# DEVELOPMENT OF RISK ANALYSIS MODELS FOR DECISION-MAKING IN PROJECT MANAGEMENT

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CHAPTER 1 INTRODUCTION I
1.1 Nature of construction projects 1
1.2 A risk management framework 2
1.3 Research objectives 5
1.4 Outline of thesis 7
CHAPTER 2 LITERATURE REVIEW 9
2.1 Introduction 9
2.2 Probability theory 9
2.2.1 Basic probability concepts 9
2.2.2 Useful probability distributions 10
2.2.2.1 Normal distribution 10
2.2.2.2 Logarithmic Normal distribution 12
2.2.2.3 Beta distribution 14
2.2.2.4 Triangular distribution 16
2.2.2.5 Uniform distribution 17
2.3 Monte Carlo Simulation (MCS) techniques 18
2.3.1 Introduction 18
2.3.2 MCS applications in construction management 19
2.3.4 @Risk MCS computer package 22
2.4 Literature review of network analysis in construction 23
2.4.1 Introduction 23
V
2.4.2 History of Project Network Techniques (PNT) 23
2.4.2.1 Early development 23
2.4.2.2 Gantt chart 24
2.4.2.3 Families of PNT 26
2.4.2.4 AoA networks 31
2.4.3 Critical Path Method (CPM) 34
2.4.3.1 CPM calculations 35
2.4.4 Program Evaluation and Review Technique (PERT) 36
2.4.4.1 Differences between PERT and CPM 37
2.4.5 Probabilistic Network Evaluation Technique (PNET) 39
2.4.5.1 Probability of project completion time 39
2.4.5.2 Bounds and approximations 41
2.4.5.3 Basis of PNET method 43
2.4.5.4 PNET Algorithm 44
2.4.6 Monte Carlo Simulation (MCS) 46
2.4.6.1 Problems encountered in MCS method 47
2.4.7 Other methods in network analysis 48
2.4.8 Concluding remarks 50
CHAPTER 3 COMPARISON OF THE PER AND MCS METHODS 51
3.1 Introduction 51
3.2 The PERT method 51
3.3 The MCS method 52
3.3.1 Introduction 52
3.3.2 Assessment of the parameters for the different distributions 52
3.3.2.1 Normal and Log-Normal distributions 53
3.3.2.2 Uniform and Triangular distributions 54
3.3.2.3 Beta distribution 54
3.3.3 Altering the manner of setting the mean and standard deviation 55
3.4 Example project results 56
3.4.1 Example 3.1 — a house construction project 56
3.4.1.1 PERT results 59
vi
3.4.1.2 Different number of iterations and distributions of MCS 59
3.4.1.3 Different distributions with altered means and standard deviations 60
3.4.1.4 Comparison of different iterations 60
3.4.1.5 Comparison of different distributions forms 60
3.4.1.6 Comparison of different distributions when the mean is altered 60
3.4.1.7 Comparison of PERT with MCS 61
3.4.2 Example 3.2 — a hypothetical project HABITAT 73
3.4.2.1 PERT results 73
3.4.2.2 Different number of iterations and distributions of MCS 73
3.4.2.3 Different distributions with altered means and standard deviations 73
3.4.2.4 Comparison of different iterations 76
3.4.2.5 Comparison of different distributions forms 77
3.4.2.6 Comparison of different distributions when the mean is altered 77
3.4.2.7 Comparison of PERT with MCS 78
3.5 Discussion 90
3.5.1 Sensitivity analysis of Monte Carlo simulations 90
3.5.1.1 Effect of different number of iterations 90
3.5.1.2 Effect of different distributions 92
3.5.1.3 Effect of the manner of setting the mean and standard deviation 95
3.5.2 Comparison of PERT and MCS methods 97
