CASE STUDY
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Assoc.Prof. Dipl.-Ing. Dr.techn.
Expert Survey
Fitting
Application:
Performing arts centre
Christian Hofstadler
Associate Professor
Institute of Construction Management and Economics
Graz University of Technology, Austria
hofstadler@tugraz.at
www.christianhofstadler.at
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
1
Application of the Monte Carlo Method: Fitting with @RISK
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Determining labour consumption for works requiring a high amount of labour is
crucial both for the client at the project planning stage and for enabling bidders to
prepare their quotations.
This paper describes the deterministic calculation of the total labour consumption
rate and construction time for reinforced concrete works and demonstrates the
individual computation steps using a built example.
The computation chart for applying the Monte Carlo method with @RISK is
shown, and calculations are demonstrated using various distribution functions
(symmetric and asymmetric triangular distribution, rectangular distribution and
beta distribution).
Another point to be clarified was to determine the labour consumption rate
distribution function that comes closest to the real situation.
An expert survey was carried out at Graz University of Technology in order to
arrive at a conclusion regarding the most accurate distribution function for floor
slab shuttering works.
Conclusion
Seven different building layouts were presented to selected construction industry
experts who were to indicate labour consumption rates for each of these layouts.
In this survey, 19 experts stated labour consumption rates for simple and complex
layouts.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
2
Application of the Monte Carlo Method: Fitting with @RISK
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
The outcomes were summarised and analysed for the individual building layouts.
The @RISK software was used for fitting the most appropriate distribution
function.
The Kolmogorov-Smirnov test proved that the LogLogistic distribution came
closest to the real situation.
Monte Carlo simulations performed using the LogLogistic distribution determined
in the fitting process after the expert surveys should show the degree of difference
to the previously used distribution functions.
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
3
Construction Projects: Main Problems
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Quantities?
Qualities?
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Costs?
Fitting
Time?
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
4
Construction Projects: Main Problems
Analysis of Situation
Objective
Calculation Mode 1:
Deterministic
Approach
Uncertainty
Reinforced Concrete
Works – Basics
Development
Planning
Tendering
Construction
Accounting
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Time
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
5
Construction Costs/Time: From Rough Planning to Detailed Planning
Analysis of Situation
Objective
Construction Time/
Costs
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Rough Planning
Detailed Planning
Expert Survey
Fitting
Entire structure
Component
assembly
Component
assembly per floor
Components/
production units
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
6
Construction Costs/Time: From Rough Planning to Detailed Planning
Construction Time/
Costs
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Rough Planning
Calculation Mode 3:
Monte Carlo Method
Entire structure
Component
assembly
Detailed Planning
Component
assembly per floor
Components/
production units
Expert Survey
+
Fitting
Accuracy
_
+
Application:
Performing arts centre
Processing Effort
Conclusion
_
+
Certainty
Source: Hofstadler
ChristianHOFSTADLER | 2012
_
2012|Palisade Risk Conference | London
Construction Management
7
Calculation of Construction Time/Costs
Analysis of Situation
Objective
Calculation
Construction time/costs
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Calculation Mode 1
Calculation Mode 2
Calculation Mode 3
Deterministic approach
Simplified stochastic
approach
Application of Monte
Carlo method
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
8
Calculation of Construction Time
Analysis of Situation
Objective
Calculation
Construction time/costs
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Calculation Mode 1
Calculation Mode 2
Calculation Mode 3
Deterministic approach
Simplified stochastic
approach
Application of Monte
Carlo method
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
9
Calculation of Construction Time: Deterministic Approach
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
10
Calculation Equation: Rough Planning
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation of Construction Time for Reinforced Concrete Works
DRCW , BU 
Calculation Mode 1:
Deterministic
Approach
QC
 WRCW WTRCW

 TCRRCW




BU

T , RCW 
 1 
100 % 
 

 


 
Calculation Mode 3:
Monte Carlo Method
DRCW , BU
………. Duration of the reinforced concrete works incl. buffer [d]
Expert Survey
QC
………. Concrete quantity [m³]
WRCW
………. Average number of workers [wh/hr]
WTRCW
………. Average daily working time [hr/d]
TCRRCW
Average total labour consumption rate for
………. reinforced concrete works [wh/m³]
BU T , RCW
………. Buffer for construction time [%]
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
11
Calculation Equation: Rough Planning
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Calculation of construction time for reinforced concrete works
DRCW , BU 
QC
 WRCW WTRCW

 TCRRCW




BU

T , RCW 
 1 
100 % 
 

 


