable to scale.
Farrell study is complemented by the work of Charnes,
Cooper and Rhodes [4], which started at constant yield
CRS, such that a change in the levels of inputs leads to a
proportional change in the output level, which requires
many optimizations as decision units (DMU). It has two
orientations: input (a comparison between the minimum
level of inputs required for a given level of outputs, and
actually taken) and output orientation: (A comparison of
the maximum attainable output for a given level of inp uts,
and the actually achieved). The CCR model works with
constant returns to scale, which means that the DMU
which has the highest ratio of input product (higher slope)
establish the efficiency frontier and DMUs would be
accepted under this frontier are considered inefficient
DMUs. It can be written in general terms in 3 ways: frac-
tional, multiplicative and enveloping.
It shows the linear programming model guidance out-
maxs.t 1
kkpj jp
kkij j
iVU kj
 (1)
The assumption of CRS is not always appropriate in
real life contexts, later, Banker, Charnes and Cooper [9]
extended the original model to include variable return s to
scale (VRS). They considerated various circumstances
such as imperfect competition, restrictions on access to
funding sources, etc. It can cause the units not operating
at optimal scale and modifying the linear program so that
they enter a convexity constraint. To d ifferentiate it from
the previous model is called variable returns to scale
(VRS). Being the output-oriented model as follows:
0; 01
fif iz
rzf r
This modification allowed to decompose the global
technical efficiency (GTE) into Pure Technical Effi-
ciency (PTE) and Scale Efficiency (SE). For this, it is
necessary calculate two models: CRS and VRS on the
same data, if there is a difference in the two measure-
ments for a particular DMU, then it means that the DMU
has scale inefficiency and inefficiency value is the dif-
ference between the CRS and VRS measurement.
Pure Technical Efficiency matches with VRS meas-
urement. Scale inefficiency arises of producing a scale
level is not optimal, considering as such the scale ob-
tained from the efficient activity of the signatures (CRS =
The Global Technical Efficiency is the product of the
two efficiencies: pure technical and scale and its meas-
urement matches with CRS.
Global technical efficiency is then represented fol-
If SE = 1, then ETG = ET P, indicating that the unit has
no scale inefficiency and therefore operates in an optimal
scale [10]. Scale efficiency measures the impact of scale
size on the productivity of a DMU (see Figure 1).
The scale efficiency of firm D relates to the distance
from the technically efficient data point E, to the CRS
technology and is equa l to [11]:
Figure 1. Scale efficiency.
Open Access IB
Technical Efficiency in the Container Terminals in Mexico, 1982-2010: Through Data Envelopment Analysis (DEA)
After calculating the scale inefficiency, it can analyze
what kind of returns are those which cause such ineffi-
ciency, if the DMU exceeds the size of production scale,
and therefore presents decreasing returns to scale, or if it
has returns to scale, and therefore not has reached the
limit of growth provid ed by this situation.
Ports Efficiency
Several authors have studied the efficiency of the ports as
it shows:
Eduardo Martínez-Budria, Díaz-Armas and Navarro
Ibañez [12]. They analyzed the efficiency of Spanish port
services, using the DEA-BCC technique and they used
for inputs number of employees, quay length, surface
area, labor cost, capital cost and number of passengers
and for outputs: containerized cargo, general bulk cargo,
liquid bulk, solid cargo bulk, income payment area and
Payment for private users.
Park and De [13] realized an analysis of port effi-
ciency using the DEA-CCR model and DEA-BCC in
Korean ports. They used for inputs berthing capacity,
cargo handling capacity, profitability and Revenues for
outputs they used loading throughput, number of vessels,
commercialization, global throughput, customer satisfac-
tion. The study finds that altern ative DEA is a potentially
powerful approach to the evaluation of the overall effi-
ciency of seaports.
