Develop a project planning method based on building information model (bim) to optimally reduce activity overlaps and time cost

VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY TU ANH NGUYEN DEVELOP A PROJECT PLANNING METHOD BASED ON BUILDING INFORMATION MODEL BIM TO OPTIM

VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

TU ANH NGUYEN

DEVELOP A PROJECT PLANNING METHOD BASED ON BUILDING INFORMATION MODEL (BIM) TO OPTIMALLY

REDUCE ACTIVITY OVERLAPS AND TIME COST

Major: Construction Management Major code: 8580302

MASTER’S THESIS

HO CHI MINH CITY, July 2023

THIS THESIS IS COMPLETED AT

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY – VNU-HCM

Supervisor: Assoc Prof Long Duc LUONG

Examiner 1: Assoc Prof Hoc Duc TRAN

Examiner 2: Dr Cuong Viet CHU

This master’s thesis is defended at HCM City University of Technology, VNU-HCM on July 13th, 2023

Master’s Thesis Committee:

(Please write down full name and academic rank of each member of the Master’s Thesis Committee)

2 Dr Minh Nhat HUYNH - Member, Secretary

3 Assoc Prof Hoc Duc TRAN - Reviewer 1

Approval of the Chairman of Master’s Thesis Committee and Dean of Faculty

of Civil Engineering after the thesis being corrected (If any)

ENGINEERING

VIETNAM NATIONAL UNIVERSITY-HO CHI MINH CITY

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom – Happiness

THE TASK SHEET OF MASTER’S THESIS

Date of birth: October 16th, 1999 Place of birth: Quang Nam, Vietnam

Major: Construction Management Major code: 858032

Develop a project planning method based on building information model (BIM)

to optimally reduce activity overlaps and time costs

Phát triển phương pháp hoạch định dự án dựa trên mô hình thông tin BIM để giảm tối ưu sự chồng lấn của các công tác và thời gian – chi phí

II TASKS AND CONTENTS: Optimization in Construction Project

III TASKS STARTING DATE: February 2nd, 2023

IV TASKS ENDING DATE: June 10th, 2023

DEAN OF FACULTY OF CIVIL ENGINEERING

Assoc Prof Dr Tuan Anh LE

ACKNOWLEDGEMENT

I would like to express my deepest appreciation and gratitude to all those who have supported and contributed to the completion of my master thesis in Construction Management as part of the International Master Programs (IMP) at the Ho Chi Minh City University of Technology, Department of Civil Engineering

First and foremost, I would like to extend my heartfelt thanks to my advisor, Assoc Prof Luong Duc Long Your guidance, expertise, and unwavering support throughout the research process have been invaluable Your profound knowledge and insightful suggestions have helped shape and improve the quality of this thesis I am truly grateful for your patience, encouragement, and dedication

I would also like to express my sincere gratitude to the faculty members of the Department of Civil Engineering for their continuous encouragement, wisdom, and valuable inputs Their commitment to academic excellence and their willingness to share their expertise have greatly enhanced my understanding and knowledge in the field of Construction Management

I would like to extend my appreciation to my fellow classmates and friends who have provided me with valuable insights, discussions, and support throughout my academic journey Your presence and camaraderie have made this experience enjoyable and memorable

Additionally, I am deeply grateful to the staff and librarians at the Ho Chi Minh City University of Technology for their assistance and resources, which have greatly facilitated my research

Finally, I would like to acknowledge my family for their unconditional love, encouragement, and understanding throughout my studies Their unwavering support has been the foundation of my success

Thank you all once again for your guidance, encouragement, and support

Tu Anh NGUYEN

ABSTRACT

With the rise in usage of building information modeling (BIM) systems, there is a greater demand for a construction schedule management system that can make more sophisticated decisions When there is a significant overlap between construction activities,

it can lead to poorer performance in those areas As a result, a suitable construction timetable should be created to reduce the overlap of nearby construction operations One potential solution for this problem is an active system This research aims to provide a methodical approach and computer system for simulating an ideal construction timetable that eliminates overlapped tasks and improves operational performance The primary objectives of this study are to identify overlapping activities, apply fuzzy theory, and evaluate the risks associated with schedule overlap problems The genetic algorithm (GA) theory is also applied to optimize the overlap of high-risk activities The study created a four-dimensional (4-D) environment system that utilizes building information modeling (BIM), and it includes a scheduling simulator, as well as fuzzy and GA analysis tools To demonstrate the effectiveness of this approach, the study presented a case study based on

a real project

Keywords: BIM implementation in construction projects, 4-D modeling, ratio

analysis of schedule overlaps, optimization of schedules using genetic algorithm, and time and cost management

Từ khóa: Triển khai BIM trong các dự án xây dựng, mô hình 4-D, phân tích tỷ lệ

chồng chéo lịch trình, tối ưu hóa lịch trình bằng thuật toán di truyền, quản lý thời gian và chi phí

AUTHOR’S COMMITMENT

The undersigned below:

