Evaluating Project Planning and Control System in Multi-project Organizations under Fuzzy Data Approach Considering Resource Constraints (Case Study: Wind Tunnel Construction Project)

Abstract

Projects can be repetitive tasks in specified periods of time and also it may involve some functions which are performed just once. However, in any project, managers and experts consider three basic and important goals: least time, lowest cost and best quality, so all efforts are directed toward achieving these basic goals. Statistics indicate that projects are either conducted on estimated time or delayed and rarely are delivered before due date. Even if an activity is completed earlier in implementation phase, its post requisite activity would not be performed due to resource constraints and unavailability or project manager's mistakes in estimating right time for activities. According to planning for technology advances within next years and gaining independence in this engineering field, our country is not an exception to this rule and there are urgent needs of scattering and promoting wind tunnel technology in different types and velocities at university and industry level. Wind tunnels are available in both open and closed circuit modes and are classified into subsonic, transonic, supersonic and ultrasonic based on their speed, each of which are used for specific purposes and have their own unique advantages and disadvantages.

Full text

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Evaluating Project Planning and Control
System in Multi-project Organizations
under Fuzzy Data Approach Considering
Resource Constraints (Case Study: Wind
Tunnel Construction Project)
Mohammad Taghipour1*, Nader Shamami2, Ahad Lotfi3, Shahrooz
Parvaei Maryan4
1Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University,
Tehran, Iran
2Industrial Engineering-Operations Research and Systems Engineering of Qazvin, Islamic Azad
University, Qazvin, Iran
3Islamic Azad University, Maku Branch, Iran
4Department of Mangement, Faculty of Management, Rasht Branch, Islamic Azad university,
Rasht, Iran
Email Address
Mohamad.taghipour@srbiau.ac.ir (Mohammad Taghipour)
*Correspondence: Mohamad.taghipour@srbiau.ac.ir
Received: 17 March 2020; Accepted: 5 April 2020; Published: 16 April 2020
Abstract:
Projects can be repetitive tasks in specified periods of time and also it may involve
some functions which are performed just once. However, in any project, managers
and experts consider three basic and important goals: least time, lowest cost and best
quality, so all efforts are directed toward achieving these basic goals. Statistics
indicate that projects are either conducted on estimated time or delayed and rarely are
delivered before due date. Even if an activity is completed earlier in implementation
phase, its post requisite activity would not be performed due to resource constraints
and unavailability or project manager’s mistakes in estimating right time for activities.
According to planning for technology advances within next years and gaining
independence in this engineering field, our country is not an exception to this rule and
there are urgent needs of scattering and promoting wind tunnel technology in different
types and velocities at university and industry level. Wind tunnels are available in
both open and closed circuit modes and are classified into subsonic, transonic,
supersonic and ultrasonic based on their speed, each of which are used for specific
purposes and have their own unique advantages and disadvantages.
Keywords:
Project Management, Fuzzy Logic, Wind Tunnel, Activities
1. Introduction

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Setting up a factory, developing a new product, launching a space program,
conducting a heart transplant surgery, holding a seminar, writing or publishing a book,
providing travel arrangements and myriad of tasks of this kind which is performed by
a person or a group of people, each are considered to be a project. Projects can be
repetitive tasks in specified periods of time (such as closing a factory bank accounts at
the end of fiscal year, biennial refinery overhaul) or it may involve some functions
which are performed just once (like construction, development or research projects).
[1]
Actually, projects are a set of activities while having logical dependency to each
other, should be executed on a given date with certain costs and quality. This is not
possible unless in light of appropriate methods of planning and control which could
lead project to the end by taking advantage of resources and facilities. [1]
Since 1950s operational researchers have strived to innovate and develop
appropriate methods for project control and management by using mathematical and
experimental techniques. These techniques have been able to create a systemic
attitude in project control and management, offer the needed insight into predicting
the behavior of projects in real world, perform uniform and effective resource
planning and by and large help to reduce the time of research and as well as costs
arising from the use of resources and facilities.
2. Review of Literature
Croxatto et al. [2], This review aims at presenting a general overview of project
management with an emphasis on selected critical aspects. It is important to define
clearly beforehand the objective of a project, its perimeter, its costs, and its time frame
including precise duration estimates of each step. Then, a project management plan
including explanations and descriptions on how to manage, execute, and control the
project is necessary to continuously monitor the progression of a project to achieve its
defined goals.
Kivila et al. [3], The goal of this study is to identify the control practices that a
project organization uses for sustainable project management. The results reveal that
sustainable project management is implemented using not only indicators but a
holistic control package in which control mechanisms are used differently for
different sustainability dimensions.
L. Martens et al. [4], This research looks at sustainability through the triple-bottom
line perspective: economic, social, and environmental. The results show that four
factors stood out: Sustainable Innovation Business Model, Stakeholders Management,
Economic and Competitive Advantage, and Environmental Policies and Resources
Saving.
E Papke-Shields et al. [5], was examined the application of strategic planning
characteristics from prior strategic planning research to project management. Drawing
from prior research in strategic planning, strategic information systems planning and
strategic manufacturing planning, this research combines strategic planning
characteristics derived from a rational approach with a second set of adaptive
characteristics to create a comprehensive model. Findings indicate that PM is captured
by varying degrees of a rational adaptive approach, which is positively correlated with
PM success and use of PM tools/techniques. These results suggest that strategic
planning characteristics can be effectively incorporated into a generalized PM

