Engineering, Technology & Applied Science Research Vol. 7, No. 3, 2017, 1670-1675 1670
www.etasr.com Naderpour et al.: Application of Fuzzy Expert Systems to Manage the Projects Time in Iranian Gas Refineries
Application of Fuzzy Expert Systems to Manage the
Projects Time in Iranian Gas Refineries
Abbas Naderpour
Department of Civil Engineering
Islamic Azad University
Central Tehran Branch, Iran
Aba.Naderpour.eng@Iauctb.ac.ir
Javad Majrouhi Sardroud
Department of Civil Engineering
Islamic Azad University
Central Tehran Branch, Iran
J.Majrouhi.eng@Iauctb.ac.ir
Masood Mofid
Department of Civil Engineering
Sharif University of Technology
Tehran, Iran
Mofid@Sharif.edu
Abstract-The National Iranian Gas Company (NIGC) is one of the
top ten gas companies in the gas industry in the Middle East and
is comprised of 7 gas refineries. So this company needs to apply
the most optimum time management methods to achieve its goals.
Custom scheduling calculation of project planning uses the
Critical Path Method (CPM) as a tool for Planning Projects
activities. CPM is now widely used in planning and managing
projects but in spite of its wide application, this method has a
critical weak point of not taking into account the uncertainties in
scheduling calculation. This article aims to present a precise
method based on the application of Fuzzy Expert Systems in
order to improve the Time Estimation Method in construction
projects and in this regard, reviews the results of the
implementation of this method in construction projects of Iranian
Gas Refineries. The results show that the proposed method
increases the accuracy of time estimation about 7 to 22 percent.
Keywords-Critical Path Method; Fuzzy Expert Systems;
Uncertainty; Time Estimation Method
I. INTRODUCTION
Time management can be effective in a project when the
project schedule is based on reasonable and comprehensive
time estimation. In industries with complex processes such as
gas refineries, considering limitations and risks involved in the
project implementation and also many uncertainties that affect
the project activities, the importance of the time management is
great. As the ongoing projects are directly or indirectly linked
with continuous production in gas refineries, operational
condition and site classification based on the HSE risks,
increases more uncertainties to the project schedule.
Considering the very low reliability of planning with certainty
and project control by this approach, using more secure
methods for control and interaction with uncertainty is to be
placed on the agenda. This article presents a method for
implementing an extended method of CPM based on the
application of fuzzy expert systems (FCPM) to manage
schedule uncertainties in Iranian gas refinery projects. The
concept of FCPM is explained by a real and applicable
example and then, the proposed model and the method of its
implementation in projects will be described.
II. FUZZY CRITICAL PATH METHOD (FCPM)
FCPM is an extension of Critical Path Method in terms of
fuzzy approach. In this method, fuzzy function defines the time
of project activities to manage their uncertainties. For
understanding the main concepts of FCPM, consider the project
network indicated in Figure 1. This project network is a part of
a small one-story building construction planning that contained
excavation, concreting and installing the building structures.
The resistance system against the earthquake is A.D.A.S
bracing. The description of all activities regarding the
mentioned project is presented in Table Ι.
Fig. 1. CPM of small one-story building construction
As it could be seen from Table Ι, 10 out of whole 11
activity times have triangular fuzzy type format and only the
remaining one (related to A.D.A.S braces) is in trapezoidal
form. Equations (1) to (8) represent the stages of FCPM
calculations of the project network. The calculations indicate
that the project total time is the maximum of three fuzzy
numbers (Eq.8). Consequently, in order to determine the
project time, it is necessary to rank the fuzzy numbers and
select the maximum.