Student full name: Tu Anh NGUYEN

Place and date of born: Quang Nam Province, Vietnam, October 16th, 1999

Address: Binh Tan District, Ho Chi Minh City

With this declaration, the author finishes his master’s thesis entitled “DEVELOP

A PROJECT PLANNING METHOD BASED ON BUILDING INFORMATION MODEL (BIM) TO OPTIMALLY REDUCE ACTIVITY OVERLAPS AND TIME COST” under the advisor's supervision All works, ideas, and materials that was gain from

other references have been cited correctly

Ho Chi Minh City, June 10th, 2023

Tu Anh NGUYEN

TABLE OF CONTENTS

TABLE OF CONTENTS v

TABLE OF FIGURES viii

TABLE OF TABLES x

LIST OF ABBREVIATIONS xi

CHAPTER 1: INTRODUCTION 1

1.1 General Introduction 1

1.2 Problem Statement 1

1.3 Object and Range of Study 2

1.4 Scope of the Study 3

1.5 Research Methodology 3

1.6 Structure of the Study 4

CHAPTER 2: LITERATURE REVIEW 5

2.1 Definitions and Concepts 5

2.1.1 Schedule 5

2.1.2 Overlapping principle 7

2.1.3 Overlapping time impact 11

2.1.4 Overlapping costs and benefits 12

2.1.5 Overlapping Time-cost tradeoff 12

2.1.6 Fuzzy logic 13

2.1.7 Mamdani and Sugeno Fuzzy Inference Systems 14

2.1.8 BIM implementation in construction planning and scheduling 15

2.1.9 Optimization in Construction 16

2.1.10 Optimization Method 18

2.2 Genetic Algorithms 19

2.2.1 Genetic Operators 21

2.2.2 Advantages of Genetic Algorithm 27

2.3 Previous research 27

CHAPTER 3: RESEARCH METHODOLOGY 29

3.1 Algorithm for Finding Overlapping Schedule in Project Activities 30

3.2 Fuzzy-Based Risk Analysis Algorithm 35

3.3 Algorithm for Optimizing Schedule Overlapping using Genetic Algorithm 40

3.3.1 Schedule optimization application process 40

3.3.2 Function and constraints utilized in the optimization of the project’s schedule 42

3.3.3 The process of generating an initial solution for the GA algorithms 43

3.3.4 Establishing the fitness function 44

3.3.5 Analysis of Genetic Algorithm operation 44

3.3.6 Tradeoff between the total cost of risk and the total overlapping duration 45

3.3.7 Pareto Front 46

3.4 System for Optimizing Schedule Overlapping using BIM-Based Simulation 46

CHAPTER 4: MODEL IMPLEMENTATION AND VALIDATION 48

4.1 Model Implementation 48

4.1.1 Case study 1 48

4.1.2 Case study 2 – Bloomsdale Residence 62

4.2 Model validation 73

4.3 Result Discussion 73

CHAPTER 5: CONCLUSION AND RECOMMENDATION 75

5.1 Conclusion 75

5.2 Research contribution 75

5.3 Future works 76

REFERENCES 77

APPENDICES 81

1.ANNEX A: Case study 2 detail work in MS Project 81

2.ANNEX B: Case study 2 detail project time 82

3.ANNEX C: Case study 2 detail risk analysis 85

4.ANNEX D: Proposed MATLAB code 87

TABLE OF FIGURES

Figure 2.1: Activity on Node (AON) (P B Tarigan, 2021)[8] 6

Figure 2.2: Activity on Arrow (AOA) (P B Tarigan, 2021)[8] 7

Figure 2.3: Four types of activity relationships (Adopted from (Prasad, 1996)[11]; (Dehghan, Hazini, & Ruwanpura, 2011)[3] 9

Figure 2.4: The mechanism of activity overlapping (Dehghan & Ruwanpura, 2011)[10] 10

Figure 2.5: Semi-independent activities' overlapping (Dehghan & Ruwanpura, 2011)[10] 10

Figure 2.6: Schedule compression comparison 11

Figure 2.7: Overlapping time impact on the project schedule (Dehghan & Ruwanpura, 2011)[10] 12

Figure 2.8: Overlapping cost function (Dehghan, Hazini, & Ruwanpura, 2011)[3] 12

Figure 2.9: Fuzzy inference example 15

Figure 2.10: Direct Cost, Indirect Cost, and Total Cost in Construction (Hegazy, 2002)[19] 17

Figure 2.11: Optimization in Exact Method (P B Tarigan, 2021)[8] 18

Figure 2.12: General structure diagram of Genetic Algorithm 21

Figure 2.13: The Single Point Crossover Method 24

Figure 2.14: The Two-Point Crossover Method 24

Figure 2.15: Uniform Crossover Approach 25

Figure 3.16: Overall Process of the Model 29

Figure 3.17: Typical condition of schedule overlapping 32

Figure 3.18: The process of checking for schedule overlapping for each activity 33

Figure 3.19: Membership function for Probability (P), Intensity (I), Output and Fuzzy

Simulink 36

Figure 3.20: Fuzzy rule surface in MATLAB 38

Figure 3.21: A process of schedule optimization using GA to optimize overlapping schedule and time cost 41

Figure 3.22: TF-based solution generation method utilizing activity relationships 44

Figure 4.23: Case study 1 bar chart 49

Figure 4.24: Genetic algorithm with penalty value and average distance in case study 155 Figure 4.25: Optimized project schedule 57