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framework, yielding potentially useful insights regarding the relationship of PM
behaviors to eventual project success.
Koshkina et al. [6], in This article discusses application of the internal control
means and key control factors in order to evaluate the economic security of academic
research projects. An integral indicator of the academic research project economic
security is suggested. Credibility, probability, compliance, efficiency and
competitiveness are suggested as primary indicators of the academic research project
internal control evaluation.
Wang et al. [7]. This paper fills the gap by investigating the possibility of using 5D
CAD for project cost and schedule control. Initiated by Woodside Energy Ltd, a
prototype of a 5D CAD system has been developed specifically for Liquefied Natural
Gas (LNG) industry. The system was tested with the project data of an example
module from an LNG plant provided by Woodside Energy Ltd. The functions of the
system include: visualization of schedule data and verification of cost in real time and
facilitation of periodic planning and progress reporting. It is concluded that 5D CAD
could be a very powerful project cost and progress control tool.
Taghipour et al. [8], studied the Study of the Application of Risk Management in
the operation and Maintenance of Power Plant Projects. one of the methods used in
good decision making, pay attention to risk management, which is known as an
important part of project management and control. Risk management has evolved
over time and its systematic method has provided managers with a definite path so
that they reduce potential threats to a minimum and reach project goals by the least
possible deviations. In this paper, subsequent to an introduction of fundamental
concepts of risk, risk management, an account of risk management, methods and its
techniques are presented. In the end, following a discussion on how it is practically
used in projects in a real and practical sample, risk management and its application are
implemented and essential investigations are undertaken into its effects.
Rezvani Befrouie A et al. [9], discussed the design of high-rise building with
ecological approach in Iran(Alborz Province). The present study aimed to evaluate the
ecological architecture with the concept of increasing energy storage, reduction of
fossil energy, reduction of CO2 emission and replacing clean energy. This study
aimed to minimize the need of high-rise buildings to fossil fuels, achieving. The
results showed that by curve form (oval) for the lowest aspect in east and west and
extension in eastern and western (aerodynamic), we can use renewable and clean
energy in high-rise buildings in Alborz (Azimie). Also, by solar space (Atrium),we
can minimize energy consumption in high-rise buildings in Alborz (Azimie).
Taghipour et al.[10], studied Risk analysis in the management of urban
construction projects from the perspective of the employer and the
contractor.Imbalance between anticipated and actual progress in the development of
urban construction projects suggests that there are many obstacles and risks which not
only causes the urban management be unsustainable, but the reconstruction and
development of urban space is also seriously threatened. the results indicated that the
experts listed the most significant risks as the delays in the payment of contractors'
claims and statements due to the lack of handling financial instruments, the
governance of relationships rather than rules in the tenders resulting from employer
actions, low commitment to the quality of work provided by their subcontractors,
failure to complete the detail engineering by foreign contractors on time, weaknesses
in contractors' financial resources, and offering lower prices than reasonable by

