Hybrid forecasting system based on case-based reasoning and analytic hierarchy process for cost estimation.
Kim, Sangyong
1. Introduction
Successful management within the limited budget is an important
concern in any construction project. Lack of information and reliable
methods that support estimating process made it difficult to initiate
estimating report during the project planning stage (Chou, O'Connor
2007). In order to control the cost within an acceptable level, it
requires appropriate and accurate measurement of various project related
determinants and the understanding of the magnitude of their effects. As
such, the importance of early estimating cannot be over emphasized.
Number of cost estimating models, however, has been limited in road and
bridge construction.
Several studies have demonstrated focus on highway construction
cost estimating in the past. Owing to the lack of detailed design
information and drawings during the early stages, several technical
methods have been developed to estimate construction costs based on
limited information (Chou 2009). Although MRA (Multiple Regression
Analysis) has been used to cost estimating based on statistics many
times, it is not appropriate when describing non-linear relationships,
which are multidimensional, consisting of a multiple input and output
problem (Tam, Fang 1999). Chou et al. (2005) suggested heuristic
simulation models to improve the accuracy and efficiency of highway
budgeting estimates based on useful data from the TxDOT (Texas
Department of Transportation). Parametric cost estimating models were
developed using ANNs (Artificial Neural Networks) for reasons of its
limitation, and the models were demonstrated that they were very useful
at the early stages of a project life cycle (Hegazy, Ayed 1998;
Al-Tabtabai et al. 1999; Wilmot, Mei 2005). However, ANNs can lose their
effectiveness when the patterns are very complicated or noisy, knowledge
representation and problem structuring are ill-defined, and training is
trapped in local minima (Hegazy et al. 1994).
CBR (Case-based reasoning) is a relatively recent problem solving
technique that is attracting increasing attention because it seems to
resemble more closely the psychological process humans follow when
trying to apply their knowledge to the solution of problems. CBR is
problem solving technique that reuses past cases and experiences to find
solution to the problems. While other major AI (Artificial Intelligence)
techniques rely on making associations along generalized relationships
between problem descriptors and conclusions, CBR is able to benefit from
utilizing specific knowledge of previously experienced, evaluate the
proposed solution and update the system by learning from this experience
(Kolodner 1993; Shin, Han 1999; Kim, K. J., Kim, K. 2010).
Especially CBR systems have been proposed as effective alternatives
to the support of decision-making. Several studies have demonstrated
potential applications of CBR in construction areas. K. J. Kim and K.
Kim (2010) proposed a preliminary cost estimation model using CBR and
GAs (Genetic Algorithms) for determining the important weights of
attributes. Kang et al. (2010) developed quantity-based construction
cost estimating system using CBR and GAs. Ji et al. (2010) suggested CBR
model for improving cost prediction accuracy in multifamily housing
projects. Yau and Yang (1998) confirmed that CBR is a quite effective
for selecting a retaining wall system at the project planning stage.
Dzeng and Tommelein (2004) developed a generic CBR system to facilitate
schedule reuse and the new CBR system to develop a decision-support
system to aid a project manager in seeking subcontractor registration.
Luu et al. (2005) approached to procurement criteria selection and
modeling bridge deterioration (2002), and suggested the ways to reduce
the problem of hazard identification. CBR has also been used for
cost-estimating of construction projects (An et al. 2007; Dogan et al.
2008), bid mark-up estimation (Dikmen et al. 2007), and cost budgeting
for pavement maintenance (Chou 2009). Learning from previous researches
and applications CBR can make very reasonable estimating without using
specific experts and rules. For example, the cost of a construction
project is influenced by a number of factors including the duration, the
location, the year of construction, and the size of a project. The
problem to be investigated is whether using the values for these
factors, collected from completed previous projects, realisation cost
for future projects can be reliably estimated. Therefore, the new
innovative CBR approach was used to express the concept of the system
developed in this study.
