prioritization of bridges for maintenance planning using data envelopment analysis
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Prioritization of bridges for maintenance planningusing data envelopment analysisSanjay Sampat Wakchaure & Kumar Neeraj Jha aa Department of Civil Engineering, IIT Delhi, New Delhi, IndiaPublished online: 14 Oct 2011.
To cite this article: Sanjay Sampat Wakchaure & Kumar Neeraj Jha (2011) Prioritization of bridges for maintenanceplanning using data envelopment analysis, Construction Management and Economics, 29:9, 957-968, DOI:10.1080/01446193.2011.614267
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Prioritization of bridges for maintenance planningusing data envelopment analysis
SANJAY SAMPAT WAKCHAURE and KUMAR NEERAJ JHA*
Department of Civil Engineering, IIT Delhi, New Delhi, India
Received 23 December 2010; accepted 10 August 2011
Resources—especially funds allotted—for the maintenance of bridges, are generally scanty. Thus, it becomes
difficult to select bridges for maintenance from among several competing bridges to ensure their safety and
serviceability to the desired level. A bridge health index is considered a reasonably accurate depiction of the
condition of a bridge and hence is the basis for most of the decisions on fund allocation. However, it still
remains to be seen whether such a decision-making tool results in an efficient fund allocation. From data
collected on Indian bridges, it is observed that fund allocation based on bridge condition is not always judi-
cious. Rather, a number of factors affect the final decision on fund allocation. Hence, an alternative
approach of data envelopment analysis (DEA) has been used for scoring the efficiency of 14 bridges selected
for the study. Depending on the availability of data, this method can take into account other factors besides
the bridge health index that influence decisions on maintenance planning. The variables selected for the
DEA are: bridge health index, deck area of the bridge, maintenance cost of the bridge, and the age of the
bridge. The allocation of funds for the maintenance of bridges based on DEA has proved to be compara-
tively more efficient. This has been illustrated with the help of a numerical example. The proposed method
would enable bridge authorities to formulate better strategies for planning and executing bridge maintenance
activities in a cost-effective manner.
Keywords: Analytical hierarchy process, bridge, bridge health index, condition states, data envelopment analysis.
Introduction
India has a total road network of length 4.11 million
km, which includes 70 934 km of National Highways
which are directly under the control of the central gov-
ernment. There are about 93 000 bridges (length > 6
m) and over 1.1 million culverts (length 6 6 m) of dif-
ferent types along Indian roads. About 14 500 bridges
are on National Highways of which 1713 bridges/over-
bridges are in a distressed condition requiring repair/
rehabilitation and 2018 bridges are old and weak,
requiring reconstruction.
Bridges are also an inseparable part of the Indian
railways. There are more than 127 000 bridges of dif-
ferent types with varying spans on railway networks.
About 40% of these bridges are over 100 years old.
Sixteen per cent of these bridges are reported to be
deficient and require rehabilitation and strengthening
(Jain, 2002). The fund allocation for bridge mainte-
nance is about 2% of the total allocation for the total
highway budget. In the case of India, only 40% of the
amount required for maintenance is generally avail-
able. As the funds allocated are meagre, it is impera-
tive that they are spent judiciously.
Bridge maintenance is specialized and expensive
work. Bridge owners all over the world face difficulty in
maintaining bridges with the available funds, and thus
the issue of lack of funds for maintenance is not only
specific to India, but is of global significance. Within
the available budget for maintenance, a large number
of bridges compete. Very often, the ranking of bridges
for maintenance planning is derived from personal
judgment (Sasmal and Ramanjaneyulu, 2008).
The most popular method of prioritizing the
bridges for their maintenance need today is the bridge
health index/maintenance priority index/health index/
*Author for correspondence. E-mail: [email protected]
Construction Management and Economics (September 2011) 29, 957–968
Construction Management and EconomicsISSN 0144-6193 print/ISSN 1466-433X online � 2011 Taylor & Francis
http://www.tandfonline.comhttp://dx.doi.org/10.1080/01446193.2011.614267
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condition index. A number of countries use these
indices for prioritizing the bridges for their mainte-
nance needs. The index invariably involves evaluation
of various bridge components to arrive at their relative
importance (Hsu et al., 2006). The index relies heav-
ily on condition states of various bridge components
mostly derived from visual inspection, and some other
factors for deciding the maintenance priority. For
example, in the United Kingdom (Woodward et al.,
2001), bridge age, traffic volume, route importance,
etc. are taken into account for the assessment rating.
Valenzuela et al. (2010) have considered the annual
average daily traffic, length and width of bridge, avail-
ability of alternative routes, social and economic
development of the area and load restriction to
develop the index. Hai (2008) has taken into consid-
eration location, width, and traffic volume for the
determination of bridge importance. Load capacity,
remaining life, deck width, horizontal and vertical
clearances, etc. have been used by different States in
the USA for the development of ranking formulae
(Gralund and Puckett, 1996). Traffic load, environ-
mental conditions, bridge age, river bed characteris-
tics, foundation and superstructure type have been
used by Chassiakos et al. (2005) when developing a
priority index.