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contractors to win the tender. Finally, the solutions for eliminating or reducing risks in
high risk areas have been offered to provide tranquility for contractors and employers.
Mahboobi et al. [11], discussed Assessing Ergonomic Risk Factors Using
Combined Data Envelopment Analysis and Conventional Methods for an Auto Parts
Manufacturer. occupational injuries are currently a major contributor to job loss
around the world. They are also costly for business. The absence of rational analysis
is felt in this area, so mathematical analysis is needed to obtain the logical results of
these injuries in order to find gaps or loss points of industry. OBJECTIVE: This paper
assesses the effect of five demographic factors on ergonomic risk and occupational
injuries using an integrated mathematical programming approach. The obtained
results will help managers to carry out any required corrective actions or establish
benchmarks.
Taghipour et al. [12], discussed Insurance Performance Evaluation Using Bsc-Ahp
Combined Technique.one of the most effective practices used by organizations is the
use of performance evaluation in order to determine weaknesses and strengths of
organizations and fix them and enhance their strengths. Performance management and
evaluation play a prominent role in determining and implementing strategies, as well
as contributing to organizations’ competition power. In this regard, possessing a
model for evaluating organization’s strategic performance seems essential. One of the
techniques is the balanced scorecard which was introduced to evaluate organizations’
performance for the first time and is still recognized as a method of strategic planning
which can be applicable. The balanced scorecard is a managerial concept which helps
managers at all levels controls their key activities. In this research, we aim to assess
the performance of various representatives of Kosar Insurance Co. in Qazvin using a
combined approach, the balanced scorecard (BSC) and analytical hierarchy process
(AHP), and prioritize them and explore their strengths and weaknesses.
Rezvani Befrouei MA et al. [13], discussed Identification and Management of Risks
in Construction Projects. Today, risk management in construction projects is
considered to be a very important managerial process for achievement of project’s
objectives in terms of time, costs, quality, safety, and environmental sustainability.
Instead of employing a systematic approach for identification of risks, their
probability and their effects, most of the studies conducted inthis area have focused
only on a few aspects of risk management in construction project. the present study
aims to identify and analyze the risks associated with development of construction in
the greater city of Tehran, employing a comprehensive approach that is consisted of
five aspects. After the collection and observation of the data, the output was examined
by Pearson correlation also, using charts and tables. The results indicated that “tight
project schedule” present in all five categories- imposed the maximum risk .Also
“design variations”, “excessive approval procedures in administrative government
departments” and “unsuitable construction program planning” were identified as next
high risk factors.
Colin et al. [14], was proposed two new project control approaches, which
combines elements of both top down and bottom up control. To this end, we integrate
the earned value management/earned schedule (EVM/ES) method with multiple
control points inspired by critical chain/buffer management (CC/BM). We show how
the EVM/ES control approach is complementary with the concept of buffers and how
they can improve the project control process when cleverly combined. These
combined top down approaches overcome some of the drawbacks of traditional

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EVM/ES mentioned in the literature, while minimally increasing the effort spent by
the project manager.
Sabeghi et al.[15], was used an adapted version of the facility location model (FLM)
to find the optimal timing of project control points. Initially, the adapted FLM
determines the optimum timing of the control points in the projects duration. A
simulation model is then used to predict the possible disruptions in the time period
between the beginning of the project and the first control point (monitoring
phase).Safe and successful completion of complex projects in industrial environments
requires careful planning and collaboration of different stakeholders.
N. Balfe et al. [16], was presented the integration of three methods (task analysis,
safety analysis, and project optimization) to apply a holistic approach to complex
project planning. The results from the case studies indicate that significant benefits in
terms of time, cost and safety can be achieved through the application of the
integrated methodology.
Taghipour et al. [17], studied The Evaluation of the Relationship between
Occupational Accidents and Usage of Personal Protective Equipment in an Auto
Making Unit. One of the problems that encounter each work society is occupational
accidents. Today, despite the improvements of facilities and working conditions, the
possibility of accident occurrence in workplaces and especially in industrial places is
inevitable. Since the non-use or misuse of PPE is one of the main causes of accidents
in industrial units, the aim of this study is to evaluate the association between
occupational accidents and the use of PPE in the body section of a vehicle
manufacturing unit. The results showed that there is a meaningful positive
relationship between the factor of inadequate PPE and probable hazards of the
industrial workplace.
Baghipour sarami et al. [18], studied Modeling of Nurses’ shift Work schedules
According to Ergonomics: A case study in Imam sajjad (As) Hospital of Ramsar. In
this study, 35nurses working in the emergency ward of Imam Sajjad (AS) Hospital of
Ramsar city, Iran, were considered. The final model was implemented with GAMS
and at the end, shift working with ergonomic criteria were proposed. The results
showed that the proposed working program on one hand will improve satisfaction and
efficiency of nurses and on the other hand it can decrease the effects of disorders on
shift work
Yun et al. [19], was presented a phase-based framework and 10 input measures for
measuring project management efforts in a capital project. The measures are planning,
organizing, leading, controlling, design efficiency, human resources, quality,
sustainability, supply chain, and safety. This study quantifies and assesses the inputs
and further sorts the results by industry sectors and project phases. The results
indicate that infrastructure sector tends to exert fewer and less consistent efforts than
building and industrial sectors. This study contributes a new benchmarking
framework and is the first to quantify project management inputs of a capital project
systematically.
Taghipour et al. [20], studied Construction projects risk management by risk
allocation approach using PMBOK standard. Projects' managers in plenty of
construction projects which are assumed that are under control, are facing risk as an
unknown occurrences and they are attempting to control it and are suffering more
costs. Construction projects are encountering uncertainties in regard with achieving