Figure 4.26: Pareto front time-cost tradeoff for Case study 1 59

Figure 4.27: Updated schedule for objective 1 optimization 60

Figure 4.28: Updated schedule for objective 2 optimization 61

Figure 4.29: Pareto front of multi-objective optimization 62

Figure 4.30: Some perspective views of the project 63

Figure 4.31: Project’s ground floor plan 63

Figure 4.32: Project's first floor plan 64

Figure 4.33: Risk degree of activity number 20 and 24, respectively 67

Figure 4.34: Multi objective optimization in Case study 2 68

Figure 4.35: Process of applying GA in MATLAB for achieving Multi-Objective Optimization 72

TABLE OF TABLES

Table 2.1: Mamdani and Sugeno advantages 14

Table 3.3: Determine ES and EF 30

Table 3.4: Determine LS and LF 31

Table 3.5: Membership function and five Euclidean distance values 35

Table 3.6: If-then rules in MATLAB 36

Table 4.7: The project activities, description, duration and predecessors of case study 148 Table 4.8: Case study 1-Calculate project schedule 49

Table 4.9: Overlapping check for activity '2' 50

Table 4.10: Initial SOR value for all activities 51

Table 4.11: Probability (P) and Intensity (I) calculation 52

Table 4.12: Initial overlapping duration of all activities 53

Table 4.13: Case study 1 updated schedule after optimizing 56

Table 4.14: Optimized SOR values for case study 1 57

Table 4.15: New table activity for best solution 1 59

Table 4.16: New table activity for best solution 2 60

Table 4.17: Project's activity, duration, predecessors of case study 2 64

Table 4.18: Top 10 risky activities of the project based on 5 Euclidean distance values66 Table 4.19: Movable duration corresponding with objective 1 68

Table 4.20: Movable duration corresponding with objective 2 69

Table 4.21: Movable duration exported from MATLAB 70

Table 4.22: Comparison of the Optimum Solution from GA and Excel Solver 73

LIST OF ABBREVIATIONS

BIM Building information modeling

AEC The architecture, engineering, and construction industry

CPM Critical path method

PERT Program evaluation and review technique

PSO Particle swarm optimization

DEA Data envelopment analysis

SOR Schedule overlapping ratio

1.2 Problem Statement

Construction projects often involve numerous activities that overlap with each other, meaning that multiple tasks are executed at the same time based on the construction schedule [1] Besides, overlapping activities are occurred due to the reduction of schedule

or to reasonable resource usage Real-life instances of schedule overlap can be observed in various construction projects, such as the cleanup/de-mob (demobilization) and mob/setup (mobilization/setup) stages of sequential tasks These stages involve transitioning from one task to another, where the cleanup and demobilization of resources from a completed task overlap with the mobilization and setup activities for the next task When multiple activities overlap in a construction project, it can lead to various challenges with managing time and resources, which are often unavoidable in most cases This study specifically focuses on activity overlaps and does not consider the actual distance between activities as a factor that can present obstacles The efficiency of building operations can be increased by

minimizing concurrent progress between tasks if there are few overlaps in the nearby work area Hossain and colleagues devised a simulation model to approximate the overall duration of a project that incorporates overlapping tasks, as well as to predict the anticipated number of reworks If a project schedule can be optimized successfully, a suitable system to consider would be an active Building Information Modeling (BIM) system equipped with the required decision-making capabilities Such a system would enable efficient and effective decision-making throughout the project lifecycle The results indicate that the anticipated reduction in project duration and the number of reworks are influenced by the reliability of information obtained during earlier stages and the sensitivity

of subsequent operations Furthermore, unplanned overlap could result in excessive design and construction work that could be very expensive rather than necessarily shortening the project’s duration The suggested optimization method helps in selecting an overlay strategy by decreasing the expected amounts of reworks while keeping the project completion date [2] If activities overlap, there may also be a shortage of working area and defection

Various schedule compression techniques have emerged in response to the need for project completion in a shorter amount of time Fast-tracking is recognized by the Project Management Body of Knowledge (PMOK) as a method for compressing the timetable Fast-tracking involves doing stages or operations that would typically be done in succession in parallel, or more precisely, by overlapping them As a result of these overlaps, there may be more work and risk [3] Implementing this approach may involve completing tasks without having all the required information, leading to a trade-off between the cost and benefits of time savings However, this also increase the risk of meeting the shortened project timeline [4]

1.3 Object and Range of Study

Object: The purpose of this research is to assess different levels of risk associated with carrying out construction tasks that overlap and to create a systematic approach and computer program for simulating schedules that minimize such overlaps in a specific project Additionally, the model will produce a range of ideal solutions, including the schedule, expected duration, and risk cost for each task