Problem of estimating future highway construction cost with regard
to both 4 main divisions and total construction cost is discussed in the
paper. The study is organized as follows. The next section describes the
objectives and methodology of this study. The following section shows
how this data was analyzed to verify its consistency and completeness
and to obtain the knowledge required for the highway application. Then,
48 actual cases of highway project data constructed in South Korea, from
1996 to 2008, have been used as the source of cost data and in
developing a CBR application for systematic highway project cost
estimation. The next section briefly presents the CBR system that was
developed specifically to generate CBR applications for modelling cost
estimates and the steps followed in developing an application. Finally,
the testing procedures and the validation results are discussed.
2. Objectives and methodology
The major aim of this study is to develop the hybrid CBR decision
support system for estimating of highway project costs. The study goals
included: (1) estimation of highway project costs at the early stage by
4 main divisions and total cost as well; (2) extracting significant CFs
(Cost Factors) based on previous studies and interview with experts; (3)
developing weighs values for CF using AHP (Analytic Hierarchy Process).
As a result, the developed system provides a useful benchmark which is
capable of assisting in identifying the CFs which demonstrated a strong
relationship with highway project costs.
CFs are very complicated which requires intelligent processing to
get a precise view of the effects of the cost attributes on project cost
(Boussabaine, Elhag 1999). The data is required which corresponds to all
the CFs which are known from previous studies. First of all, this study
summarized literature review and identified significant CFs which affect
a highway project costs. Furthermore, industrial interviews were
conducted to assist with selecting these factors. When potential CFs
were identified, the weights of data were calculated by AHP. In
addition, appropriate CBR system was developed and examined, and
preliminary testing of developed system was carried out, using a
relatively small number of data sets. The system is developed by means
of an MS Excel-Based Visual Basic Application.
3. Case-based reasoning
CBR is a not a kind of computerized tool that imitate the
analogical reasoning of human brains in problem solving (Rivard et al.
1998). The principle of CBR is based on the assumption that similar
problems have similar solutions. According to Riesbeck and Schank
(1989), CBR solves problems by capturing previous experiences and
matching the important features of new problem to those of the old cases
that have been successfully solved. The main source of knowledge in CBR
is the case that can be reused even if it is partially matching the
problem in hand (Yang, Yau 1996). Especially, CBR can deal efficiently
with both numerical and nominal data, and can handle effectively cases
that have incomplete data or variable data structures (Arditi, Tokdemir
1999). Furthermore, CBR has powerful learning capabilities that do not
require time-consuming training and testing operations (Yang, Yau 1996).
Table 1 lists CBR applications in various domains.
Aamodt and Plaza (1994) call the top level task of CBR problem
solving and learning from experience which directly matches two phases,
maintenance and application, as shown in Fig. 1. In the six-Re
processes, changes initiated from outside of the CBR can be modelled
easily:
--Retrieve the most similar cases from stored previous cases;
--Reuse the retrieved cases to attempt to solve the problem;
--Revise the proposed solution if necessary;
--Retain the new solution as a part of a new case;
- Review the results from applying the solution;
--Restore the case into case base library.
4. Selection of cost factors
The factors affecting the project cost were selected as the
attributes that would be used as the input data for prediction CBR
system. The data came from application of the selecting procedure
presented in Fig. 2. At first, the literature review was conducted to
identify which CFs were used in order to accomplish the cost estimating
of highway projects. While there are only a few studies available on CFs
which are suspected to influence construction cost, numerous studies
have taken place in the highway construction projects. They are listed
in Table 2.
A questionnaire survey was designed to obtain the primary data for
this study. A pilot survey was first carried out to test the relevance
and comprehensiveness of the questionnaires before a full scale survey
was conducted. The respondents were given a choice of being interviewed
by telephone or to self-administer the questionnaires, and to send them
back to the researchers. Three construction firms and 18 practitioners
have been contacted to get feedback and comments about CFs of the data.