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their goals. They have to be controlled and appropriately responded by risk
management methods. In this regard, risk management process in PMBOK standard
can be a suitable approach to solve this problem. In this project, 11 important risks in
Mehr housing project in Hashtgerd city have been identified.
3. Project Control Problem
The main objectives of any project are:
Finding the time of project implementation or end of project event using estimated
times.
Planning for the optimum use of resources and facilities
Determining the optimum time for activities so that total costs of projects be at the
minimum level.
Determining the optimum time for activities so that project completion time does
not exceed a given date and or its total costs do not deviate from the allocated amount.
[21]
To achieve one or more of the above objectives, definitions and techniques involved
in project control are discussed below:
Hurricane wind tunnel:
Hurricane wind tunnel plan is divided into 8 phases: 1. Needs assessment 2.
Conceptual design 3. Preliminary design 4. Detailed design 5. Equipment provision
(buying) 6. Manufacturing and assembly 7. Testing and calibration 8. Final test and
delivery. In this section, the above phases are explained briefly.
Needs assessment: this phase includes the following sections:
a. Review a variety of wind tunnel types and their components
b. detailed review of vertical wind tunnels
c. Review wind tunnels of Sky venture Company.
d. Statistical analysis of vertical wind tunnels
e. Patents for vertical wind tunnel
f. Review structure and building methods
g. Review vertical wind tunnel for aerodynamic research purposes
h. Review wind tunnel flow measurement and control methods
i. Review wind tunnel noise (sound) reduction methods
j. Visit the Emirates wind tunnel
k. Wind tunnel Feasibility study
The report of above items have been briefly presented in 2009 last quarter. Also, the
executive has provided the detailed reports on the above items. In this phase, the wind
tunnel type (blowdown open wind tunnel) as well as vertical configuration and parts
of wind tunnel were specified (according to Figure 1).

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Figure 1. The original plan wind tunnel.
Conceptual design: this phase includes the following sections:
a. Investigating the design of wind tunnel parts
b. Calculation of hurricane vertical wind tunnel pressure-drop
c. Examining fan types and characteristics
d. Selecting fan, electric motor and remote control
Conceptual design of hurricane vertical wind tunnel
In this phase, wind tunnel parts were checked and designed in detail and
preliminary design became more complete. Following detailed review and design of
wind tunnel parts, pressure drop calculation was done based on semi-empirical
relationships, then the intended fan was selected. Also, in order to better understand
fan performance, its types and characteristics were examined. Following the necessary
checks on fan type and dimensions, the electric motor, electric power and
manufacturer company were selected. Given that the airflow speed in wind tunnel is
based on fan’s rotational speed control, therefore, hurricane wind tunnel speed was
reviewed and selected. Figure 2 exhibit the characteristic curve of the selected fan.
Figure 2. Selected fan characteristic curve.