Range of study: Ho Chi Minh City, Vietnam

1.4 Scope of the Study

To refine the research problem, the study delimits its scope by outlining the following specifics:

a Initially, a method is created for an automated exploration of potential overlaps in the construction schedule

b If required, fuzzy algorithms and risk simulation model are established

c An optimization algorithm that employs the genetic algorithm (GA) is used for activities with higher risks of overlap

d A Building Information Modeling (BIM) tool is utilized to generate a visually dynamic representation of optimized schedule options

e The models are executed using the Genetic Algorithm in MATLAB

f Case studies used in the research are borrowed from prior studies and actual project

b Model development

A MATLAB programming-based model is developed through a thorough examination of existing research, aiming to strike a balance between time and cost considerations The main objective of this model is to produce a range of optimal solutions that minimize both project duration and expenses

c Validation of the developed model

To show the model's functionality, it was then put into a case study The case study

is chosen from the previous research, and the result will then be compared to the earlier findings of the primary research This serves to verify the results and demonstrate the effectiveness of the approach in solving the problem Analysis and development of two

case studies are underway One is a basic model to get at a decent outcome, while the other

is an example of how the model can handle a more challenging project

1.6 Structure of the Study

The thesis includes five chapters:

- Chapter 1: Introduction

- Chapter 2: Literature review

- Chapter 3: Methodology

- Chapter 4: Model implementation and validation

- Chapter 5: Conclusion and recommendation

- References

CHAPTER 2: LITERATURE REVIEW

2.1 Definitions and Concepts

Three factors play a significant role in planning and controlling construction projects: time, cost, and quality [5] There are often various pathways in project schedules, and one or more of them is critical In many cases, overlapping non-critical activities are negative to the project On the other side, while overlapping critical activities might be advantageous, it can also turn other noncritical activities become critical ones The overlapping principle, fuzzy logic, the Genetic Algorithm, and the trade-off between time and cost in construction projects will be addressed in more detail in the following part

2.1.1 Schedule

In project management, a schedule is a tool that is most commonly used to plan the project step by step A simple explanation of a schedule is that it's a plan indicating the timing of every task within a project By systematically analyzing each activity and its relationship to the other activity, the project manager will be able to build a project on paper before starting it The schedule determines the start, duration, and finish date of activities in the project Knowing precisely the duration of the activities will have an impact

to the project cost For instance, rent an equipment to do an activity without knowing clearly how long the activity will take quickly reduce the planned profit So, the project manager must schedule the whole activities properly and effectively to meet the deadline and not reduce profit

Below is the process for scheduling the project:

1) Identify project activities

2) Determine activities sequence

3) Determine activities duration

4) Perform schedule calculation

5) Revise and adjust

6) Monitor and control

Several methods are commonly employed for scheduling construction projects The following are a few examples:

2.1.1.1 Critical Path Method (CPM)

The critical path method is the sequence of activities that results in the longest total duration It is the shortest possible time for the project’s completion [6]

When any activity in the critical path is delayed, it will impact the overall duration

of the project There are two ways to do CPM; they are AOA (Activity on Arrow) and AON (Activity on Node) In AON, an activity is denoted by a box or node, whereas in AOA, the activity is denoted by an arrow AON, on the other hand, is preferred over the AOA network due to its simplicity [7] The two figures below describe the scheduling for AON and AOA, respectively

0 0 0 START

2 2 0 1

ES TF EF

LF D LS ID Legend:

4 1 3 3

4 1 3 4

6 2 4 5

4 2 2 2

Figure 2.1: Activity on Node (AON) (P B Tarigan, 2021) [8]

0

2 2

A1 2

3 4

4 4

3 4

6 6

ES LS

ID Duration

EF LF

Legend:

A2 2

A3 1

A4 1

A5 2

Figure 2.2: Activity on Arrow (AOA) (P B Tarigan, 2021) [8]

2.1.1.2 Program Evaluation and Review Technique (PERT)

PERT (Program Evaluation and Review Technique) is a statistical approach that is utilized to analyze the tasks involved in completing a project It is typically employed for complex and uncertain projects when the specifics and durations of all activities are not precisely defined To use PERT, three-time estimates are assigned for each activity: the optimistic time estimate (To), the most likely or normal time estimate (Tm), and the pessimistic time estimate (Tp) [9] The expected time can then be calculated as follows:

a Dependent activities: The first type of relationship involves an activity that is dependent on another activity for final information

b Semi-independent activities: The second type of relationship occurs when an activity requires only partial information from other activities to begin

c Independent activities: The third type of relationship occurs when there is no information dependency between two activities

d Interdependent activities: The fourth type of relationship involves a two-way information exchange between activities until they are both completed

The risk of the relationships mentioned above varies significantly in terms of activity overlap The riskiest situation is when dependent activities overlap This type of connection is commonly referred to as a finish-to-start dependency, which implies that the first activity (predecessor) must be finished before the second activity (successor) can commence Failing to complete the predecessor before starting the successor may necessitate rework, as the successor may need to begin before the predecessor has supplied all of the necessary information Independent activities can overlap to any level without losing any hazards The availability of all necessary resources, including humans, equipment, and materials, for both operations, must occur simultaneously A typical project schedule contains the majority of individual tasks Activities that are semi-independent by definition overlap to some extent More overlapping, like dependent activities, will be dangerous Finally, for information to be shared and progress to be made, interdependent activities must overlap In other words, they overlap naturally rather than just as a means

to save time Although its overlap carries the risk of delay and rework, it is necessary for interdependent activities and should not be considered an additional risk Based on the above, no specific overlapping risk exists when independent or interdependent design activities are overlapped Risks are significant when overlapping dependent or semi-independent design activities