The need for developing criteria that better
describe the overall condition of a bridge (health
index) has also been emphasized by the White Paper
on Bridge Inspection and Rating by ASCE/SEI-
AASHTO Ad-Hoc Group on Bridge inspection, rat-
ing, rehabilitation, and replacement (2009).
Currently, moves are being considered for the
development of bridge management systems which
consist of various scientific methods and tools for
determining efficient allocation of funds. Reliable data
on the history of bridge condition and maintenance
are of prime importance for the development of these
systems.
In today’s competing business environment, bridge
owners are looking for a method for effectively eval-
uating the efficiency of fund allocation to different
competing bridges at a given time period. As noted
earlier, fund allocation based on bridge health indi-
ces relies heavily on the condition of a bridge. Some
of the questions that remain unanswered and need
to be probed are: (1) whether allocation based on
indices results in an efficient utilization of funds; (2)
whether some alternative method using a more or
less similar framework (without making drastic
changes) of fund allocation can be made; and (3)
how the new method compares with the existing
method of fund allocation. Addressing these ques-
tions is important especially if funds are scarce, as is
usually the case. Thus, the objective of the study is
to evaluate the efficiency of fund allocation based on
the bridge condition as depicted by the bridge health
index.
In the following sections, first, the existing methods
of fund allocation are reviewed. The emphasis here is
on pointing out their inherent weaknesses. Subse-
quently, an alternative method, viz., data envelop-
ment analysis (DEA) is proposed for fund allocation.
The DEA is a mathematical method based on pro-
duction theory and the principles of linear program-
ming (Ozbek et al., 2009). The DEA is a non-
parametric method of measuring the efficiency of
decision making units (DMUs) (Ray, 2004; Li and
Liu, 2010). The proposed method is compared to
one of the most widely used methods and the
supremacy of the former is illustrated with a numeri-
cal example.
Literature review
Bridge health indices and maintenance priority indices
are quite commonly used in the bridge management
field. The basic principle behind using the indices is
to categorize or rank the bridges in the order of their
condition. The poorer the condition of a bridge, the
higher its rank in terms of priority and thereby higher
is its claim for funds. The indices may be broadly
classified into: (1) bridge health index; and (2) main-
tenance priority index/priority ranking functions. The
general form of a bridge health index may be given by
the equation:
BHI ¼ Pn
i¼1
KiCi,
where BHI = bridge health index; Ki = weight of the
ith component; Ci = condition of the ith component;
n = number of bridge components. The general form
of a maintenance priority index according to Hearn
(1999) is:
MPI ¼ P
i
KiFiða; b; c; ::::::Þ,
where MPI = maintenance priority index; Ki = weight
of the ith deficiency; Fi = ith deficiency; and a,b,c,. . . =attributes of the deficiency.
The expressions for the indices are mostly of the
weighted average form where the prime requirement
is to ascertain the weights or the relative importance
of bridge components and their condition states at the
time of inspection. Depending on the number of com-
ponents considered for a bridge and the methodology
to describe the condition states of components, the
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expressions for these indices vary across countries and
a few notable ones are discussed.
Roberts and Shepard (2001) assumed that each
bridge component has an initial asset value at the
time of its completion which declines or decreases
over time. Conversely, the asset value increases when
maintenance and rehabilitation actions are carried
out. The current element condition state distribution
is ascertained by field inspection. From the condition
distribution, current element values for all the ele-
ments can be determined in the form of a bridge
health index which is expressed as the ratio of current
value to the initial value of all the elements of a
bridge.
In order to calculate the bridge health index of a
network of bridges, the entire network is treated as
one large structure containing the summation of all
element quantities and condition distributions within
the network.
The bridge health index expression used by
Tserng and Chung (2007) took into account 20
components for inspection of bridges and the condi-
tion states are defined in terms of deterioration,
extent of the deterioration, and relevancy to safety of
the deterioration. Wakchaure (2010) categorized a
bridge into seven components and 49 sub-compo-
nents for the development of BHI. The relative
importance (weights) of the components and their
sub-components was ascertained by using the analyt-
ical hierarchy process (AHP). The model relies on a
comprehensive definition of the condition states and
correlates them with the distress types. The model,
to an extent, addresses the concern raised by Enright
and Frangopol (1999), who opined that there are
considerable uncertainties in the interpretation of
inspection data for reinforced concrete (RC) bridges,
and favoured redefining the condition states.
Wakchaure (2010) also identified 28 different types
of distress and quantified them in terms of percentage
of defects in the element cross-section; surface area or
defects per unit length of the affected element, num-
ber of missing components and so on and the range
of values specified. This has further helped in remov-
ing the subjectivity and bias of the bridge inspector.
The BHI obtained by using the method mentioned
above can be used to rank all the bridges in a network
for deciding the maintenance priorities. In addition to
the bridge health index, the other criteria used for
deciding the maintenance priority are: importance of
the bridge, deck area of the bridge, the maintenance
cost required, traffic volume, age of the bridge, etc.
(Gralund and Puckett, 1996; Woodward et al., 2001;
Chassiakos et al., 2005; Hai, 2008; Valenzuela et al.,
2010). The maintenance priority of bridges is deter-
mined on the basis of the availability of information
about the aforementioned factors along with the
bridge health index.