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With respect to selection of fan and other parts of wind tunnel as well as pressure-
drop calculations, the conceptual design of vertical wind tunnel was carried out and
the above design was determined as the wind tunnel action plan. Most detailed reports
on the above have been presented by the executor.
Preliminary design: in this phase, to troubleshoot conceptual design and complete
the design, research has been conducted using experimental and numerical fuzzy data.
This phase consists of the following sections:
a. Design calculations and model fabrication plan
b. Tests conducted for wind tunnel with similar fan
c. Experimental research on wind tunnel model (nozzle)
d. Experimental research on wind tunnel model (screen)
e. Experimental research on wind tunnel model (diffuser1)
f. Experimental research on wind tunnel model (diffuser2)
g. Experimental research on wind tunnel model (diffuser3)
h. Experimental research on wind tunnel model (corner and triangle exit)
i. Airflow numerical simulation (nozzle)
j. Airflow numerical simulation (diffuser1)
k. Airflow numerical simulation (diffuser 2)
l. Airflow numerical simulation (diffuser 3)
m. Review and check Numerical and experimental results
n. Calculation and design of structure and foundation
o. Architectural design
p. Design of heating and air conditioning
q. Design of Power system
As mentioned above, in preliminary design phase, conceptual design must be
troubleshot and completed. In this section, wind tunnel model which is in 7/8 scale of
wind tunnel plan was calculated and designed, then fabricated as both blower
(blowdown) and suction configurations. To collect project data, numbers obtained
from the conducted tests and experts opinions (qualitative data) using fuzzy data
approach were evaluated. For blower mode, centrifugal fan and settling chamber were
utilized.
4. Fuzzy Theory and Project Control
Approximation argument plays a major role in human thoughts. Although statistical
inference and probability in data analysis generate desired results, there are some
experimental data which could not be justified and need some other forms of
approximation argument. Sentences like “this device is made of reliable equipment”
or “this work is highly valued” or “the quality of this work is good” all raise questions
which have approximate essence. In this regard, Professor L. Asgharzadeh says:
“most of human arguments are naturally approximate rather than accurate.” [22].

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The word “fuzzy” versus crisp was first applied in 1965 by Prof. L. Asgharzadeh in
his well-known article entitled “fuzzy sets”. Fuzzy sets theory was developed to
further improve and simplify vigorous and flexible models to solve real world systems
based on human implications. In addition, this theory not only helps decision maker to
identify the best option under existing restrictions, but assist him/her to develop new
options (designing new system).
4.1. Introduction to Fuzzy Theory
Where available information is not complete and accurate, precise mathematics
could not model complex systems. Conventionally, probability theory is has been the
dominant approach to address this inaccuracy and uncertainty. Law of total
probability    and law of contradiction    are two
axioms of probability theory. Accordingly, the probability that a fruit being apple or
not is 1 and the probability that an animal being both male and female is zero. For
these cases in which events have specific scope and definition, probability methods
are appropriate approach to determine how they behave against the other components
in universal set. But there are some events such as “Good person” or “Bad test” which
have no clear definitions. In these cases, it is obvious that it is not possible in
probability theory to determine whether someone is good or a test is bad. So, fuzzy
sets theory has been developed to define and solve problems in which events have no
clear and certain extents. [23]
4.2. Basic Definitions and Operations
In this sections, basic definitions and concepts of fuzzy sets theory which are
needed in this thesis are presented.
4.3. Fuzzy Set Definition
If a function could be attributed to sub elements of a universal set so that it
represents the membership degree of these elements in a set like A, such that higher
values represent membership degree. In this case, this is called membership function
and the set defined by this function, is called fuzzy set. [24]
Generally, for universal set X, membership , which is defined by fuzzy set A, is
a function which represents the elements of universal set X over the interval [1]. This
definition is mostly used to represent membership degree of the elements of fuzzy set
A. [25]
Figure 3. General cut of a membership function.
In this case, fuzzy set A is represented by one of the following forms:
      

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Another form to represent fuzzy set A is as follows:
Provided the elements of limited fuzzy set X are countable:
 

Provided set X is a continuous set:
 