The data included estimated material costs, actual costs, and general
information based on 24 CFs, which was deemed potentially important to
the accuracy of early estimates. The CFs were categorized as shown in
Table 3.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
Time Standardization
A cost index represents the relative scale of cost for a fixed
quantity of goods or services between different periods, and provides a
good means for forecasting future construction costs that change over
time in response to changing demand, economic conditions, and prices
(Ostwald 2001). The data collected for developing a CBR system have
diverse characteristics and differences, such as when and where the
projects were constructed. Such differences may cause incorrect
prediction results (Kim, Kang 2003; Kim et al. 2005). A cost index ought
to be a reliable tool for estimating future costs of construction
activities, where construction activities are conducted months or years
after costs were estimated (Huang 2007). The developed CBR cost
estimation system includes therefore appropriate means which allow to
reflect the change in overall highway construction costs over time.
At first, the data used to establish the CBR system were collected
from projects completed in 1996 and 2008. The data had to be converted
to the identical time reference point defined by the Korea Institute of
Construction Technology (KICT). The cost data of all the reference cases
were converted to May 2005 cost level using the road cost index provided
by the KICT. The detailed source of the road cost index of South Korea,
which is announced monthly, was used for the construction cost
adjustments. For example, May 2008 data were converted into May 2005
data by multiplying May 2008 cost data by the value (100.0/122.8 =
0.81433) calculated by dividing 100.0, the index value for May 2005, by
122.8, i.e. the index value for May 2008. The road cost index applied to
the conversion was official statistical data prepared to estimate the
price fluctuation of input resources by 100.0 time scale as the price of
a direct road construction cost input in a project at a certain point in
time.
5. Determining the weight
The "weight" indicates how much attention should be paid
to the factor during the matching process in CBR cycle (Kolodner 1993).
It reflects the importance of that factor relative to other factors. It
was found that considered values of weights influence the project cost
prediction at most (Arditi, Tokdemir 1999; Chua et al. 2001; Luu et al.
2005; An et al. 2007; Kim, K. J., Kim, K. 2010). The determination of an
appropriate CF weighting method is a major issue for effective case
retrieval and indexing in CBR cycle (Park, Han 2002; An et al. 2007).
The major issue in CBR is to retrieve not just a similar past case but a
usefully similar case to the problem. Previous approaches used GAs,
gradient search, and feature counting. The problem with GA applications
comes from difficulty in identification of appropriate fitness function
which would successfully incorporate problem specific information (GA
2008). Gradient search may stagnate at local optima and fail to find the
optimal global solution for certain starting solutions (Albright,
Windston 2007; Kim, K. J., Kim, K. 2010). It is very difficult for
feature counting to reliably state that one feature is more or less
important than another based solely on human intuition (Arditi, Tokemir
1999).
For this reason, the integration of domain knowledge into the case
retrieving and indexing process is highly recommended in developing a
CBR system. This section utilizes a hybrid approach using AHP to case
base retrieval process in an attempt to increase overall cost accuracy.
If this hybrid approach is carried out well, the CBR system can deliver
better estimation of costs (Shin, Han 1999). It can operate more
accurately or at a lower cost level, it will be able to provide a better
understanding of the effects of CFs interaction and variation.
Analytic Hierarchy Process
AHP is a multi-factor decision-making method that uses hierarchical
structures to represent a decision problem and then delivers priorities
for the decision-maker throughout judgments (Saaty 1986, 1987, 1990;
Dyer 1990). Many previous studies (Dyer, Forman 1992; Al-Harbi 2001;
Chwolka, Raith 2001; An et al. 2007; Podvezko 2009; Medineckiene et al.