Apart from the application of bridge health indices
for determining priority, some other methods, such as
the net present value, cost/benefit analysis, optimiza-
tion, life cycle costing, etc. have also been used in the
past to recommend optimum utilization of available
funds in the context of bridge management.
Net present value analysis can be carried out to
allocate the funds to the bridge that deserves mainte-
nance the most in terms of monetary value. However,
the method does not account for factors which cannot
be converted into monetary values. The cost/benefit
analysis can also be used, though its application is not
as simple as has been reported by Yanev (2001).
Traditional algorithms for minimizing the life cycle
maintenance cost are also available for the existing
bridge maintenance planning. There are difficulties in
using these classical single-objective optimization
problems for handling multiple and conflicting objec-
tives. Such difficulties can be overcome by formulat-
ing a multi-objective optimization problem that treats
the lifetime condition, safety levels, and life cycle
maintenance cost as separate objective functions (Liu
and Frangopol, 2005).
Researchers have used different objective functions.
For example, Miyamoto et al. (2001) considered min-
imization of maintenance cost and maximization of
bridge load-carrying capacity and durability while
investigating optimal maintenance of existing bridges.
Furuta et al. (2006) simultaneously considered min-
imization of life cycle cost, maximization of service
life, and maximization of target safety level for main-
taining civil infrastructure systems. However, these
methods do not take into account some of the factors
that help decide the maintenance priorities, such as
importance of the bridge, deck area of the bridge,
traffic volume, age of the bridge, etc.
Frangopol et al. (2001) developed the basis for cost-
effective bridge management incorporating lifetime
reliability and life cycle cost. Reliability and life cycle
cost models are powerful tools for optimal bridge main-
tenance planning (Frangopol et al., 2004). Despite the
advantages offered by the life cycle cost approach,
there are certain difficulties in implementing this
because of the complexities in predicting bridge deteri-
oration and residual life; uncertainties in discount rate
and inflation rate, to name a few (IRC, 2004).
The need to compute efficiency in the context of
bridge maintenance has been addressed in the study
by Ozbek et al. (2010b) wherein the DEA was used
to measure the efficiency of bridge maintenance units
which consisted of a number of bridges. Ozbek et al.
(2010a) have presented an overview of the data and
modelling issues faced in the implementation of DEA
Bridge maintenance 959
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for the maintenance of bridges by the Virginia
Department of Transportation. Other researchers
have also used the DEA in measuring efficiency of
different types of infrastructure problems. For exam-
ple, Jian and Yang (2008) used the DEA model to
measure operating efficiency in China’s aviation
industry; Lin and Huang (2010) measured baseline
productivity (BP) in construction sites; Horta et al.
(2010) measured performance of construction compa-
nies; Sun et al. (2010) measured transfer efficiency of
urban public transportation terminals; Kulshrestha
and Mittal (2004) assessed the relative performance
of water supply utilities; Rodrıguez-Dıaz et al. (2004)
measured irrigation efficiency, and Xue et al. (2008)
measured the productivity of China’s construction
industry using DEA.
Most of the above studies including that of Ozbek
et al. (2010b) have aimed to measure efficiency at the
macro level. For example, Ozbek et al. (2010b) con-
sidered the efficiency at the county level (a county has
a number of bridges) which was considered the deci-
sion making unit (DMU) in the study. Similarly,
other studies mentioned above considered the aviation
industry, construction sites, construction companies,
etc., as the DMUs.
The efficiency of fund allocation to the competing
bridges (at the micro level) has not been measured in
the past. The individual bridges are considered
DMUs and factors affecting the selection of bridges
for maintenance planning are used as variables in
DEA. The efficiency scores obtained by DEA are
used for ranking the bridges. Also, the comparison of
fund allocation efficiency using both methods has
been made, an area not addressed by Ozbek et al.
(2010b). It is good to allocate funds for weak bridges
but to what extent? Should the fund be allocated for
a weak bridge despite it not resulting in an efficient
allocation? The following section gives a detailed
account of the research method adopted to achieve
the stated objective.
Research method
The study started with the visual inspection of 14
bridges. The bridge health indices of the 14 bridges
were computed using the equations suggested by
Wakchaure (2010). All of the 14 bridges were under
the jurisdiction of one National Highway Division,
located within a distance of 100 km and thus were
convenient for inspection. The ease of data collection,
grant of permission for inspection, and the minimiza-
tion of decision variables by removing common vari-
ables were the main considerations in selecting the
bridges. The different distress types shown by the
bridges during inspection were easily mapped by the
range of values for distress types suggested by Wakch-
aure (2010), and thus the bridges could be ranked
based on the bridge health indices.
Subsequently, DEA was used to evaluate the
efficiency scores of the 14 bridges.
The steps in the application of DEA are briefly
explained below.
(1) The first step is to decide the decision making
units (DMUs). The DMUs are compared to
each other, and hence they must be engaged in
a similar set of operations. DMUs must be
homogeneous, i.e. (1) they perform the same
tasks; (2) they perform such tasks under the
same market conditions; and (3) they use the
same technologies (Ozbek et al., 2009). Individ-
ual bridges are proposed to be used as DMUs
in the study.