Fuzzy numbers:
Fuzzy number consists of a fuzzy set over R, membership function of which is
continuous in small intervals and its value in the interval [0,1]. Depending on
membership function type and possibility distribution, infinite fuzzy numbers could
be defined. In this section, we introduce two kinds of these fuzzy numbers and math
operations on them.
4.4. Triangular and Trapezoidal Fuzzy Numbers
Triangular and trapezoidal fuzzy numbers are the most important among the various
types of fuzzy numbers. In particular, these numbers are applied to solve possibility
mathematical programming problems.[26]
A triangular fuzzy number can be represented by an ordered triple such as  
 in which X (central value or the most possible value of  ) is left
range and β is called right range. Also, this number can be represented by an ordered
triple in which xm is central value of    is its pessimistic
or lowest value and xo is optimistic and highest value of . [27]
Figure 4. Representation of triangular fuzzy number.
Trapezoidal fuzzy number can be represented by ordered quadruple such as  
 where (the most likely value of   ) are left
and right range, respectively. Also, this number could be represented as the ordered
quadruple   , where is the most likely value of 
 and is its optimistic and highest value.  
Figure 5. Representation of trapezoidal fuzzy number.

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cut of fuzzy number
By definition, cut of fuzzy number X is defined as follows:
a. in general form:



b. triangular fuzzy number
 
c. trapezoidal fuzzy number



Time- cost trade-off models solution
In this section, appropriate mathematical models are formed for any models
discussed above through mathematical, crisp and fuzzy programming methods and
their solution will be provided through the methods discussed in chapter 2 for the
following states:
crisp time and cost
fuzzy time and crisp cost
crisp time and fuzzy cost
fuzzy time and cost
it should be noted that all the models in this chapter is based on Activity on Arrow
(AOA) and all the non-crisp (Uncertain) numbers and parameters are as triangular
fuzzy numbers (p,m,o). [28]
Figure 6. Determining optimal project time with no time-cost constraint.
The purpose in this model is to find optimal time for activities so that costs be in
minimum level. The components of objective function are:
direct surplus cost of activity ij for time decrease from TN to t
 
so, direct surplus cost of project for activity time decrease is:


 
indirect costs of project are: Htk
direct costs in the cases where all activities are done in normal time.
Constraints are as follow:

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According to the principles of network methods, practical time for doing activities
could not be more than the difference between start and end dates of events,[29] , that
is: 
Practical time of doing an activity lies between normal and crash times, that is:
   
Occurrence time of network events could not be smaller than zero, that is:
           
Now, given the above, this model is solved in different scenarios:
Crisp time and cost:


    


 
   
          
The above is a crisp linear programming problem. Note that direct costs have been
omitted in normal conditions, because those costs have no impact on objective
function.
Fuzzy time and crisp costs


  
  

Objective function is as follows:
following separating expressions:


   
 

 




  

 

This is a fuzzy linear programming problem in which fuzzy constraints are in the
right hand side. To solve this problem, the method presented in the first section is
used. First, the following two auxiliary linear programming problem are solved to find
optimistic (z1) and pessimistic (z0) limits of objective function:
 

  


Volume 3, 2020 ISSN: 2617-4596
DOI: https://doi.org/10.31058/j.mana.2020.31003
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  
  
 

          
 

  


  
  

 

          
Next, optimal decision is achieved by solving the following linear programming
problem:

 
  
   
Data entry
Preserved data by this software for any project activity are:
a. Activity code: consists of a 5-digit unrepeatable code.
b. Activity name: a 25-letter label to write necessary name and specifications.
c. Activity normal time
d. Activity crash time
e. Compression cost per unit of time
f. Prerequisites: a 60-letter location including maximum 5 letter for activity code
and a comma sign (,) accepts up to 10 prerequisites for any single activity.
It should be noted that any of the above 3,4,5 are embedded as a triangular fuzzy
number (p,m,o) in a 25 letter location.
When entering data, an appropriate tabular page allows user to easily do any change,
add or remove. Data are entered into computer as Activity On Node (AON) which is
the simplest way possible. While entering data, the following intelligent tests are
performed by the software:
a. Prevent entering duplicate codes
b. Prevent wrong triangular fuzzy numbers so that (p,m,o) form is regarded.
c. Prevent entering illogical data such as crash time being greater than normal time