2010) consider the AHP methodology to be well suited for decision-making
due to its role as a synthesizing mechanism in decisions. For example,
An et al. (2007) compared three different weighting methods and
concluded that the AHP was more accurate, reliable, and explanatory than
decent gradient methods for determining the relative important weights
for making preliminary estimates of new construction costs. Once the
hierarchy is built, the decision-maker systematically evaluates its
components, which represent considered factors, by comparing their
importance in a pair-wise manner. This study applies the AHP to
calculate the weights of the aspects and the attributes within each
aspect. Pair-wise comparisons of importance of the factors at each level
of an AHP are made in terms of importance when comparing factors with
respect to their relative importance (Zahedi 1986; Harker, Vargas 1987;
Podvezko 2009; Medineckiene et al. 2010) (see Table 4).
The last step is devoted to the measurement of the overall
consistency of provided AHP judgments by means of the CR (Consistency
Ratio) proposed by Saaty. The CR provides a way of measuring errors
introduced during elicitation of expert opinions. The value of
consistency index is applied with this regard Eq. (1) (Chen et al.
2010):
CI = ([[lambda].sub.max]-n)/n-1, (1)
where n is the number of compared factors, and [[lambda].sub.max]
is the maximum eigenvalue of a judgment matrix which corresponds to the
group of compared factors. The CR value is given by division of the CI
value by the Random consistency index value. The RI value depends on
number of compared factors. RI values for different numbers of factors
are presented in Table 5.
Appropriate CR value justifies extracting expert knowledge that can
guide effective retrievals of useful weights. The weight values
expressing importance of each CF are presented in Fig. 3. They will be
assigned to the considered attributes for case based retrieval of the
most similar process plans due to the effective similarity function in
the proposed application area.
[FIGURE 3 OMITTED]
6. Case study
Expert knowledge can be applied to assess importance weights. The
expert is expected to have the required knowledge and experience to
decide which model or system makes good predictions. CBR applications
can be created using the hybrid AHP-CBR application development tool.
The CBR system searches for matched cases contained in the case base and
summarises them into a set of acceptable solutions. Decision-makers
select then one of the recommended solutions. The system's
interface is organized following the basic process used to construct the
AHP-CBR application. The reasoning structure of proposed system is
presented in Fig. 4. The following six steps are involved in CBR
application:
Step 1. Case base definition:: the first step is used to define the
initial components of the system. The names and value types for CFs are
defined. The selected CFs should provide the best description of
relevant construction cost influencing attributes which result from
prior experience. Table 2 presents an illustrative example of a case
based library contents.
[FIGURE 4 OMITTED]
Step 2. Similarity definition: the step deals with a way the
similarity between a new problem description and the case based library
items is assessed. The methodology and various metrics for determining
similarity during case base retrieval are defined. SI (Similarity Index)
is assessed both at the case level (comparing cases against each CF) as
well as at the CF level (comparing the value of each CF value to the new
entered CF values). Weighted case similarities between the new problem
and cases included in the case base library are estimated according to
the following formula:
SI = [n.summation over (i=1)] ([W.sub.i] x [SS.sub.i])/[n.summation
over (i=1)]([W.sub.i]) x 100. (2)
In Eq. (2), SI is a calculated numerical value which demonstrates
the degree of similarity between a case in the case based library and
the investigated problem case (Yau, Yang 1998). SI is normalized into a
scale from 0 to 1 for easy comparison. Weights (W) of each CF can be
either assigned by the decision-makers or AHP. SS (Similarity score) is
calculated on the basis of values of the CFs: numerical and nominal. For
the nominal factor, the SS equals 1 when the two values are identical
and 0 otherwise.
For the numerical factor, SS is calculated by Eq. (3). In Eq. (3),
[V.sub.case based] represents value of a factor for the cases stored in
a case based library. [V.sub.problem] value corresponds to the target
case for predicting highway costs. A more detailed classification method
is applied to improve the accuracy in this study when decision-maker
selects one of retrieved cases. It is possible to select the best
matching case from the case based library. Consequently, the new SS
formula has been developed and proposed here which not only expresses
the difference of compared cases but also makes verification of the
minimum and maximum relationship of the cases possible. The similarity
score in the developed formula is referred to as [SS.sub.revised] to
distinguish it from the SS used to retrieve similar cases:
[SS.sub.revised] = 1/[absolute value of [V.sub.case based] -
[V.sub.problem]]+1 (3)
Finally, SI is calculated due to Eq. (2).