Ramón Sala, Molinos-Senante and Amparo Medal [14]
analysed the efficiency of 28 Spanish ports using a non-
radial DEA model: the Russell Measure. They used for
inputs quay length, surface terminal, number of cranes
and number of employees and for outputs: number of full
containers 20’, number of empty containers of 20’, num-
ber of full containers of 40’, number of empty containers
of 40’. They used this methodology in order to obtain the
efficiency score for each of the inputs analyzed. As re-
sults of the analysis, they conclud ed that the Spanish Port
System has generally a high average level of efficiency
but it could grow around 20% to consider that all ports
operate on the efficient frontier.
Cullinane et al. [15] studied the technical efficiency of
port container terminal, using the DEA model CCR and
DEA-BCC too. They used for inputs Terminal length,
terminal area, quayside gantry, yard gantry and straddle
carrier and for outputs they used Containers throughput.
The paper presents the pros and cons of port privatization
and provides an empirical examination of the relationship
between privatization and relative efficiency within the
container port industry.
Joyce Low [16] realized a study to provide an assess-
ment on the required waterside and quayside capacity of
23 major Asian ports and estimate their inefficiency cost
associated with excess capacity . She applied an integrated
suite of DEA models (CCR, BCC, SBM, Congestion and
Measure-Specific) to measure the efficiency in the ports.
The application of an integrated suite of DEA models
enables more insights to be gleaned and better result
validation, since ports differ in terms of their scale of
operations, output demand and natural endowments. The
findings from this research show that ports in Asia are
generally characterized by constant or increasing returns
to scale.
3. Methodology
Model Specifications: In the measurement of technical
global efficiency, we works the Constant Returns to
Scale (CRS) and Variable Returns to Scale ( VRS ) DEA
models, with output-oriented because it is intended to
analyze the possibility of maximizing the number of
TEUs1 with the inputs you have.
One calculates the technical global efficiency, as well
as pure technical and scale efficiency, that the Decision
Making Units (DMU’s) have had. The sample ports are
those that moved containers during the period 1982-201.
They are ports of Mazatlan, Manzanillo, Lazaro Car-
denas, Altamira, Tuxpan, Veracruz, Progress and Salina
Cruz. It is necessary also to consider that the number of
DMUs must be at least two times the total number of
inputs and outputs considered [17]. In this research in-
puts used are: dock length and number of employees and
outputs: number of TEUs handled annually (see Table
In order to obtain data that model the production func-
tion, differe nt s ou rces were used:
1) Statistical yearbooks of ports in México in the Sec-
tion Container Movement Coordination Ports and Mer-
chant Marine SCT [18],
2) Port’s development plans for selected periods.
4. Results and Discussion
In general there was a low global technical efficiency in
the port sector in Mexico during the period under study.
However, the port of Manzanillo stands out as it is effi-
cient for the period 2000-2 010, while the ports of Lazaro
Cardenas and Veracruz, although efficient for some years
are not known for having continuity in this indicator. In
the particular case of Lazaro Cardenas in 2000, was
minimal movement of containers that had compared to
other years, which led to the fact that it had the lowest
level of efficiency in the figures obtained for this port.
Tuxpan, Salina Cruz and Mazatlan are in a difficult posi-
tion in terms of technical global efficiency, not only for
its steep downward trend but for their minimum values
on measures of efficiency (see Table 2).
1Twenty-foot equivalent unit (TEU) it is used to describe the capacity
of container ships and container terminals. It is based on the volume o
a 20-foot-long.
Open Access IB
Technical Efficiency in the Container Terminals in Mexico, 1982-2010: Through Data Envelopment Analysis (DEA)
Open Access IB
Table 1. Number of containers handled at the ports of Mexico 1982-2010.
1982 1990 1995 2000 2005 2010
Mazatlan 2611 4086 10,012 16,813 17,559 25,795
Manzanilo 3133 32,792 86,938 426,717 872,386 1,511,378
Lázaro Cárdenas 2088 24773 55,109 752 132,479 796,023
Altamira 14,620 55,093 102,996 182,545 324,601 488,013
Tuxpan 18,066 1020 391 104 15 18
Veracruz 33,575 110,019 222,959 540,014 620,858 661,653
Progreso 82 3125 11,545 56,581 71,769 56,434
Salina Cruz 12,009 20,311 14,404 5413 922 5432
Source: General Coordination of Ports and Merchant Marine, 2012.
