1. Introduction

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 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 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 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, 35 nurses 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 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:

Review a variety of wind tunnel types and their components

detailed review of vertical wind tunnels

Review wind tunnels of Sky venture Company.

Statistical analysis of vertical wind tunnels

Patents for vertical wind tunnel

Review structure and building methods

Review vertical wind tunnel for aerodynamic research purposes

Review wind tunnel flow measurement and control methods

Review wind tunnel noise (sound) reduction methods

Visit the Emirates wind tunnel

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).

Figure 1. The original plan wind tunnel.

Conceptual design: this phase includes the following sections:

Investigating the design of wind tunnel parts

Calculation of hurricane vertical wind tunnel pressure-drop

Examining fan types and characteristics

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.

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:

Design calculations and model fabrication plan

Tests conducted for wind tunnel with similar fan

Experimental research on wind tunnel model (nozzle)

Experimental research on wind tunnel model (screen)

Experimental research on wind tunnel model (diffuser1)

Experimental research on wind tunnel model (diffuser2)

Experimental research on wind tunnel model (diffuser3)

Experimental research on wind tunnel model (corner and triangle exit)

Airflow numerical simulation (nozzle)

Airflow numerical simulation (diffuser1)

Airflow numerical simulation (diffuser 2)

Airflow numerical simulation (diffuser 3)

Review and check Numerical and experimental results

Calculation and design of structure and foundation

Architectural design

Design of heating and air conditioning

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].

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:

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.

cut of fuzzy number

By definition, cut of fuzzy number X is defined as follows:

in general form:

triangular fuzzy number

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:

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:

s.t

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:

s.t

s.t

Next, optimal decision is achieved by solving the following linear programming problem:

s.t

Data entry

Preserved data by this software for any project activity are:

Activity code: consists of a 5-digit unrepeatable code.

Activity name: a 25-letter label to write necessary name and specifications.

Activity normal time

Activity crash time

Compression cost per unit of time

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:

Prevent entering duplicate codes

Prevent wrong triangular fuzzy numbers so that (p,m,o) form is regarded.

Prevent entering illogical data such as crash time being greater than normal time

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:

Review and prepare entered data including removing unnecessary prerequisites and identifying improper relations and loop occurrence.

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.

Develop mathematical model with objective function of minimizing tend for possibility-space test.

Solve mathematical model in pessimistic and optimistic cases

Generate primary auxiliary programming problems for optimistic and pessimistic cases and solving them.

Answer recall from solver software (such as LINGO) and determine upper and lower bound of auxiliary objective function.

Model development and solution

Transfer obtained answers to the main software.

(1) Reports

Reporting is an important section in this program. In the following some reports are presented:

Basic information reports

Reports on information converted from AON to AOA

Represent auxiliary problems formulation for pessimistic and optimistic cases.

Represent auxiliary problems answers for pessimistic and optimistic cases.

Represent final problem formulation for pessimistic and optimistic cases.

Represent final answer for pessimistic and optimistic cases.

Present possibility distribution function of project completion time in preset alpha cut

Present distribution function of total compression costs for pessimistic and optimistic cases

Present distribution function of total costs in general case of all alpha cuts which is calculated through defining two possibility distribution functions.

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

To demonstrate performance and results of the software, the following sample problem is considered.

Table 1. Activity data list for project.

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:

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.

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.

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.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.