(2) Once the DMUs are selected, input and out-
put for each DMU is decided. In DEA it is
necessary to specify both the output and input
variables. Input variables should be defined
such that an increase in the input variables
should be accompanied by an increase in the
output variables. This is referred to as the iso-
tonicity principle. Table 1 shows the list of
possible variables that can be considered for
the analysis (Gralund and Puckett, 1996;
Woodward et al., 2001; Chassiakos et al.,
2005; Hai, 2008; Valenzuela et al., 2010).
The reasons for exclusion of a particular vari-
able are given under the ‘remarks’ column of
Table 1. It may be recalled that the 14
bridges belonged to a single National Highway
Division and thus it was possible to exclude
some of the variables from the analysis, such
as the cost of materials, environment, public
demand, maintenance policy, etc., as they
were common for all the bridges. However, in
terms of age, structural configuration, and
method of construction, they differed. The
variables, viz., bridge maintenance/repairs cost,
bridge area, bridge condition, and bridge age
were considered suitable and feasible for the
analysis and thus selected.
(3) The next step is the selection of the appro-
priate DEA model. For the study, a DEA
model experiencing variable returns to scale
(convex radial input oriented model) has been
used.
(4) Efficiency Measurement System (EMS 1.3)
software of DEA has been used for deter-
mining efficiency scores of the selected
bridges.
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After the efficiency scores for different bridges have
been determined, the ranks of the bridges are com-
puted on the basis of the efficiency scores. The ranks
obtained using efficiency scores and the bridge health
index are compared with a numerical example. The
application of DEA is illustrated in the following sec-
tions. The sections are in line with the steps men-
tioned in the previous section.
Application of DEA
Selection of variables for DEA
Bridge condition and urgency of maintenance may
not be the sole criteria for selecting bridges for main-
tenance. The amount spent on the basis of bridge
condition alone may not be presumed to have been
used in an economic or efficient manner. The other
factors affecting the selection of bridges for mainte-
nance are given in Table 1. The reasons for inclusion
and exclusion of a given factor are also provided in
Table 1. Most of the factors presented in the table
are not quantifiable and hence excluded from the
study. Besides, gathering the data for some of the fac-
tors is difficult and thus they have also been excluded
from the analysis.
The variables finally used in the DEA are: (1)
bridge condition data represented by BHI; (2) bridge
maintenance/repairs cost data; (3) bridge area data;
and (4) bridge age data. The individual bridges are
regarded as DMUs in the study. The bridges are
presumed to have satisfied the criteria for DMUs
(mentioned under research method) as they are
meant for vehicular traffic having the same objective
and functions under similar conditions.
Bridge condition
The condition ratings of the bridges with respect to
all the components were obtained by visual inspec-
tion. The ratings were assigned on the basis of stan-
dard condition states and the corresponding distress
Table 1 List of variables used in DEA
S. No. The possible variable
Whether consideredfor DEA analysis Remarks/reasons for exclusion
1 Bridge condition (healthindex)
Yes Computations are based on the equations mentioned in thetext
2 Category of the road No All bridges are on the same National Highway3 Location/strategic
importanceNo All bridges are on the same National Highway
4 Carriageway width Yes Combined as bridge area5 Length of the bridge Yes6 Clearances (horizontal/
vertical)No Not applicable in the selected bridges
7 Waterway No Not applicable in the selected bridges8 Traffic volume No There are no diversions in the stretch of highway selected, so
traffic volume is same in the selected stretch9 Age Yes Obtained from the concerned project director10 Environment No All bridges are located in the same geographical area11 Deterioration rate No Not possible to evaluate by visual inspection12 Remaining life No Not possible to evaluate in the absence of suitable
deterioration model13 Load carrying capacity No Not possible to evaluate by visual inspection14 Maintenance cost Yes Based on computation explained in the text15 Life cycle cost of bridge No Not considered in the light of lack of information on
remaining life16 Benefit-cost ratio of
maintenance optionsNo Not possible to do because of lack of information on benefit
and cost17 Diversion cost No Same for all the bridges18 Maintenance policy No Same for all the bridges19 Safety to road users No Similar importance given to safety for all the bridges as they
are under the control of same agency.20 Economic development of
surrounding areasNo Same for all the bridges
21 Public demand No Same for all the bridges22 Political considerations No Not possible to quantify23 Cost of basic materials No Same for all the bridges
Bridge maintenance 961
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type and the extent of distress. The condition rating
of bridge components and their weights, ascertained
by AHP, were used for calculating the bridge health
index. In this manner, BHI values for the 14 bridges
were established. It was presumed that a bridge
attains an excellent condition (condition state I) after
the maintenance actions are carried out and the corre-
sponding bridge health index is taken as 100. The
change in the overall bridge condition is measured by
subtracting the BHI obtained from 100. The change
in the overall bridge condition in terms of BHI is used
as output variable.
Bridge maintenance/repairs cost
Bridge maintenance/repair cost comprises the amount
required to be spent so as to mend the observed
defects. Bridge cost data have been computed on the
basis of the type of distress and condition state of the
bridge elements. Bridge condition data were gathered
by the researchers on the basis of visual inspection in
November 2009, aided by the definitions of condition
states and severity of distress types.