Table 2. Global technical efficiency in ports of México 1982-2010.
1982 1990 1995 2000 2005 2010
Mazatlán 0.2946 0.1649 0.1856 0.1081 0.0635 0.1394
Manzanillo 0.3142 0.4633 0.5259 1 1 1
Lázaro Cárdenas 0.5982 1 1 0.0087 0.3451 1
Altamira 0.733 0.7784 0.623 0.4449 0.4031 0.505
Tuxpan 1 0.0432 0.0079 0.0012 0.0001 0.0002
Veracruz 1 0.876 1 1 0.647 0.5892
Progreso 0.0247 0.1147 0.2095 0.5304 0.3291 0.349
Salina Cruz 0.7373 0.4304 0.2751 0.0534 0.0044 0.0236
Source: Personal compilation based on DEA resul ts .
Subsequently it performed global technical efficiency
(GTE), disaggregated into technical pure efficiency (TPE)
and efficiency scale (ES). The results allow us to distin-
guish situations in which a production unit may be tech-
nically efficient but not placed in the optimal scale of
By 1982, the most efficient ports were Tuxpan and
Veracruz, as both pure technical efficiency and scale
efficiency had the highest weight. They could use a
smaller amount of inputs required to meet demand, plus
they had an optimal production scale. On the opposite
side are Mazatlan, Manzanillo, Altamira and Salina Cru z,
who were not efficient in any of the categories consid-
ered. The port of Progreso although proved to be techni-
cally efficient in the area of pure efficiency, was not
placed in the optimal scale of production (see Table 3).
In the year 2010 the ports of Manzanillo and Lazaro
Cardenas are the most efficient in both pure and scale
efficiency. Tuxpan was the one that had the lowest tech-
nical global efficiency score, this was due to substantially
decreased the number of TEUs, reflecting the efficiency
of very small scale, although in pure technical efficiency
it was shown to be efficient.
4.1. Benchmarking
With Benchmarking analysis one identifies the DMUs
that are considered as a reference for the inefficient
DMUs, having similar characteristics. It is observed that
both in the year 1982 and 2010, the Port of Lazaro
Cardenas is the one most often taken as the reference
port. The ports of Mazatlan, Manzanillo, Altamira and
Salina Cruz were less efficient ports in 1982, so one
makes reference to Lazaro Cardenas, Tuxpan and Ve-
racruz. Already in 2010, the most inefficient ports took to
Manzanillo and Lazaro Cardenas as reference (see Table
4.2. Slacks Analysis
The analysis of the slacks variables, allows you to see
where you can make further reduction on some factor or
increasing the output. In 2010, 50% of the ports had ex-
cess workers. Specifically Mazatlan cut 18 workers
needed in 1982 and 30 in 2010 to be more efficient. In
Technical Efficiency in the Container Terminals in Mexico, 1982-2010: Through Data Envelopment Analysis (DEA)
the case of quay length for 1982 the port of Manzanillo
and Altamira had 134.06 and 48.14 meters wasted re-
spectively while the port of Salina Cruz in 2010 had
178.92 meters unused. It would have been more efficient
to use this input at its full strength (see Table 5 ).
The most important con tribution in this study is th at it
Table 3. Efficiency in ports of México 1982-2010.
1982 2010
Mazatlán 0.2946 0.794 0.3711 0.1394 0.3061 0.4554
Manzanillo 0.3142 0.4501 0.6979 1 1 1
Lázaro Cárdenas 0.5982 1 0.5982 1 1 1
Altamira 0.733 0.7753 0.9454 0.505 0.5543 0.9109
Tuxpan 1 1 1 0.0002 1 0.0002
Veracruz 1 1 1 0.5892 0.7428 0.7931
Progreso 0.0247 1 0.0247 0.349 0.989 0.3528
Salina Cruz 0.7373 0.8026 0.9186 0.0236 0.2765 0.0852
Source: Personal compilation based on DEA resul ts .