Figure 2.3: Four types of activity relationships (Adopted from (Prasad, 1996) [11] ; (Dehghan,

Hazini, & Ruwanpura, 2011) [3]

Figure 2.3 illustrates the process of overlapping two dependent activities, where the start of one activity is reliant on the completion of another activity This is because the information generated by the predecessor activity is necessary for the successor activity However, in order to compress the timeline, the successor activity may intentionally begin before the conclusion of its predecessor activity This can be achieved if the predecessor activity provides the successor activity with some preliminary information before it is completed The successor activity can then begin more quickly by using this initial data and making relevant assumptions and predictions During the time that the two activities are in progress, some intermediate information may also be exchanged Once the predecessor activity is completed, it will provide its final information to the successor activity

The amount of rework required may be greatest when the successor activity needs

to implement a significant adjustment, and the final information provided by the predecessor activity is substantially different from the preliminary information The worst-case scenario in this situation is that the successor has to completely undo all of its overlapping progress and start over Because of this, any amount of rework cannot be logically more than the time spent overlapping

Figure 2.4: The mechanism of activity overlapping (Dehghan & Ruwanpura, 2011) [10]

Figure 2.5: Semi-independent activities' overlapping (Dehghan & Ruwanpura, 2011) [10]

The concept of overlapping dependent activities, as explained earlier, can be expanded to semi-independent activities by treating the predecessor as two sequential activities (A1 and A2) In this scenario, A1 takes place before the information exchange, followed by A2 (as depicted in Figure 2.5) Consequently, A1 serves as the predecessor for both A2 and B This allows for the overlapping of activity A1 with activity B, utilizing the mechanism of dependent activities, while activity A2 and activity B can overlap seamlessly

as they are independent

There are two cases of overlap Firstly, the overlapping of normal activities can be reduced due to the unaffected project duration and risks Secondly, the overlapping of critical activities shall be decreased if the project manager determines the tradeoff between time-cost and time-cost-quality because the more reduction in activities overlaps the more project’s time lengthens Besides, the critical activities are overlapped can lead to many conflicts in worker’s productivity and rework time

Construction overlap occurs when different stages of construction occur concurrently instead of being completed sequentially, leading to a faster overall construction schedule Fast-tracking is a common cause of construction overlap, as it involves compressing the construction schedule by overlapping tasks that would typically

be done separately

While fast-tracking can speed up the construction process, it also increases the risk

of construction overlap When different construction stages occur simultaneously, there is

a higher likelihood of conflicts arising between workers, materials, and equipment This can lead to delays, rework, and even safety hazards

Fast-tracking also increases the complexity of project management, as it requires close coordination and communication between different teams and contractors This can

be challenging, as different teams may have different priorities and schedules, and it can

be difficult to ensure that everyone is on the same page

Figure 2.6: Schedule compression comparison

2.1.3 Overlapping time impact

To accurately determine the time saved by overlapping design activities, it is important to incorporate the overlapping mechanism in the project plan (as shown in Figure 2.7) While it may seem like overlapping two activities on the critical path of a project will save time, this is not always the case The actual time saved can be calculated by

subtracting the rework time from the overlapping time However, the study conducted for this research revealed that schedulers do not typically consider the rework period in their scheduling, leading to unrealistic timetables However, in certain industries, risk analysts take the possibility of rework into account when performing schedule risk analyses

Figure 2.7: Overlapping time impact on the project schedule (Dehghan & Ruwanpura, 2011) [10]

2.1.4 Overlapping costs and benefits

Figure 2.8 demonstrates the impact of varying levels of overlap on costs by utilizing bar charts to depict four different scenarios of activity B in relation to activity A The first scenario shows no overlap between activity B and activity A However, in the second, third, and fourth scenarios, the degree of overlap progressively increases to 25%, 50%, and 75% respectively The curve below the bar charts represents the cost of overlapping activities at different degrees of overlap, with the height of the curve proportional to the amount of time required

Figure 2.8: Overlapping cost function (Dehghan, Hazini, & Ruwanpura, 2011) [3]

2.1.5 Overlapping Time-cost tradeoff

The aim of the time-cost tradeoff strategy is to reduce expenses and increase the advantages of overlapping The total cost of overlapping, taking into account its effects on both project time and cost, can be represented by Equation (4):

𝑍 = ∑ 𝐶𝑖𝑗𝑘 − 𝐵𝑒𝑓(𝑇𝑛− 𝑇𝑜𝑙) (4)

Where:

𝑖: Index denoting predecessor activities

𝑗: Index denoting successor activities

𝑘: Index denoting degrees of overlapping (overlapping intervals) between predecessor activity 𝑖 and successor activity 𝑗

𝐶𝑖𝑗𝑘: Additional costs imposed on the project because of overlapping 𝑘 between 𝑖 and 𝑗

𝐵𝑒𝑓: Project daily early finish benefits

𝑇𝑛: Normal project duration before overlapping

𝑇𝑜𝑙: Project duration after overlapping

Equation (4) can be solved in two ways: To fix a value for 𝑍 ,and find the minimum

𝑇𝑜𝑙 achievable, or to fix desirable project duration (𝑇𝑑), and find the minimum 𝑍 In this paper, only the second option is addressed as the first option can be solved similarly