3.6 Summary of findings 99
3.6.1 Sensitivity analysis of Monte Carlo simulations 99
3.6.2 Comparison of PERT and MCS methods 101
CHAPTER 4 THE MODIFIED STOCHASTIC ASSIGNMENT MODEL (MSAM)
103
4.1 Introduction 103
4.2 The original SAM 105
4.2.1 Description and terminology 105
4.2.2 Assumptions 107
4.2.3 The Clark approximation 110
4.2.4 The SAM algorithm 113
4.2.5 SAM applied to a simple transportation network 116
4.2.6 Concluding remarks 119
4.3 The proposed new method- Modified SAM (MSAM) 119
4.3.1 Similarities of transportation and construction networks 119
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4.3.2 The MSAM algorithm 121
4.3.3 The MSAM as applied to a construction network 124
4.3.4 Validations and applications 132
4.3.4.1 Introduction 132
4.3.4.2 Example 4.1 - the case study project 133
4.3.4.3 Example 4.2 - a house construction project 135
4.3.4.4 Example 4.3 - a hypothetical project HABITAT 136
4.3.4.5 Example 4.4 - road pavement project 137
4.3.4.6 Example 4.5 - industrial building project 142
4.3.5 Discussion 147
4.3.5.1 Accuracy of the MSAM 147
4.3.5.2 Comparison of the MSAM with other methods 151
4.4 Summary of findings 152
CHAPTER 5 THE FIRST ORDER SECOND MOMENT METHOD (FOSNP 155
5.1 Introduction 155
5.2 The FOSM method 156
5.2.1 The basic problem of reliability of engineering systems 156
5.2.2 Second-moment formulation 158
5.2.3 Linear performance functions 167
5.2.3.1 Equivalent Normal distributions 168
5.2.3.2 Correlated variates 170
5.2.4 Non-linear performance functions 174
5.2.4.1 Numerical algorithm 176
5.2.4.2 Accuracy of linear approximation 177
5.2.5 Concluding remarks 179
5.3 Use of FOSM for risk analysis in construction economics 179
5.3.1 Applicability of the FOSM in construction economics 179
5.3.2 Validations and applications 180
5.3.2.1 Example 5.1 — Linear, uncorrelated Normals 180
5.3.2.2 Example 5.2 — Linear, uncorrelated non-Normals 181
5.3.2.3 Example 5.3 — Linear, correlated Normals 186
5.3.2.4 Example 5.4 — Linear, correlated non-Normals 187
5.3.2.5 Example 5.5 — Non-linear, uncorrelated Normals 192
5.3.2.6 Example 5.6 — Non-linear, uncorrelated non-Normals 195
5.3.2.7 Example 5.7 — Non-linear, correlated Normals 198
5.3.2.8 Example 5.8 — Non-linear, correlated non-Normals 202
5.3.3 Practical applications 208
5.3.3.1 Example 5.9 — Elemental cost analysis 208
5.3.3.2 Example 5.10— Setting realistic plant hire rate 210
5.3.4 Discussion 216
5.3.4.1 Discussion of individual examples 216
5.3.4.2 Accuracy of the FOSM 220
5.3.4.3 The algorithm of the FOSM 222
5.4 Summary of findings 229
CHAPTER 6 CONCLUSIONS AND FURTHER DEVELOPMENTS 231
6.1 Introduction 231
6.2 Summary of conclusions 231
6.2.1 Literature review conclusions 231
6.2.2 PERT and MCS methods 232
6.2.3 MSAM method 234
6.2.4 FOSM method 235
6.3 Recommendations for further research 236
REFERENCES 239
APPENDIX A RESULTS OF MCS FOR EXAMPLE 3.1 252
APPENDIX B RESULTS OF MCS FOR EXAMPLE 3.2 276
APPENDIX C DATA INPUTS AND OUTPUTS OF MSAM FOR EXAMPLES
4.1-4.5 300
APPENDIX D RESULTS OF MCS FOR EXAMPLES 4.1-4.5 306
APPENDIX E RESULTS OF MCS FOR EXAMPLES 5.1-5.10 311
APPENDIX F PUBLISHED PAPERS 326