The extent of repair work is ascertained on the basis
of the condition state of the elements and size of the
bridge components. The rate analysis (determination
of cost of repairs) of items related to various defects is
carried out to determine bridge maintenance/repair
cost. Bridge cost data do not include any overheads
incurred by the agency responsible for the mainte-
nance. Overhead charges are presumed to be the same
for all bridges, as they are located within the jurisdic-
tion of one project director. An illustrative example of
the computation of the maintenance cost of one of the
bridges is shown in Table 2. In this bridge, signages
were missing and thus condition state V was accorded
to this component. The cost of two sign boards at the
rate of $90.47 is $180.94 (say $181). A railing was
missing for a length of three metres and thus condition
state V was accorded to this sub-component. The rate
of railing per running metre is $83.93. Thus, the total
cost of the railing comes to be $251.80 (say $252).Similarly, the costs of maintenance of the other
affected bridge components are calculated and the total
maintenance cost of the Kali Nadi Bridge is estimated
to be $12 300 (rounded to the nearest hundred dol-
lars). The components that were not applicable for this
bridge are not shown in Table 2. Similarly, those com-
ponents that did not show any signs of distress have
not been shown in Table 2.
Bridge area and age
The area of an individual bridge is calculated on the
basis of the number of lanes and the length of the
bridge. All the bridges studied are of two lanes (7.0 m
width). The bridge area is used as an input variable.
The age of a bridge is computed as the period from
the year of construction to 2009. The year of con-
struction was made available by the project director
responsible for the maintenance of the national high-
way section.
Other variables such as environment, importance of
the road, traffic volume, diversion cost, etc. are indi-
rectly taken care of as the bridges under consideration
are on the same National Highway, spanning about
100 km. The details of these input and output vari-
ables are given in Table 3. The input variables,
namely bridge age and bridge area, do not satisfy the
isotonicity principle. Other factors being the same, an
increase in bridge age is presumed to result in a
reduction in the change in the overall condition of the
bridge. Similarly, as the bridge area increases, it may
not be possible to maintain the bridges with the avail-
Table 2 Details of maintenance cost for Kali Nadi bridge
S. No. Bridge components Distress type
Conditionstate no. Quantity Unit
Unit rate($)
Amount($)
C 1.2 Signages Missing elements V 2.00 No. 90.47 181C 1.4 Railing/crash barriers/guard
stones/parapetMissing elements V 3.00 m 83.93 252
C 1.5 Approach slab Unevenness III 6.33 m2 111.11 703C 1.8 Slope protection Vegetation II 0.01 Ha 242.53 2C 2.5 Abutment protection works Pitching missing II 2.93 m3 79.33 232C 5.1 Girders/main beams Cracking III 17.60 m2 602.42 10 603C 6.1 Wearing surface Potholes V 22.00 m2 7.33 147C 7.1 Bearings Corrosion II Lump 222
sumTotal 12 342
Say12 300
Note: The above table provides details of only those components which showed distress during inspection. The remaining components arenot shown.
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able funds. The study of available literature on DEA
suggests that such variables may be used either by
deducting from large values, taking the inverse, or
treating them as output variables (Thanassoulis,
2001; Ozbek et al., 2010b). In the study, the inverse
values of bridge area and bridge age are used as input
variables. The final input and output variables along
with their observed values are also shown in Table 3.
DEA model selection
After selection of the input/output variables it is nec-
essary to determine the returns to scale experienced
by the DMUs under investigation. According to
Ozbek et al. (2010a), DEA models can be mainly
classified into the model experiencing constant returns
to scale—CCR formulation (Charnes-Cooper-
Rhodes) or the model experiencing variable returns to
scale—BCC formulation (Banker-Charnes-Cooper).
In constant returns to scale, output increases by the
same proportional change of each proportional
increase in the input. It is a special case of the vari-
able returns to scale in which output does not
increase by the same proportional change for each
proportional increase in the input. A constant return
to scale model is not frequently encountered in pro-
cesses. As the two variables, namely area of the bridge
and the BHI, are fixed, only one variable—mainte-
nance cost—is changing, depending on the available
funds. It cannot be said that the change in mainte-
nance cost is accompanied by a change in BHI in the
same proportion, as it depends on the distress type,
component and severity of distress. In view of this, a
variable returns to scale model is used.
It is also necessary for the analyst to decide on
the orientation, i.e. input orientation or output ori-
entation of the model once the aforementioned selec-
tion is made. If the decision makers are more
flexible in modifying the outputs, the output-oriented
model is chosen. It seeks, for the inefficient DMUs,
the level by which the outputs produced can be
increased without changing the levels by which
inputs are used. An output-oriented measure quanti-
fies the necessary output expansion, while holding
the inputs constant. If the decision makers are more
flexible in modifying the inputs, the input-oriented
model should be chosen, as it seeks, for the ineffi-
cient DMUs, the level by which the inputs used can
be decreased without changing the levels by which
outputs are produced. An input-oriented measure
quantifies the input reduction which is necessary to
become efficient, while holding the outputs constant
(Ozbek et al., 2010b). In the present case, the input-
oriented model is selected to better view how the
various factors influence the selection of bridges for
maintenance.