2.1.6 Fuzzy logic

Construction projects encompass a multitude of intricate and unique tasks that occur within a dynamic environment [12] Various factors such as unfavorable weather conditions, equipment status, resource availability, site conditions, and labor productivity can significantly influence the project's progress During the pre-construction phase, schedule overlaps between activities can directly impact the overall duration of the project There are two approaches that can be used when considering overlapped activities The initial approach is probability-based, leveraging historical data from previously executed similar activities This data is subsequently employed to assess the likelihood of successfully completing a project within a designated time period The second approach is fuzzy-based, which relies on expert knowledge and estimation [13]

In 1965, Lotfi A Zadeh introduced fuzzy logic, which allows for precise results to

be produced from ambiguous and erroneous data Fuzzy logic is useful in solving problems that involve linguistic descriptions It extends Boolean logic, which only specifies objects

as either 1 or 0, yes or no, true or false Fuzzy logic allows for elements to be partially

included in a set due to its flexibility Each element is assigned a membership value between 0 and 1, indicating how much it belongs to the set The fuzzy logic process consists

of three main phases, which are as follows:

a Fuzzification

b Fuzzy operation

c Defuzzification

d Centroid method

e Weighted average method

f Mean max method

In this thesis, student will use Mamdani systems in MATLAB software to analyze risk for each activity in the project based on the advantages comparison below:

Table 2.1: Mamdani and Sugeno advantages

Fuzzy Inference System Advantages

Mamdani - Easy to understand and use intuitively

- Suitable for incorporating human knowledge and expertise

- Rules are easier to interpret and understand

- Widely accepted by various industries and applications

- Compatible with linear methodologies, such as PID control

- Effective integration with optimization and adaptive techniques

- Ensures smooth continuity of the output surface

- Well-adapted for mathematical analysis

The Mamdani fuzzy inference technique is employed to construct control systems

by synthesizing linguistic control rules derived from human operators Within the Mamdani system, each rule generates a fuzzy set output Due to their intuitive and comprehensible rule bases, Mamdani systems are well-suited for applications that rely on human expert knowledge to formulate rules, such as medical diagnostics Fuzzy inference involves the utilization of fuzzy logic to map input values to corresponding outputs, serving

as a foundation for decision-making or pattern recognition This process encompasses key

elements such as membership functions, logical operations, and if-then rules The tipping problem is used as an example to illustrate the fuzzy inference process for a two-input, one-output, three-rule system In this problem, the fuzzy inference system takes service and food quality as inputs and calculates the tip percentage using the specified rules

1 When the service is unsatisfactory or the food is spoiled, the resulting tip tends

to be minimal

2 If the service is satisfactory, the tip typically falls within an average range

3 When the service is exceptional or the food is delightful, it is common to provide

a generous tip

Figure 2.9: Fuzzy inference example

The fuzzy inference process has the following steps:

1 Fuzzification of the input variables

2 Application of the fuzzy operator (AND or OR) in the antecedent

3 Implication from the antecedent to the consequent

4 Aggregation of the consequences across the rules

5 Defuzzification

Building Information Modeling (BIM) is an intelligent representation of a building, encompassing three-dimensional aspects and facilitating the integration of data, processes, and resources throughout various stages of the building's life cycle The National Building

Information Model Standard provides a definition of BIM as a digital model that captures both the physical and functional attributes of a facility, serving as a reliable reference for informed decision-making throughout the entire life cycle of the building [14] By utilizing BIM, it becomes feasible to visually represent the building's elements and intricate details, including materials, dimensions, geometric arrangements, structural aspects, and design limitations

According to Wang & Chien [15], BIM is predominantly used in the design stage

of the project life cycle However, only 45% of respondents were aware of BIM being used

in the construction phase, and out of these, 52% reported using a BIM model for construction planning and scheduling Among the respondents who had observed BIM being utilized for construction planning and scheduling, 94% perceived that the technology had increased the effectiveness of project management

2.1.9 Optimization in Construction

Optimization is a mathematical process used to find the highest or lowest value of

a given objective within a feasible set In general, optimization involves identifying the best available values from a set based on predetermined criteria This is achieved through the use of an objective function, which is a mathematical representation of the criteria The construction industry relies heavily on optimization due to the complexity and unique nature of construction projects It provides a fast way to do simulations for analyzing and planning the project [16] There are two types of optimizations, which are:

a Single objective optimization

This type of optimization only has a single objective function or set of requirements The goal is to shorten the project's time, reduce the overall cost, or increase the profit The optimal answer to the specified aim is what single objective optimization aims to accomplish The result of this will be the optimum possible solution This tool proves valuable in providing decision-makers with a comprehensive understanding of the challenge at hand However, it often falls short in generating a diverse range of alternative solutions that effectively balance multiple objectives [17]

b Multiple objective optimization

The capability to improve a problem with multiple targets is known as multiple objective optimizations Take time cost optimization, for example It has the dual

objectives of minimizing both time and cost, as well as time-cost-quality optimization, which maximizes quality while minimizing both time and expense When planning and reviewing a building project, a variety of objectives are offered for trade-off, including those related to energy, the environment, risk, and even life cycle performance [18] It should be noticed that the goals are in opposition This means that reducing the time will result in increased costs since more resources will need to be added to the project On the other hand, it should be noted that shortening the project duration does not always result in

an increase in direct costs, as it can also lead to a reduction in indirect costs, ultimately lowering the total cost of the project However, if the duration is excessively shortened, it may lead to an increase in costs