FES1 = (0, 0, 0) + (1, 2, 4) = (1, 2, 4) (1)
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FES2 = (0, 0, 0) + (1, 5,10) = (1, 5,10) (2)
FES3 = (0, 0, 0) + (1, 2, 3) = (1, 2, 3) (3)
FES5 = (0, 0, 0) + (2,14,18) = (2,14,18) (4)
FES4 = Max ((1, 2, 4) + (2 , 3 ,4) , (1, 4,10)
+ (1, 2, 3) , (1, 2, 3) + (1, 2, 3)) = (2, 6,13)
(5)
FES6 = (2, 6,13) + (3, 4, 5) = (5 ,10,18) (6)
FES7 = Max ((5,10,18) + (4, 5, 9), (2,14,18)
+(1, 4, 6), (0, 12, 21, 24))
(7)
FES7 = Max ( A , B, C) St: A= (9, 15, 27) ;
B= (3, 18, 24) & C =(0, 12, 21, 24)
(8)
The calculations indicate that the project total time is the
maximum of three fuzzy numbers (8). Consequently, in order
to determine the project time, it is necessary to rank the fuzzy
numbers and select the maximum. Since fuzzy numbers do not
form a natural linear order (similar to real numbers) a key issue
in applications of fuzzy set theory is how to compare fuzzy
numbers. Various approaches have been developed for ranking
fuzzy numbers up to now. Initially a method using the concept
of maximizing set to order the fuzzy numbers was proposed in
[1]. In [2] four indices which may be employed for the purpose
of fuzzy ranking were introduced. In [3], an index for ordering
(ranking) fuzzy numbers was proposed. In [4] a new method of
fuzzy numbers ranking with integral value was described.
In [5], fuzzy sets were ranked based on the concept of
existence of vibration frequencies. In [6] a new approach for
ranking fuzzy numbers by distance method was proposed. In
[7], ranking alternatives with fuzzy weights by maximizing and
minimizing set was introduced. A new methods for ranked
fuzzy sets was described in [8]. In [9], authors ranked fuzzy
numbers with an area between centroid point and original point
while in [10] authors used fuzzy distance measure for fuzzy
numbers comparison in the same year. In [11], authors
proposed another fuzzy ranking method based on distance
method. In [12], authors ranked fuzzy numbers by sign
distance. In [13], authors ranked fuzzy numbers by distance
minimization. In [14], authors ranked trapezoidal fuzzy
numbers with integral value. In [15], authors published the
result of their research about fuzzy ranking. In [16], authors
ranked fuzzy numbers with an area method using a radius of
gyration in torsion stiffness. In [17], authors ranked trapezoidal
fuzzy numbers based on mode, spread, and weight. In [18],
authors improved the ranking method for fuzzy numbers based
on centroid-index. In [19], authors proposed a new method
based on angle measure and finally in [20] a new
lexicographical approach for ranking fuzzy numbers was
proposed.
For ranking the three fuzzy numbers of (8), five methods
were considered. Table II shows the results of this ranking and
Figure 2 compares the results in bar charts. Also, the project
total time and critical path for each method are indicated in
Table III.
TABLE I. THE PROJECT INFORMATION OF ACTIVITIES
Activity Activity Description Time (days)
0 - 1 Steel Bars Cutting (1, 2, 4)
0 - 2 Excavation (1, 5, 10)
0 - 3 Base Plate Making (1, 2, 3)
0 - 5 Making the Beams (2, 14, 18)
0 - 7 Making & Installation of A.D.A.S braces (0, 12, 21, 24)
5 - 7 Installing the Beams (1, 4, 6)
1 - 4 Making Reinforce Cage (1, 2, 3)
2 - 4 Foundation Forming (1, 2, 3)
3 - 4 Base Plate Installation (1, 2, 3)
4 - 6 Concreting (3, 4, 5)
6 - 7 Columns Making and Installation (4, 5, 9)
TABLE II. RESULTS OF FUZZY RANKING BY 5 METHODS
Fuzzy Ranking
Method
Result of Ranking Method Calculation
A B C Result
Choobineh & Li 17.5 18.33 15 18.33 C < A < B
Yager 15.75 16.5 13.5 16.5 C < A < B
Cheng 21.77 21.72 21.32 21.77 C < B < A
Chen
& Sanguansat 17.1 18.75 15.6 18.75 C < A < B
Abbasbandy
& Hajjari 15.75 15.73 14.25 15.75 C < B < A
TABLE III. RESULTS OF PROJECT CRITICAL PATH
Fuzzy Ranking Method Project Critical Path project time (days)
Choobineh & Li 0 – 5 – 7 18.33
Yager 0 – 5 – 7 16.5
Cheng 0 – 2 – 4 – 6 - 7 21.77
Chen & Sanguansat 0 – 5 – 7 18.75
Abbasbandy & Hajjari 0 – 2 – 4 – 6 - 7 15.75
Fig. 2. Project time calculation by various fuzzy ranking methods
According to the results of FCPM calculations, selecting
the fuzzy ranking method for project scheduling has a great
influence on the determination of project total time and critical
path. As a result, a suitable fuzzy ranking method, compatible
Engineering, Technology & Applied Science Research Vol. 7, No. 3, 2017, 1670-1675 1672
www.etasr.com Naderpour et al.: Application of Fuzzy Expert Systems to Manage the Projects Time in Iranian Gas Refineries
to project nature should be considered by project management
team.