Volume 3, 2020 ISSN: 2617-4596
DOI: https://doi.org/10.31058/j.mana.2020.31003
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d. Prevent defining an undefined activity as a prerequisite to an activity.
4.5. Model Solution
Activities which are done in this stage are as follow:
a. Review and prepare entered data including removing unnecessary prerequisites
and identifying improper relations and loop occurrence.
b. Convert data from AON to AOA. This function is necessary to match data with
model as well as making mathematical model. This stage includes defining Activity
On Arrow and creating dummy activities to provide proper relations and marking
nodes.
c. Develop mathematical model with objective function of minimizing tend for
possibility-space test.
d. Solve mathematical model in pessimistic and optimistic cases
e. Generate primary auxiliary programming problems for optimistic and pessimistic
cases and solving them.
f. Answer recall from solver software (such as LINGO) and determine upper and
lower bound of auxiliary objective function.
g. Model development and solution
h. Transfer obtained answers to the main software.
(1) Reports
Reporting is an important section in this program. In the following some reports are
presented:
a. Basic information reports
b. Reports on information converted from AON to AOA
c. Represent auxiliary problems formulation for pessimistic and optimistic cases.
d. Represent auxiliary problems answers for pessimistic and optimistic cases.
e. Represent final problem formulation for pessimistic and optimistic cases.
f. Represent final answer for pessimistic and optimistic cases.
g. Present possibility distribution function of project completion time in preset
alpha cut
h. Present distribution function of total compression costs for pessimistic and
optimistic cases
i. Present distribution function of total costs in general case of all alpha cuts which
is calculated through defining two possibility distribution functions.
j. 10-present the results of upper and lower bound of auxiliary objective function
and many other useful reports.
Basic software
This program has been written in FOXPRO language and LINGO software was
used as solver.
Sample problem

Volume 3, 2020 ISSN: 2617-4596
DOI: https://doi.org/10.31058/j.mana.2020.31003
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To demonstrate performance and results of the software, the following sample
problem is considered.
Table 1. Activity data list for project.
Code
Nodes
Normal Time
Crash Time
Crash Cost
A
1-2
(5,8,9)
(1,1,2)
(12,15,19)
B
2-3
(5,6,6)
(2,2,2)
(20,25,30)
C
2-4
(5,7,9)
(1,2,3)
(20,23,27)
D
2-5
(8,10,12)
(3,4,5)
(28,35,40)
E
5-6
(7,7,9)
(3,4,4)
(18,18,18)
F
4-6
(5,7,7)
(3,4,5)
(30,32,35)
G
3-7
(6,8,10)
(2,3,4)
(16,20,22)
H
7-8
(7,7,7)
(2,3,4)
(15,17,20)
I
6-8
(6,7,8)
(2,4,6)
(23,30,33)
J
8-9
(9,10,13)
(3,4,6)
(25,27,29)
Planed Project Completion Time: (40,50,60)
Total Available Crash Cost: (900,940,980)
This problem is solved for 0, 0/2, 0/4, 0/6, 0/8, 1 cuts and the results are :
5. Conclusion
Using prior research and their results, a considerable part of project control and
planning goals such as setting possibility distribution function of project completion
time and solving time-cost trade-off problems is achievable. However, there are
numerous contexts which researchers can address to have a significant contribution to
overload project control discussion with fuzzy data and to make these techniques
more practical as well. Some of these contexts are presented in the following:
a. Fuzzy resource allocation: research in this context will result in more effective
use of available resources and facilities and decrease in costs due to fluctuation in
resource which has a significant contribution to reduce investments and executive
operations regarding facility planning and utilization.
b. Fuzzy Gantt chart: although network methods (techniques) mainly give the
results of Gantt charts, ease of understanding and transfer rate of these charts for
managers and non-specialist persons has made these charts more popular. But it seems
that providing a proper technique which could convey the uncertainty in time while
having general properties of Gantt charts with the same speed and easiness, would be
an efficient tool.
c. Use of fuzzy relations: so far, in project control, precedence relationships
between activities have always been stated crisply. Hence, an activity is either
predecessor to another activity or not. However, according to the ability of fuzzy logic
to represent and model linguistic variables, it is possible to define various degrees of
relations between activities. The results of this context can be used in controlling and
planning projects in which relationships between activities are not well defined such
as research or scientific projects as well as human sciences, economic and agricultural
research.
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of
this article.

Volume 3, 2020 ISSN: 2617-4596
DOI: https://doi.org/10.31058/j.mana.2020.31003
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Funding
This research received no specific grant from any funding agency in the public,
commercial or not-for-profit sectors.
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