Figure 2.10: Direct Cost, Indirect Cost, and Total Cost in Construction (Hegazy, 2002) [19]

There is no single best solution when there are multiple objectives to optimize; instead, there are many diverse solutions that may be developed Pareto optimum solutions are those that give the best trade-off between the objectives [20] There are three options

to consider while comparing the various solutions, and they are:

1 X1 dominates X2

2 X1 dominated by X2

3 X1 and X2 are not dominated each other

The solution that cannot be replaced by the other solution is referred to as a dominated solution The Pareto front is the set of non-dominated solutions Decision-makers are required to select a solution from the pool of effective solutions because this challenge rarely delivers a singular answer [16]

Figure 2.11: Optimization in Exact Method (P B Tarigan, 2021) [8]

b Heuristic Method

In addition to exact methods, heuristic methods use practical methods in a shorter amount of time than exact methods Although it still achieves the purpose, it does not ensure that it will be the best answer Numerous researchers discovered that this algorithm may become stuck in local optima and be unable to find the overall best answer Local optimum refers to the optimal result (for instance, the minimum point it produces), but global optimum denotes the minimum point among all points, with no other point being superior to it This algorithm then resulted from it The algorithm that was created is known

as a metaheuristic algorithm

c Metaheuristic Method

The next level up from a heuristic is a metaheuristic Almost every optimization issue can be solved using this technique, and it has been used to do so A better solution can be found by using a metaheuristic algorithm to investigate the problem area Meta-heuristic algorithms have recently been praised for their use in project development [21] Many scientists and engineers from many disciplines have employed metaheuristic algorithms to address optimization issues that came up in their professions Garg (2016) suggested combining the genetic algorithm (GA) with particle swarm optimization, two well-known restricted optimization methods (PSO) To handle limited optimization issues, Garg (2019) recently merged evolutionary algorithms with gravitational search The proposed method GSA-GA was validated using nine well-known structural engineering design issues Rahimian (2019) evaluated the efficiency of data envelopment analysis (DEA) using differential evolution (DE) There are so many kinds of metaheuristic algorithms, some of them are:

Metaheuristics are advanced optimization techniques that can be applied to almost any optimization problem, and have been widely used to find better solutions They are particularly useful in project development, and have been employed by scientists and engineers across various disciplines Garg (2016) proposed a combination of the genetic algorithm (GA) and particle swarm optimization (PSO) to address certain optimization issues, while Garg (2019) combined evolutionary algorithms with gravitational search to handle limited optimization problems Rahimian (2019) also evaluated the effectiveness of data envelopment analysis (DEA) using differential evolution (DE) There are various types of metaheuristic algorithms available, including:

1 Particle Swarm Optimization

2 Ant Colony Optimization

the fittest principle Stronger species in nature can live longer, giving them more opportunities to mate and pass on their powerful genes to future generations Weaker animals have shorter lifespans and are less likely to reproduce; their weak genes will die with them GAs solves complicated multi-objective optimization problems using the same method They produce an initial population of solutions at random These solutions are referred to be genomes or chromosomes Each chromosome is a series of genes, and each gene can have several values Each solution's fitness is determined by comparing its performance A chromosome is composed of multiple genes, forming a string, and each gene can hold various values The fitness of each solution is evaluated by assessing its performance against an objective function

In order to improve the solutions, the initial population of solutions undergoes evolution This involves combining the more robust genes from different solutions through marriage or crossover, resulting in the creation of new solutions with offspring genes These new solutions are evaluated, and if they outperform the weakest solutions in the population, they are incorporated This iterative process continues indefinitely, aiming to generate increasingly superior solutions until an optimal population is obtained The fittest member of the population represents the best solution

Occasionally, a random offspring chromosome is chosen, and its genes are altered

to create a distinct chromosome This process, known as mutation, serves to prevent being stuck in local optima and promotes exploration of the solution space [22]

Genetic Algorithm (or any evolutionary program) solving a specific problem must consist of the following five components:

1 A representation of the genetic material for the solutions to the problem

2 A method for initializing the initial population

3 An objective function that serves as the environment to evaluate the fitness

of the solutions

4 Genetic operators that manipulate the genetic material

5 Other parameters (such as population size, probability of applying genetic operators, etc.)

Create initial, random population of organisms (potential solutions)

Evaluate fitness for each

organism

Optimal or good solution found?