III. FUZZY TIME ESTIMATION
Several methods have been proposed for finding the fuzzy
time management. The main common topic in all of these
methods is converting the classic time of project activities to
fuzzy numbers for schedule calculation. For the reason that
CPM calculation needs to compare the time of activities to
determining critical path, ranking of fuzzy numbers is
necessary. Consequently, fuzzy numbers ranking is the most
important factor in these methods. In [21], authors introduced
the preliminary concept of Fuzzy CPM. They presented the
time of project activities by fuzzy set in the time space. Their
method provides more direct processing verbally expressed
opinions of experts. The significant problem not quite solved in
their method was the question of deriving membership
functions for activity duration times. In [22] algebraic operators
were used to estimate the time of project activities and project
critical path. In [23] a way to to compute total floats and find
critical paths in a project network by the fuzzy approach was
described. In [24], a methodology to calculate the fuzzy
completion project time was presented and in [25] an extension
of fuzzy schedule networks was proposed. New methods were
recently introduced in [26]. They proposed a method for
ranking fuzzy numbers without the need for any assumptions
and used both positive and negative values to define ordering
which is applied to CPM.
In [27], authors presented an approach to the critical
concept in a network with fuzzy activity times. In [28], a
taxonomy of fuzzy graphs that treated fuzziness in vertex
existence, edge connectivity and edge weight was presented. In
[29], a new approach to implementing a fuzzy CPM for activity
networks based on statistical confidence interval estimates and
a ranking method for level fuzzy numbers was introduced. In
[30], authors presented an algorithm to perform fuzzy critical
path analysis for project network problem. In [31], authors
presented another method to calculate fuzzy critical paths and
critical activities and activity delays and in [32] authors
extended some results for interval numbers to the fuzzy case
for determining the possibility distributions to describe latest
starting time of activities. In [33], authors proposed an
approach based on the extension principle and linear
programming (LP) formulation to critical path analysis in
networks with fuzzy activity durations. In [34], authors
introduced the problems of determining possible values of
earliest and latest starting times of an activity in networks with
minimal time lags and imprecise durations that are represented
by means of the interval of fuzzy numbers. In [35], authors
proposed a new approach based on fuzzy critical path
calculation. They used fuzzy arithmetic and the fuzzy ranking
method to determine the fuzzy critical path of the project
network without converting the fuzzy activity times to classical
numbers and compared their method with other methods. In
[36], authors proposed a new method of fuzzy critical path
analysis based on the centroid of centroids of fuzzy numbers
and in [37] authors proposed new algorithms identify the
critical path in a fuzzy environment of project network..
IV. PROPOSED FUZZY BASE METHOD
The uncertainties that must be managed in each project are
categorized into two main groups; the First group includes
probable uncertainties which are managed by risk management
and the second group covers non-probable uncertainties that are
related to project nature and its complexity. Many industries,
such as gas refineries manage probable uncertainties in their
projects by risk management but in the field of non-probable
uncertainties, actions are very scarce. This article considers the
managing of non-probable uncertainties in gas refineries
projects. The diagram of proposed model is shown in Figure 3.