Table 4. Benchmarking analysis of the port sector in Mexico 1982-2010.
Port 1982 2010
Mazatlán 3 (0.97) 5 (0.03) 3 (0.11) 5 (0.89)
Manzanillo 3 (0.97) 6 (0.03) 2
Lázaro Cárdenas 3 3
Altamira 3 (0.6) 6 (0.4) 2 (0.12) 3 (0.88)
Tuxpan 5 5
Veracruz 6 2 (0.13) 3 (0.87)
Progreso 7 3 (0.07) 5 (0.93)
Salina Cruz 3 (0.68) 5 (0.02) 6 (0.31) 2 (0.01) 5 (0.99)
Source: Personal compilation based on DEA resul ts .
Table 5. Slacks variables analysis 1982-2010.
1982 2010
Port Quay length Workers Teus Quay length Workers Teus
Mazatlán 0 18.61 0 0 30.01 0
Manzanillo 134.06 0 0 0 0 0
Lázaro Cárdenas 0 0 0 0 0 0
Altamira 48.14 0 0 0 12.7 0
Tuxpan 0 0 0 0 0 0
Veracruz 0 0 0 0 97.54 0
Progreso 0 0 0 0 16.27 0
Salina Cruz 0 0 0 178.92 0 0
ource: Personal compilation based on DEA result s.
Open Access IB
Technical Efficiency in the Container Terminals in Mexico, 1982-2010: Through Data Envelopment Analysis (DEA) 159
presents an analysis of the efficiency of container termi-
nals in Mexico, which has not been done in the way pre-
sented in this work, one of the main differences is the
study period (1982-2010) which includes both stage
where it was managed entirely by the government as the
stage where there was already interventionism on the part
of private. On the other hand besides indicating the level
of efficiency of ports showing pure, scale and global ef-
ficiency, we present a benchmarking analysis in order to
identify those ports that are inefficient and they were
compared to other ports with similar characteristics and
that are efficient and finally with slack analysis shows
the number of inputs that must reduce to be more effi-
5. Conclusions
We have introduced the measurement of global technical
efficiency Mexican ports in the period 1982-2010 , which
in turn can be decomposed into pure technical efficiency
(PTE) and scale efficiency (ES).
In this research, we work the CRS and VRS DEA
model of output oriented. Input needs to consider quay
length and the number of workers, while output needs to
consider the number of containers handled annually. The
hypothesis is true, since the results show that on averag e
the ports have a global low technical efficiency because
most ports show a reduced scale efficiency.
Tuxpan and Veracruz were ports that had a higher
global technical efficiency in the year 1982. This was
due to the fact that production scale remained at its
maximum scale operating efficiently as shown in Table
2, as well as its resources properly optimized, thereby
realizing pure technical efficiency. The port that is char-
acterized by having the lowest efficiency in the period
was Progreso, despite having a high level of pure techni-
cal efficiency. In 2010, Manzanillo and Lazaro Carden as
were ports with the great global technical efficiency
while Tuxpan was the one that obtained less efficiency,
mainly because in that year they moved only 18 contain-
With Benchmarking analysis, one is able to identify
efficient ports that served as reference to the inefficient,
with the ports of Manzanillo and Lazaro Cardenas refer-
enced in the year 2010. In Slacks analysis, there must be
50% of the ports for this year that had a surplus of work-
ers, making it necessary to rethink hiring, where profiles
are evaluated as indicated for the management of these
terminals, and also to have ongoing training in techno-
logical areas as is true today the port of Manzanillo.