Reproduce and kill organisms

Mutate organisms END

Figure 2.12: General structure diagram of Genetic Algorithm

2.2.1 Genetic Operators

2.2.1.1 Selection

The process of choosing parents for crossover is referred to as selection The main goal of selection is to identify the individuals in the population with higher fitness levels and allow them to mate, resulting in offspring with improved fitness values The selection process involves randomly selecting chromosomes from the population based on their

fitness function There are two primary selection methods: proportionate selection and

ordinal-based selection

Proportionate-based selection involves selecting individuals according to the relative comparison of their fitness values with others in the population On the other hand, ordinal-based selection schemes choose individuals based on their ranking among the population members It is important to maintain a balance between selection, crossover, and mutation

Roulette Wheel Selection

The Roulette Wheel Selection method operates by likening the population to a roulette wheel, where each individual's slot size corresponds to their fitness level in a proportional manner To make a random selection, the wheel is spun and a virtual ball is thrown in The likelihood of the ball landing in a particular slot is proportional to the slot's arc, which corresponds to the fitness level of the individual The individual's probability of selection can be calculated using this method

𝑝𝑖 = 𝑓𝑖

∑𝑁𝑗=1𝑓𝑖Where 𝑓𝑖 is the fitness of the 𝑖𝑡ℎ individual and 𝑁 is the number of individuals The following depicts the approach visually:

Rank Selection

Rank Selection is a method that orders the population according to their fitness values, with the fittest individual given a rank of N and the weakest with a rank of 1 The selection of potential parents is followed by a tournament, which determines the chosen individual to be a parent Various methods can be employed to conduct this tournament, including two potential approaches:

1 To select a pair of individuals, a random process is employed A random

number, R, is generated within the range of 0 to 1 If R is less than a specific parameter value, r, the first individual is chosen as a parent Conversely, if R is greater than or equal to r, the second individual is selected as the parent This process is repeated to determine the second parent The value of r is a parameter

that governs the selection method

2 Select two individuals randomly, and the one with the highest fitness score is selected as the parent Repeat this process to select the second parent

This method hinders the speed of convergence in order to maintain selection pressure when there is little variance in fitness, thereby preserving diversity and ultimately improving exploration of the search space Essentially, individuals with potential to be parents are identified, and a random strategy is employed to determine which individuals will be selected as parents

Random Selection

This technique randomly picks a parent from the population

Stochastic Uniform Selection in MATLAB

The default selection method in MATLAB's genetic algorithm and multi-objective genetic algorithm functions is stochastic uniform selection This method is a modified version of the roulette wheel selection approach, where individuals are chosen based on their fitness with a probability proportional to it However, stochastic uniform selection employs a uniform random sampling technique

2.2.1.2 Crossover

Crossover, also known as mating, is a genetic operation where two individuals are combined in the hope of producing a more fit offspring [23] During crossover, a random location on the chromosomes of the two parents is selected as the crossover site The genes

on either side of this site are then copied to the offspring, resulting in a new candidate solution that inherits genetic information from both parents The fitness value of this offspring is then evaluated to assess its level of fitness

Single Point Crossover

The illustration provided below shows the Single Point Crossover process: This method involves dividing the two selected segments at a randomly chosen point, also known as a locus The locus is chosen randomly The segments beyond the locus in each individual are interchanged between the two parents

Parent 1 1 0 1 1 0 0 1 0

Figure 2.13: The Single Point Crossover Method

Single Point Crossover

The figure below visually depicts the process of Two-Point Crossover An analogous approach to Single-Point Crossover, but utilizing two loci for exchange of genetic material

Parent 1 1 1 0 1 1 0 1 0 Parent 2 0 1 1 0 1 1 0 0

Child 1 1 1 0 0 1 1 1 0 Child 2 0 1 1 1 1 0 0 0

Figure 2.14: The Two-Point Crossover Method

Uniform Crossover

The Uniform Crossover Operator is a technique used to create offspring by randomly selecting genes from each parent based on a binary crossover mask This mask determines which genes are chosen from each parent, allowing for a mix of genetic information from both parents in the offspring If the value of the binary mask is 1, the genetic information is copied from the first parent, while a value of 0 indicates that information will be sourced from the second parent The distribution of the binary values

is denoted the mixing ratio Figure below depicts the technique

The mutation probability, denoted as 𝑃𝑚, is a crucial parameter in the mutation process, as it determines the frequency at which certain parts of the chromosome will be mutated If mutation probability is set to 0%, the artefacts generated by the crossover operation are considered as the ultimate offspring after mating Conversely, if the mutation probability is set to 100%, the entire chromosome will be subjected to the mutation operator [23].

2.2.1.4 Replacement

Following each evolution cycle, the replacement stage plays a pivotal role in substituting older members of the current population with new individuals Two common methods of replacement in genetic algorithms are generational updates and steady-state updates In generational updates, N/2 children are created from a population of N individuals to evolve and establish the subsequent generation population This means that the entire parent selection is replaced in order to create a new population for the next generation This method ensures that an individual can only breed with others from the same generation Conversely, the steady-state update approach involves inserting new individuals into the population as soon as they are generated, as opposed to creating an entirely new generation at each cycle When adding a new individual, one must replace an older member, aiming to replace the least fit member

Random Replacement

Random replacement is a strategy in which two individuals are randomly chosen from the population and replaced by two offspring generated from them The parents of these offspring are also considered as candidates for selection, which can be advantageous for smaller populations as it enables the replacement of weaker individuals and potentially enhances the effectiveness of the search process

Weak Parent Replacement

The Weak Parent Replacement strategy involves replacing the weaker parent of a pair that produces two offspring with the stronger child By doing so, it favors the selection

of fitter individuals and contributes to an increase in the overall fitness of the population However, this approach may reduce the diversity of the mating pool

Both Parent Replacement