Fig. 3. Diagram of the proposed model
For implementing the models, at first, two professional
questionnaires were distributed between a professional team
which was selected by the staff of 70 contractors, consultant
and employer companies. The first questionnaire was designed
to identify effective factors such as site organization, weather,
labor skills and quality of equipment on doing project
activities. Then obtained Linguistic variables were translated
into mathematical measures. For instance, the questionnaire
was designed for excavation activity is presented in Table IV.
TABLE IV. QUESTIONNAIRE OF EXCAVATION ACTIVITY
Please determine the effect of each factor in the time of excavation
Activity.
1- Excavation Equipment (Hand Tools, loader, Backhoe, Excavator, Dozer)
Very Poor Poor Medium High Very High
2- Climatic Condition (Very Warm, Warm, Moderate, Cold, Very Cold)
Very Poor Poor Medium High Very High
3- HSE Criteria (Classification of site in Operational Zones)
Very Poor Poor Medium High Very High
4- Classification of Rock (Earthy, Soft, Moderate, Hard, Very Hard)
Very Poor Poor Medium High Very High
5- The level of underground water in Meter (>15, 10-15, 5-10, 1-5, <1)
Very Poor Poor Medium High Very High
6- Depot Distance in Meter (>10000,1000-10000, 500-1000, 100-500,<100)
Very Poor Poor Medium High Very High
7- Depth of Excavation in Meter (>15, 10-15, 5-10, 1-5, <1)
Very Poor Poor Medium High Very High
8- years of driver Experience of (>20, 15-20, 10-15, 5-10, <5)
Very Poor Poor Medium High Very High
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As it can be seen in Table IV, the value of the Linguistic
variables is classified into 5 types (Figure 4). As it could be
seen in Table IV, a large number of factors are considered to
estimate the time of excavation activity. To examine the
reliability of the questionnaire, data analysis was done by
SPSS. The results of this analysis are shown in Table V.
According to SPPS analysis, the Cronbach's alpha (Reliability
Index) was 0.387, while it should be greater than 0.7. The
results show that factors 2, 3, 5, 6 and 8 do not have an
effective influence on the timing of excavation activity. So
these factors were eliminated and the calculations were
repeated. In the new analysis, the index rose up to 0.888 which
is desirable. So the main factors of excavation activity are
Excavation Equipment, Classification of Rock and Depth of
Excavation. In the next step, the second questionnaire which
relates to estimating activity durations was distributed among
team members. After summing up the results of the first and
second questionnaires, obtained results were examined by a
team of experts (composed of 8 expert project managers) to
determine its content validity. Then, according to satisfactory
results, the structural validity of survey questionnaires was
evaluated by Factor Analysis method. According to the KMO
index, the acceptable construct validity of research was
approved. The analysis results are summarized in Table VI.
Also, the results of the total variance of analysis explained that
these three factors are not reducible to the number of agent-less
(Table VII).
Fig. 4. The value of the linguistic variables classification
TABLE V. RESULTS OF RELIABILITY INDEX CALCULATED BY SPSS
Scale Mean if Item Deleted
Scale Variance
if Item Deleted
Total
Correlation
Cronbach's
Alpha if Item
Deleted
S01 12.11 5.951 0.443 0.290
S02 13.75 8.639 0.136 0.449
S03 13.75 9.231 0.110 0.505
S04 11.86 5.460 0.621 0.190
S05 13.25 8.120 0.000 0.526
S06 13.68 8.300 0.109 0.457
S07 12.75 6.861 0.368 0.153
S08 13.61 7.803 0.276 0.404
TABLE VI. THE RESULTS OF KMO TEST
Kaiser-Meyer-Olkin Measure of Sampling Adequacy 0.692
Bartlett's Test of Sphericity
Approx. Chi-Square 13.522
df 3
Sig. 0.003
TABLE VII. THE RESULTS OF TOTAL VARIANCE
Component Total Variance Explained Total % of Variance Cumulative %
1 1.823 46 46
2 1.076 28 74
3 1.041 26 100
According to the results obtained from computing of the
Pearson Correlation coefficient, the correlation between these
factors is also desirable. Table VIII indicates related results.