It is generally observed that the ports of Mexico are
inefficient mainly due to the poor results on the effi-
ciency of scale, which tells us that they are at the optimal
scale of production. As a matter of public policy, it is
necessary that they encourage that increased containers
are moved through investment policies for the procure-
ment of infrastructure and equipment that meet the re-
quired demand for there to be a better scale of production
and in turn to have a global efficiency technique.
[1] J. Ojeda, “The Port Problem in Mexico in Perspective in
1982-2004, Towards New Paradigms,” Regulation of
Transport Infrastructure, 2011, pp. 121-170.
[2] I. Igae, “Goal Setting and Performance Measurement in
the Public Domain,” Madrid, Spain, 1997.
[3] A. Aeca, “Performance Indicators for Public Entities,”
Document no. 16, Series of Principles of Managerial Ac-
counting, 2nd Edition, Madrid, 1997.
[4] A. Charnes, W. Cooper and E. Rhodes, “Measurement the
Efficiency of Decision Making Units,” European Journal
of Operational Research, Vol. 2, No. 6, 1978, pp. 429-
444. http://dx.doi.org/10.1016/0377-2217(78)90138-8
[5] T. Koopmans, “Efficient Allocation of Resources,” Eco-
nometrica, Vol. 19, No. 4, 1951, pp. 455-465.
[6] G. Debreu, “The Coefficient of Resource Utilization,”
Econometrica, Vol. 19, No. 3, 1951, pp. 273-292.
[7] R. Shephard, “Cost and Production Functions,” Princeton
University Press, Princeton, 1953.
[8] M. Farrell, “The Measurement of Productive Efficiency,”
Journal of the Royal Statistical Society: Serie A, Vol. 120,
No. 3, 1957, pp. 253-267.
[9] R. Banker, A. Charnes and W. Cooper, “Some Models for
Estimating Technical and Scale Inefficiencies in Data
Envelopment Analysis,” Management Science, Vol. 30,
No. 9, 1984, pp. 1078-1092.
[10] V. Coll and O. Blasco, “Evaluation of the Efficiency by
Data Envelopment Analysis,” 2006.
[11] T. Coelli, P. Rao, C. O’Donnell and G. Batesse, “An In-
troduction to Efficiency and Productivity Analysis,” 2nd
Edition, Springer, 2005.
[12] E. Martínez-Budría, R. Diaz-Armas, M. Navarro-Ibanez
and T. Ravelo-Mesa, “A Study of the Efficiency of Span-
ish Port Authorities Using Data Envelopment Analysis,”
International Journal of Transport Economics, Vol. 26,
No. 2, 1999, pp. 237-253.
[13] R. Park and P. De, “An Alternative Approach to Effi-
ciency Measurement of Seaports,” Maritime Economics
& Logistics, Vol. 6, 2004, pp. 53-69.
[14] R., Sala and A. Meda, “Study of Technical and Eco-
nomic Efficiency of Container Terminals,” Asepuma,
2004, pp. 1-11.
[15] K. Cullinane, D. Song and T. Wang, “The Relationship
between Privatization and DEA Estimates of Efficiency
in the Container Port Industry,” Journal of Economics &
Open Access IB
Technical Efficiency in the Container Terminals in Mexico, 1982-2010: Through Data Envelopment Analysis (DEA)
Bussiness, Vol. 57, No. 5, 2005, pp. 433-462.
[16] J. Low, “Capacity Investment and Efficiency Cost Esti-
mations in Major East Asian Ports,” Maritime Economics
& Logistics, Vol. 12, 2010, pp. 370-391.
[17] F. Lo, C. Chien and J. Lin, “A DEA Study to Evalua te t he
Relative Efficiency and Investigate the District Reor-
ganization of the Taiwan Power Company,” IEEE Trans-
actions on Power Systems, Vol. 16, No. 1, 2001, pp. 170-
[18] General Coordination of Ports and Merchant Marine,
“Monthly Statistical Report Cargo Movements, Ships and
Passengers,” Transport and Communications Sector, 2012.
Open Access IB