Output of DEA model
The output of the DEA model includes efficiency
scores, benchmarks and target costs. These are shown
in columns 5, 7 and 8 of Table 4. Bridges scoring
Table 3 Details of input and output variables for 14 bridges
S. No. DMUBridgearea (m2)
Inverse ofbridge area(INPUT)
Bridge age(year)
Inverse ofbridge age(INPUT)
Maintenancecost ($)(INPUT) BHI
Change inconditionof bridge in
termsof BHI
(100 – col.8)(OUTPUT)
(1) (2) (3) (4) (5) (6) (7) (8) (9)
1 Kali Nadi 441 0.002 15 0.067 12 300 91 92 Choya Nala (i) 490 0.002 35 0.029 14 500 81 193 Choya Nala (ii) 490 0.002 35 0.029 57 400 74 264 Anoop Shahar Canal 238 0.004 15 0.067 6900 98 25 Matwali Bridge 56 0.018 15 0.067 5400 86 146 Madhya Ganga Nahar 1155 0.001 25 0.040 2900 99 17 Ganga Bridge 4921 0.000 49 0.020 87 700 91 98 Bagad Nala 385 0.003 49 0.020 112800 80 209 Bridge 9 56 0.018 35 0.029 4600 93 710 Bridge 10 101 0.010 35 0.029 1300 94 611 Sot Nadi 435 0.002 35 0.029 9000 85 1512 Gagan river 840 0.001 7 0.143 1900 97 313 ROB 560 0.002 7 0.143 1500 96 414 Rajhera Nala 784 0.001 15 0.067 15 900 92 8
Total = 334100
Bridge maintenance 963
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100% are termed ‘efficient’ bridges and the remaining
ones ‘inefficient’.
The efficiency scores have been used for ranking
the bridges for maintenance works. The bridge with
the maximum efficiency score is given the maximum
priority. The ranks established on the basis of BHI
and efficiency scores are compared in columns 4 and
6 of Table 4.
Out of the 14 bridges, 10 (S. Nos. 2, 3, 5, 6, 7, 8,
10, 11, 12 and 13) are found to be efficient while the
remaining four bridges (S. Nos. 1, 4, 9 and 14) are
found to be inefficient. Bridge at S. No. 3 (column 1 of
Table 4) is ranked the highest by both the methods.
Bridges at S. Nos. 2, 5, 6, 7, 8, 10, 11, 12 and 13
are ranked first on the basis of efficiency scores.
Otherwise, they would have got low priority on the
basis of BHI. A bridge scoring less on efficiency
should not be given priority for maintenance, espe-
cially if the fund allocated for the maintenance work
is less.
The DEA gives the relative efficiency, i.e. the ratio
of weighted output to the weighted input. It is neces-
sary to assign weights to input and output variables.
These weights are chosen and optimized by the DEA
program so as to provide an equal chance to every
input and output variable. Most referenced bridges
(DMUs) are the efficient bridges (with efficiency
score of 100), the values of which are used to deter-
mine and optimize the weights by the inefficient
bridges. The relative weights are also given for the
referenced bridges. Benchmarks (column 7 of Table 4)
are the output of the DEA analysis. Benchmarks for
inefficient (DMU) bridges indicate the referenced
bridges (DMUs) with corresponding intensities
(weights) in brackets (see column 7 of Table 4). For
example, the bridge at S. No. 1 (Kali Nadi) is an
inefficient bridge, having a score of 62. This bridge
(DMU) has four efficient bridges at S. Nos. 2, 6, 11
and 12 as benchmarks with intensities (weights) of
0.39, 0.50, 0.05 and 0.06 respectively. This has been
shown as 2 (0.39) 6 (0.50) 11 (0.05) 12 (0.06) in col-
umn 7 of Table 4.
For efficient bridges (DMU), benchmarks indicate
the number of inefficient bridges (DMUs) which have
chosen the efficient bridge as the benchmark. For
example: Bridge at S. No. 2 is an efficient bridge
which has been chosen as a benchmark by two ineffi-
cient bridges, namely the bridges at S. No. 1 and S.
No. 14. All the inefficient bridges have an efficiency
score of more than 50%. The efficient bridges may be
selected first for maintenance as they can show maxi-
mum improvement in bridge condition for a given
maintenance cost, area, and age of the bridge. The
most referenced bridges (DMUs) are Madhya Ganga
Nahar and Sot Nadi (at S. Nos. 6 and 11) which are
referred to thrice, followed by bridges at S. Nos. 2, 7
and 10 which are referred to twice. Bridges (DMUs)
at S. Nos. 3, 5, 8 and 13 are efficient but not referred
to by any inefficient bridges.