Step 3. Case definition: this step is used to fill in the case
information for each case to be stored in the case based library. A case
collection interface is then applied for introducing data for the real
highway project cases into the library. CF values which describe the
cases must conform to the defined types. 48 highway cases are included
in the case based library in the prepared CBR system.
Step 4. Rule definition: rules are used to compute SI and to adapt
a retrieved similar case to better meet the needs of the new problem.
Rules are used to address the differences that exist between a new
problem case (target case) and the retrieved similar case. The rules are
applied to account for the differences and advise on what the plausible
outcomes of a comparison might be. Rules can be used to change CF values
based on comparison.
Step 5. Application interface: after case retrieval is complete the
system returns a list of cases with SI values indicating their
similarity to the target case. Their scores indicate their relevance to
the problem at hand. The decision-makers can apply the selected case to
help decide how to solve the current problem. The selected case can be
then adapted to better assist in making a decision.
Step 6. System validation: to determine whether the predicted
project cost provided by AHP-CBR is a good estimate of the problem case,
three methods that have been reported by Yau and Yang (1998), Arditi and
Tokemir (1999) and Koo et al. (2010) are used. Each of these methods
makes use of the overall case SI for each retrieved case. These methods
are as follows:
1. The problem case is compared to the characteristics of the
retrieved case that has the highest overall SS;
2. The problem case is compared to the most frequent
characteristics in the top ten retrieved cases, or fewer if ten are not
available, that have an overall SS greater than or equal to 0.75 (75%);
3. The problem case is compared to the average characteristics of
the top five retrieved cases, or fewer if five are not available that
have an overall SS greater than or equal to 0.75 (75%). The average of
the predicted condition is weighted using the overall SS to magnify the
importance of the retrieved cases which have higher SS.
According to the CBR concept, the case with the highest SI in the
case base library may be considered to have the most similar project
characteristics compared to the test case in this study. Also, each of
the 4 division costs (see Table 7) is identifiable from the selected
case based on retrieved SI. These results may be used as references in
the decision-making process as well.
7. Result for the sample CBR system application
As mentioned above, the research was carried out by employing AHP
method to assign importance weights to each CF. Different error
calculation formulae have been used by previous studies. The Mean
Absolute Estimation Error (MAEE) calculated due to Eq. (4) is applied
for expressing the system performance:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where: [Cost.sub.CBR] represents output for CBR application;
[Cost.sub.ACT] expresses actual cost, and n denotes the number of
testing cases.
The n-fold cross-validation was adapted in the next phase to
evaluate the performance of the AHP-CBR system and to reinforce the
reliability of results. The 6-fold approach can be considered the
effective form of reliability analysis of the measurement system. For
example, MAEE of 9.17% with 62.5% of the estimates within 10% of the
MAEE correspond to the results of the AHP-CBR system application, while
87.5% of the estimates within 15% are obtained for a 1-fold approach
application. The results as listed in Table 6. And, the mean error
(difference) rate of 1-fold compared to 6-fold is equal to 9.09%. The
corresponding output accuracy of the established AHP-CBR system meets
the fifth class requirements with regard to carrying out project
screening and feasibility study due to the definition of American
Association of Cost Engineers (AACE). Test cases allowed not only to
predicted total construction cost estimation error rate but also to
predict estimation error rate for each of the four division cost.
Obtained results are shown in Table 7. Retrieved similarity index values
obtained for the selected case based problems comprise therefore valid
reference points for the decision-making process.
8. Conclusion
Cost estimating system has become an integral part of any advanced
cost management modelling. Such systems make estimation of the accurate
project cost and improvement in cost prediction rate possible. Presented
research therefore focused on developing the hybrid AHP-CBR system which
provides accurate predictions of the future cost of different highway
projects.