TABLE VIII. THE RESULTS OF CORRELATION INDEX
Correlation Results S01 S04 S07
S01
Pearson Correlation 1 0.910 0.576
Sig. (2-tailed) 0.000 0.001
N 28 28 28
S04
Pearson Correlation 0.910 1 0.511
Sig. (2-tailed) 0.000 0.005
N 28 28 28
S05
Pearson Correlation 0.576 0.511 1
Sig. (2-tailed) 0.001 0.005
N 28 28 28
In later stages of the proposed model, membership
functions of these factors were drawn according to the second
questionnaire. The second questionnaire is about estimating the
time of each activity based on the experience of the
professional team. In this research, Fuzzy diagrams were of
triangular and trapezoidal types. In the present example,
Figures 5 to 7 indicate the Fuzzy membership functions of
excavation activity factors. These diagrams are considered as
the input of analysis.
Fig. 5. Fuzzy membership of excavation equipment factor
Fig. 6. Fuzzy membership of classification of rock factor
Fig. 7. Fuzzy membership of excavation depth factor
Then the results of the previous step as input were analyzed
in Fuzzy Toolbox of MATLAB. This toolbox follows a Rule
Base System. Analysis of model is presented in Figure 8. As it
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can be seen in Figure 8, inputs are processed by a smart and
rule base system.
Fig. 8. A pictorial view of analysis model in MATLAB
“IF …Then …” rules were set by the expert team in Rule
Base system. For example, for these three factors, about 125
operating modes may occur. Three states of these rules are
observed in Table IX and Software environment can be seen in
Figure 9.
TABLE IX. AN EXAMPLE OF ANALYSIS RULES
Rule No The Rule
Rule 1
If Excavation Equipment is a Dozer and Classification of
Rock is Very Hard and Depth of Excavation is more than 15
meter ThenThe Time of Excavation is Very Long.
Rule 2
If Excavation Equipment is a Backhoe and Classification of
Rock is Soft and Depth of Excavation is Less than 1 meter
ThenThe Time of Excavation is Very Short.
Rule 3
If Excavation Equipment is a Dozer and Classification of
Rock is Hard Or Depth of Excavation is between1 to 5 meter
ThenThe Time of Excavation is Moderate.
Fig. 9. A pictorial view of setting the rules in the software
After analysis, the duration of activities under uncertainty
and fuzzy approach can be achieved. For example, this time for
an above-mentioned activity (Excavation) will be 4.5 days for
each 200 cubic meters of concrete. (Figures 10-11). Finally,
after calculating the time of all activities by this method,
project schedule was run and the total time of project was
calculated.
Fig. 10. A pictorial view of analysis output
Fig. 11. A pictorial view of MATLAB output diagram
V. RESULTS
The proposed model of the research has been implemented
in one gas refinery in the North East of Iran. The study period
was between 2014 and 2016 and the population of this study
was composed of 30 projects by Cochran formula. The result of
the research shows the estimated project duration is about 7 to
22percent closer to actual time. Figure 12 indicates the percent
of improvement in project time estimation.
Fig. 12. Diagram of improvement in project time estimation new method
VI. CONCLUSION
This study investigated a new method for precise time
estimation in construction projects of the Iranian Gas
Refineries. A gas refinery has a complicated process and
Engineering, Technology & Applied Science Research Vol. 7, No. 3, 2017, 1670-1675 1675
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ongoing projects are directly or indirectly linked with
continuous production in this industry. Consequently managing
the project time is a critical issue and considering the very low
reliability of the project planning with certainty, using more
secure models for control and interact with uncertainty is a
necessity. It is obvious that successful project time
management should be based on comprehensive time
estimation. Therefore, considering the uncertainty in the
estimation of project time is the main object. From the above
discussion, the following conclusions were derived:
1. Many industries, such as gas refineries manage probable
uncertainties in their projects by risk management but in the
field of non-probable uncertainties, actions are very scarce.
2. This research considered the managing of non-probable
uncertainties in gas refineries projects by a proposed
method based on Fuzzy Critical Path Method.
3. The result of the implementation of proposed method
shows that the accuracy of project time estimation increases
about 7 to 22 percent. Finally, due to successful results of
this research, it has been suggested that the proposed
method could be generalized to other industries projects.
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