The target cost (shown in column 8 of Table 4) for
each bridge is calculated by multiplying its efficiency
score by its required maintenance cost. For example,
Table 4 Ranking based on BHI and efficiency scores, benchmarks, and target costs of 14 bridges
S. No. DMU BHI
Rankingbasedon BHI
Efficiencyscore (%)
Rankingbased
on efficiencyscore Benchmarks
Target costs($) (to thenearesthundreddollars)
(1) (2) (3) (4) (5) (6) (7) (8)
1 Kali Nadi 91 7 62 13 2 (0.39) 6 (0.50) 11 (0.05) 12 (0.06) 76002 Choya Nala (i) 81 3 100 1 2 14 5003 Choya Nala (ii) 74 1 100 1 0 57 4004 Anoop Shahar
Canal98 13 55 14 6 (0.69) 10 (0.13) 11 (0.18) 3800
5 MatwaliBridge
86 5 100 1 0 5400
6 MadhyaGanga Nahar
99 14 100 1 3 2900
7 Ganga Bridge 91 6 100 1 2 87 7008 Bagad Nala 80 2 100 1 0 1128009 Bridge 9 93 9 99 11 7 (0.03) 10 (0.84) 11 (0.13) 460010 Bridge 10 94 10 100 1 2 130011 Sot Nadi 85 4 100 1 3 900012 Gagan river 97 12 100 1 1 190013 ROB 96 11 100 1 0 150014 Rajhera Nala 92 8 91 12 2 (0.31) 6 (0.60) 7 (0.09) 14 400
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the target cost for Kali Nadi bridge is $7600 rounded
to the nearest hundred dollars (62% � $12300 =
$7626). This means that the requirement of Kali
Nadi bridge compared to the efficient bridges in the
data is 38% (100 – 62%) more, while keeping the
maintenance quality the same in order to be catego-
rized as fully efficient.
Validation
The rankings based on the BHI and efficiency scores
indicate that the rankings by the two methods differ
significantly. Numerical examples of priority of
bridges by both the methods subject to the availability
of funds are given below.
Numerical example
The total fund required for the maintenance of 14
bridges is obtained by summing the maintenance
costs of these bridges given in column 7 of Table 3.
The values shown in column 7 of Table 3 are derived
by performing similar computations as shown in
Table 2 for Kali Nadi bridge. It can be noted that the
maintenance fund required for Kali Nadi bridge is
$12 300, for Choya Nala (i) bridge the corresponding
value is $14 500, and so on. The sum of the mainte-
nance fund required by the 14 bridges is thus equal
to $334 100. Let us assume that the fund available for
maintenance is $170 000, which is about 50% of the
requirement. From Table 4, it can be observed that
bridges at S. Nos. 3 and 8 occupy first and second
rank based on the BHI. If bridges are selected on the
basis of the BHI then it would have been possible to
select only these two bridges which would have cost
$170 200 (sum of $57 400 and $112 800, refer to
Table 3, column 7). The improvement in terms of
BHI arising out of spending this much will be the
sum of the corresponding changes in BHI (column 9
of Table 3) of each bridge at S. Nos. 3 and 8 (ranked
1 and 2 based on the BHI). This works out to be 46
(sum of corresponding values of column 9 of Table 3).
If the bridges are selected on the basis of efficiency
scores, it is possible to select nine bridges (discarding
bridge at S. No. 8 costing $112 800 although it is effi-
cient bridge) costing $181 600. In this case the net
increase in BHI value will be 97. This indicates that
there is an increase in service level in terms of
improvement in the condition of bridges. In addition,
a larger number of bridges can be selected for mainte-
nance. Thus, it may be inferred that the ranking
based on the efficiency scores by DEA helps in more
efficient utilization of funds compared to that based
on BHI alone.
Though it is clear that DEA can be utilized to great
advantage in situations like this, one should be mind-
ful of the fact that in practice it may not be possible
to quantify each decision variable and eliminate sub-
jectivity in totality. The efficiency scores are sensitive
and an error in the measurement of input and output
variables can adversely affect the decision. This is so
because the rankings based on such efficiency scores
can vary to a considerable extent as can be seen from
Table 4. While an efficiency score of 100 marks a
bridge as efficient and rank 1 in terms of priority,
even a minor change can land the bridge lower in
rank in terms of maintenance priority, especially if
there are more efficient bridges in the network.
Limitations and future research directions
Table 1 provided a number of possible variables that
can be used for deciding the maintenance priority.
However, only few of them have been used in the
DEA analysis. More variables may be included in the
analysis if corresponding numerical values are avail-
able or if they can be established by inspection and
measurement.
The DEA method has been used here and thus the
study has three prime limitations (Thanassoulis,
2001; Ozbek et al., 2009). These limitations, along
with the measures adopted to address them, are
explained briefly below.
The DEA being a non-parametric method, statisti-
cal hypothesis tests are difficult to implement and
thus the reliability of the results is difficult to assess.
In order to address this limitation, a numerical exam-
ple resembling a real life situation has been consid-
ered wherein the superiority of fund allocation
resulting from the application of DEA has been illus-
trated. Another limitation of the DEA is that it is
greatly influenced by the quality of data in input and
output variables. Any error in recording of data for
the input and output variables may yield erroneous
results and thus all care must be taken to ensure the
accuracy of input and output variable values. The
scope of error in measuring the area and thus the
inverse of area is almost non-existent in the study as
the physical measurements taken at the sites were
cross-checked with the numeration details of different
bridges. Maintenance cost has been arrived at by
adopting established norms for all the bridges. There
is no error in computation of the BHI as well, as the
model used for the computation is not dependent on
subjective judgment.