The contribution of this research pertains to four areas. At first,
obtaining the higher predictive accuracy of cost estimate and guide to
decision-maker at the early planning stage is addressed. Developed
AHP-CBR system reduces the time required to build a cost list for
project activities and makes reduction of processing time and cost
possible. At second, the extracted CFs for highway projects
significantly improve system performance with regard to the cost
estimation. This finding contributes to the current body of knowledge on
approximate cost estimating, and may serve as a useful guide for future
data collection efforts and cost estimation system development. At
third, this research proposes the identification of an alternative
similarity score measuring formula. The introduced similarity measure
makes investigation of contrast between the developed similarity measure
and the classical SS measures possible when CFs are used to describe a
case. And finally, the weights of CFs are calculated using AHP.
In order to enhance the capabilities of the CBR approach in cost
estimating, numerous problems should be explored in the future research.
The problems include: development of proprietary indices for adjusting
the cost due to difference in a project location, development of more
justified weights using different weight estimation methods, collection
of more project cases into the case based library for improving
accuracy, and identification of important CFs in accordance with
different phases of the project planning and realisation.
doi:10.3846/13923730.2012.737829
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Sangyong Kim
School of Construction Management and Engineering, University of
Reading, Reading, Berkshire RG6 6AW, United Kingdom
E-mail:
[email protected]
Received 05 Aug. 2011; accepted 27Mar. 2012
Sangyong KIM. PhD Candidate at the School of Construction
Management and Engineering, University of Reading. MSc in construction
management and material from Korea University. A member of CIOB, RICS,
ASCE, JKIBC, and AIK. His research interests include cost estimation,
information technology in construction, decision-making and analysis by
artificial intelligence, and its applications in construction areas.
Table 1. Summary of CBR applications in various domains
Domain Authors (Year)
Design Schmitt (1993)
Fenves et al. (1995)
Demirkan (1998)
Fabrication Roddis and Bocox (1997)
Method Yau and Yang (1998)
Selection
Bidding/ Chua et al. (2001)
Prequalification
Management Tah et al. (1999)
System
Arditi and Tokdemir
(1999)
Morcous et al.
(2002)
Cost Mukhopadhyay et al.
(1992)
Marir and Watson
(1995)
Planning and Lee et al. (1998)
Scheduling
Dzeng and Tommelein
(1997, 2004)
Domain Contents System
Design Design and creativity CBD
Conceptual structural design SEED
Interior design applications N/A
Fabrication Bridge fabrication error CB-BFX
solution expert system
Method Retaining wall selection CASTLE
Selection system using ESTEEM
Bidding/ A CBR bidding system CASEBID
Prequalification
Management Large-scale data repository CBRidge Planner
System Predict the outcome of ESTEEM
construction litigation
Modeling infrastructure CBRMID
deterioration
Cost Software development Estor
effort estimates
Estimates the cost of ELSIE
refurbishing houses
Planning and Scheduling of apartment FASTRAK-APT
Scheduling construction
Scheduling of power CasePlan
plant boilers
Table 2. Highway research and relevant CFs
Authors Year Objectives Cost Factors
Hegazy and 1998 Budget cost * Project * Year
Ayed type
* Project * Season
scope
* Soil * Duration
condition
* Water * Size
bodies
* Location * Capacity
Al-Tabtabai 1999 Mark-up * Preservation * Location
et al. estimation of
utilities
* Type of * Soil
road Nature
* Type of * Hauling
consultant distance
* Construction
of detours
Wilmot 2005 Total * Price of * Duration
and Mei construction labour
cost
* Price of * Location
material
* Price of * Bid
equipment volume
* No. of * Bid
plan variable
changes
* Change in * Contract
specification type
Chou et al. 2007 Internet- * Proposed * Project
based main lane length
preliminary no.
cost
estimation * Shoulder * Location
width
* Lane width
Williams 2009 Construction * Geo. * Project
et al. data design length
collection standard
* Length of * Bridge
loops/ type
ramps
* Length of * Bridge
curb/ length
gutter
* Median * Bridge
length/ width
type
* Lane
length
Table 3. Determinants of project cost
Input variables Unit Values
No Min.
1 Completed year -
2 Actual duration months 24
3 Contract's duration months 24
4 Time extension months 0
5 Design expenses won 239,137,621
6 Contingency won 310,459,368
7 Type of site - 1.
8 Project scope -
9 Frame type of bridge - 1. Con
10 Length of highway km 3.34
11 Ratio of bridge % 0.30
12 Wide of highway m 23.4
13 Wide of bridge m 2.6
14 No. of lanes - 4
15 Pavement type -
16 Asphalt won/kg 19,000
17 Cement won/kg 1,450
18 Bar steel won/kg 210,000
19 Sheet steel won/kg 298,000
20 Shape steel won/kg 280,000
21 earthwork won 2,753,587,524
22 pavement won 178,560,000
23 drainage/structure won 991,358,249
24 appurtenant/ won 54,560,000
safety facilities
25 total cost won 8,390,793,722
Input variables Values
No Max.
1 Completed year From 1996 to 2008
2 Actual duration 85
3 Contract's duration 68
4 Time extension 36
5 Design expenses 6,371,670,030
6 Contingency 8,566,800,000
7 Type of site Narrow 2. Medium 3. Large
8 Project scope 1. New 2. Rehabilitation
9 Frame type of bridge crete 2. Steel 3. Concrete;+Steel
10 Length of highway 49.00
11 Ratio of bridge 9.80
12 Wide of highway 37.8
13 Wide of bridge 28.4
14 No. of lanes 8
15 Pavement type 1. Concrete 2. Ascon
16 Asphalt 35,200
17 Cement 3,300
18 Bar steel 363,000
19 Sheet steel 497,090
20 Shape steel 451,000
21 earthwork 86,929,808,126
22 pavement 62,218,194,183
23 drainage/structure 29,316,852,276
24 appurtenant/ 58,918,564,655
safety facilities
25 total cost 237,383,419,240
Values
Input variables Project
No Average significant
factors
1 Completed year
2 Actual duration 58 Time
3 Contract's duration 50
4 Time extension 8
5 Design expenses 2,161,041,843 Cost
6 Contingency 2,815,219,944
7 Type of site
8 Project scope
9 Frame type of bridge
10 Length of highway 8.39 General
11 Ratio of bridge 1.68 Information
12 Wide of highway 26.7
13 Wide of bridge 15.4
14 No. of lanes 5
15 Pavement type
16 Asphalt 24,647
17 Cement 2,070
18 Bar steel 263,053 Material
19 Sheet steel 387,308
20 Shape steel 351,632
21 earthwork 27,845,691,355
22 pavement 19,920,876,974 Division
23 drainage/structure 9,381,476,650
24 appurtenant/ 18,909,602,940
safety facilities
25 total cost 76,057,647,919
Table 4. Scale of relative importance (Saaty 1990)
Intensity of Definition
Relative
Importance
1 Equal importance
3 Moderate importance
of one over another
5 Essential or strong
7 Very strong importance
9 Extreme importance
2, 4, 6, 8 Intermediate values
between the two
adjacent judgments
Reciprocals If activity i has one of
of above the above nonzero numbers
nonzero assigned to it when compared
number with activity j, then j has
the reciprocal value when