In some cases, the application of DEA may even
show an inefficient bridge as an efficient bridge. This
may happen due to the flexibility the linear program
Bridge maintenance 965
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has in determining the weights of input and output
variables. Ozbek et al. (2009) suggest adding con-
straints, such as bounds on input and output weights
to avoid this limitation.
On close observation of this limitation, it can be
seen that it does not adversely affect the present
application. In fact, this limitation can be used to
advantage in the prioritization problem. An inefficient
bridge shown by the DEA method is, in fact, truly
inefficient as it turned out to be inefficient even by
the allocation of the most favourable set of weights.
Thus, this limitation can be utilized in identifying
inefficient bridges and thus ensuring the least priority
in fund allocation for these bridges. An inefficient
bridge being classified as an efficient bridge is a prob-
lematic situation, but will also not affect the results
much. This is so because a comparison of the two
methods has been made in terms of the increase in
bridge health indices, and the DEA application is
found to result in a large increase in bridge health
indices for nearly the same amount of funds.
The BHI and DEA have been used for a group
of 14 bridges in one of the National Highway Divi-
sions. In the case of a network of bridges across
various divisions/regions/states, a similar method can
be applied. The results obtained are planned to be
used in the development of a rational model for
fund allocation among competing bridges in a single
network, a model that can be extended to multiple
bridge networks in the country as well. Further
studies/research can be undertaken in refining the
bridge health index and widening the scope of its
application from concrete bridges presently to other
bridges as well. Some variables which were omitted
due to different constraints can also be taken up in
future.
Conclusions
The funds earmarked for the maintenance of bridges
are generally less than what are required. Bridge
authorities have to keep the bridges in traffic-worthy
condition using the limited funds and thus the fund
allocated to a bridge must provide maximum value
and efficiency. The existing practice of fund allocation
in general is to assign the highest priority to the
bridge with the weakest condition in a set of bridges
competing for the funds for maintenance. The condi-
tion of a bridge is assessed in most of the cases with
the help of indices, such as a bridge health index or
maintenance priority index. Whether the practice of
fund allocation based on bridge health indices results
in an efficient utilization of funds has been explored
in the paper.
It has been argued that the existing prioritization
principle behind fund allocation among competing
bridges need not result in an efficient allocation. Pri-
oritization also needs to consider other variables
affecting decision making, such as bridge area, main-
tenance cost, bridge age, etc. Thus, there is a need
to adopt an approach which has the flexibility to
consider other variables in conjunction with the
existing bridge health index. A number of
approaches, such as net present value, cost/benefit
analysis, traditional algorithms for single-objective
cost minimization, and multi-objective optimization,
do exist to address this problem, and each one has
merits and demerits. However, these methods do
not seem to fulfil the requirement that is needed in
deciding prioritization of bridges for maintenance.
The requirement here is to find an approach which
can build on the existing method of prioritization
and yet is flexible enough to consider other different
variables. The paper contributes a DEA approach as
it provides a platform wherein different decision
variables can be accounted for in the prioritization
process. The DEA can be used to evaluate the effi-
ciency scores which can be considered for ranking
bridges. With the help of a numerical example it has
been shown that the priority rankings on the basis
of BHI and efficiency scores differ significantly. The
former system results in the selection of a lesser
number of bridges in a network and less improve-
ment in the condition of bridges in the network. On
the other hand, the alternative approach of DEA has
enabled the selection of a greater number of bridges
for maintenance and a greater overall improvement
in the condition of bridges in the network. Thus,
funds are better utilized in the latter system of
prioritization besides considerable improvement in
the service level of highways comprising a set of
bridges.
It can be concluded that it is not enough to look at
the individual condition of an infrastructure in terms
of weakness or strength in an isolated manner. The
prioritization exercise should be done in a holistic
manner. The exercise should be done considering dif-
ferent decision variables and should aim at enhancing
the system’s efficiency rather than concentrating too
much on a single variable (such as condition of a
bridge in this case) and losing out in the process.
Bridge owners in India mostly rely on subjective
judgement to allot funds for maintenance to compet-
ing bridges, and there is currently a lack of a system-
atic and scientific method. As such, the DEA
approach coupled with the bridge health index can fill
this gap, which can result in judicious selection of
bridges for maintenance. The method is flexible
enough to accommodate many variables affecting
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maintenance priority, which, in the absence of the
DEA, was not easily achievable until now. Although
bridges from only one National Highway Division
have been considered in the study, the DEA method
can also be extended to identify the best performing
division among different divisions in the country and
thus different divisions can be benchmarked against
each other.
The DEA method adopted here can be applied in
all such cases wherein there are limitations on the
availability of resources and there are too many con-
tenders for them. Even though the paper is based on
data collected from Indian bridges, the method has a
broad geographical applicability. The application of
DEA is also simple and easy. However, one should
not get overwhelmed by the efficacy of the method, as
it suffers from some limitations as discussed earlier.
While most of the limitations can be overcome,
proper care needs to be taken in selecting the input
and output variables for the DEA, especially if a large
number of decision variables needs to be incorporated
in the decision model.
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