compared to i
Intensity of Explanation
Relative
Importance
1 Two activities contribute
equally to the objective
3 Experience and judgment
slightly favour one activity
over another
5 Experience and judgment
strongly favour one activity
over another
7 An activity is strongly
favoured and its dominance
is demonstrated in practice
9 The evidence favouring one
activity over another is
of the highest possible
order of affirmation
2, 4, 6, 8 When compromise is needed
Reciprocals --
of above
nonzero
number
Table 5. Random consistency index (Saaty 1990)
n 1 2 3 4 5 6 7 8 9 10
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49
Table 6. Cost reasoning errors for 6-fold cross-validation
of the AHP-CBR system
1-Fold 2-Fold 3-Fold
Error
rate (%) Fre.(%) Cum.(%) Fre.(%) Cum.(%) Fre.(%)
0-2.5 0 0 1(12.5) 1(12.5) 0
2.5-5.0 1(12.5) 1(12.5) 2(25.0) 3(37.5) 2(25.0)
5.0-7.5 2(25.0) 3(37.5) 0 3(37.5) 2(25.0)
7.5-10.0 2(25.0) 5(62.5) 2(25.0) 5(62.5) 1(12.5)
10.0-12.5 1(12.5) 6(75.0) 0 5(62.5) 1(12.5)
12.5-15.0 1(12.5) 7(87.5) 1(12.5) 6(75.0) 0
15.0-17.5 1(12.5) 8(100.0) 1(12.5) 7(87.5) 2(25.0)
17.5-20.0 0 8(100.0) 1(12.5) 8(100.0) 0
20.0-22.5 0 8(100.0) 0 8(100.0) 0
Min. 2.76 - 1.80 - 2.76
Max. 15.36 - 19.25 - 16.81
MAEE 9.17 - 9.47 - 9.25
3-Fold 4-Fold 5-Fold
Error
rate (%) Cum.(%) Fre.(%) Cum.(%) Fre.(%) Cum.(%)
0-2.5 0 2(25.0) 2(25.0) 1(12.5) 1(12.5)
2.5-5.0 2(25.0) 0 2(25.0) 2(25.0) 3(37.5)
5.0-7.5 4(50.0) 2(25.0) 4(50.0) 1(12.5) 4(50.0)
7.5-10.0 5(62.5) 0 4(50.0) 0 4(50.0)
10.0-12.5 6(75.0) 2(25.0) 6(75.0) 2(25.0) 6(75.0)
12.5-15.0 6(75.0) 1(12.5) 7(87.5) 1(12.5) 7(87.5)
15.0-17.5 8(100.0) 0 7(87.5) 1(12.5) 8(100.0)
17.5-20.0 8(100.0) 1(12.5) 8(100.0) 0 8(100.0)
20.0-22.5 8(100.0) 0 8(100.0) 0 8(100.0)
Min. - 0.79 - 2.21 -
Max. - 18.98 - 17.43 -
MAEE - 8.76 - 8.49 -
6-Fold
Error
rate (%) Fre.(%) Cum.(%)
0-2.5 1(12.5) 1(12.5)
2.5-5.0 2(25.0) 3(37.5)
5.0-7.5 1(12.5) 4(50.0)
7.5-10.0 1(12.5) 5(62.5)
10.0-12.5 1(12.5) 6(75.0)
12.5-15.0 0 6(75.0)
15.0-17.5 0 6(75.0)
17.5-20.0 1(12.5) 7(87.5)
20.0-22.5 1(12.5) 8(100.0)
Min. 1.27 -
Max. 20.07 -
MAEE 9.42 -
Table 7. The error rate of each cost division (1-fold)
Division Error rate (%)
Case 1 Case 2 Case 3 Case 4 Case 6 Case 7
Earthwork 9.52 7.07 10.53 11.72 6.53 9.57
Pavement 9.34 7.49 10.01 12.50 6.31 9.93
Drainage/ 9.57 7.14 10.66 11.85 6.49 9.49
Structure
Appurtenant/ 9.29 7.42 9.88 12.37 6.35 10.01
Safety
facilities
MAEE 9.43 7.28 10.27 12.11 6.42 9.75
Division Error rate (%)
Case 8 Case 9
Earthwork 15.90 2.69
Pavement 14.82 2.83
Drainage/ 15.72 2.65
Structure
Appurtenant/ 15.00 2.87
Safety
facilities
MAEE 15.36 2.76