 
TCRRCW  CRFW  FRBD  CRRW  RRBD  CRCW
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
12
Calculation Equation: Rough Planning
TCRRCW  CRFW  FRBD  CRRW  RRBD  CRCW
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
TCRRCW
Average total labour consumption rate for
………. reinforced concrete works [wh/m³]
CRFW
Average labour consumption rate for
………. formwork-related activities [wh/m²]
FRBD
………. Average formwork ratio for the entire building [m²/m³]
CRRW
………. Average labour consumption rate for reinforcement works [wh/t]
RRBD
………. Average reinforcement ratio for the entire building [t/m³]
CRCW
………. Average labour consumption rate for concrete works [wh/m³]
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
13
Reinforced Concrete Works
Analysis of Situation
Objective
Shuttering works
Reinforced Concrete
Works – Basics
 wh 
CRFW  2 
m 
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
14
Reinforced Concrete Works
Analysis of Situation
Objective
Reinforcement works
Reinforced Concrete
Works – Basics
 wh 
CRRW  
 t 
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
15
Reinforced Concrete Works
Analysis of Situation
Objective
Concrete works
Reinforced Concrete
Works – Basics
 wh 
CRCW  
 m³ 
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
16
Reinforced Concrete Works
Analysis of Situation
Objective
Total consumption rate for reinforced concrete works
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
 wh 
CRA, RW  
 t 
 wh 
CRA; FW  2 
m 
4 m² / m³  FRBD  6 m² / m³
0.100 t / m³  RRBD  0.150 t / m³
Calculation Mode 3:
Monte Carlo Method
Expert Survey
TCRRCW  CRFW  FRBD  CRRW  RRBD  CRCW
Fitting
 wh 
CRA,CW  
 m³ 
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
17
Calculation Equation: Rough Planning
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation of construction time for reinforced concrete works
DRCW , BU 
QC
 WRCW WTRCW

 TCRRCW




BU

T , RCW 
 1 
100 % 
 

 


 
Calculation Mode 3:
Monte Carlo Method
DRCW , MIN  DRCW  DRCW , MAX
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
18
Calculation of Construction Time: Application of Monte Carlo Method
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
19
Selection of distribution functions and input of individual values
CRFW
FRBD
CRRW
RRBD
CRCW
Selection of distribution functions and input of individual values
CRFW
FRBD
CRRW
RRBD
CRCW
Selection of distribution functions and input of individual values
CRFW
*
FRBD
+
CRRW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
*
FRBD
+
CRRW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
*
FRBD
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
*
FRBD
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
*
WTRCW
FRBD
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
*
*
WTRCW
FRBD
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
*
*
WTRCW
FRBD
/
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
*
*
WTRCW
FRBD
/
PRRCW
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
QC
*
*
WTRCW
FRBD
/
PRRCW
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
QC
/
*
*
WTRCW
FRBD
/
PRRCW
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
QC
/
DRCW
*
*
WTRCW
FRBD
/
PRRCW
+
CRRW
TCRRCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
QC
/
DRCW
*
*
WTRCW
FRBD
CRRW
+
/
TCRRCW
PRRCW
BUT,RCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
QC
WTRCW
*
/
DRCW
*
FRBD
CRRW
+
/
TCRRCW
PRRCW
+
BUT,RCW
*
RRBD
+
CRCW
Selection of distribution functions and input of individual values
CRFW
WRCW
QC
*
WTRCW
*
/
DRCW
FRBD
CRRW
+
/
TCRRCW
PRRCW
+
DRCW,BU
BUT,RCW
*
RRBD
+
CRCW
Application
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
36
Performing Arts Centre – Musiktheater Linz - Key Details
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
The figure shows an axonometric representation of the building. The building
comprises two basement levels, five above-ground storeys and a stage tower. The
load-bearing structure is mainly composed of cast-in-situ concrete.
Source: Theatre Projects Consultants
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
37
Performing Arts Centre – Musiktheater Linz - Key Details
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
The maximum length of the building equals approx. 162 metres, its maximum
width amounts to about 62 metres. The gross volume of the entire structure
amounts to approx. 290,000 m³.
Conclusion
Source: Theatre Projects Consultants
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
38
Performing Arts Centre – Musiktheater Linz - Key Details
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
The site extends over an area of about 12,000 m², the building has a ground-plan
area of approx. 11,000 m².
Source: Theatre Projects Consultants
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
39
Performing Arts Centre – Musiktheater Linz - Key Details
Analysis of Situation
Objective
Performing Arts Centre: Quantity determination
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Components
Formwork area
[m²]
Foundation slab
Walls
Floor slabs
Beams, girders
Columns
Other concrete slabs
Stairs
Balustrades
Total:
1,150.00
81,000.00
30,000.00
6,400.00
3,700.00
1,700.00
500.00
2,800.00
127,250.00
[%]
Reinforcement
quantity
[t]
0.90
63.65
23.58
5.03
2.91
1.34
0.39
2.20
100.00
1,500.00
1,500.00
1,450.00
162.00
120.00
100.00
20.00
80.00
4,932.00
[%]
Concrete volume
[m³]
30.41
30.41
29.40
3.28
2.43
2.03
0.41
1.62
100.00
[%]
9,600.00
15,500.00
10,400.00
1,380.00
400.00
400.00
90.00
505.00
38,275.00
25.08
40.50
27.17
3.61
1.05
1.05
0.24
1.32
100.00
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
40
Application
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
41
Performing Arts Centre – Musiktheater Linz - Key Details
Analysis of Situation
Objective
Input values to calculate construction time: MLV
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Average labour consumption rate - shuttering works
Average formwork ratio for the entire building
Average labour consumption rate - reinforcement works
Average reinforcement ratio for the entire building
Average labour consumption rate - concrete works
Maximum number of workers
Proportion of the average number of workers
Daily working time
Concrete quantity
Buffer
Source: Hofstadler
ChristianHOFSTADLER | 2012
MIN
MLV
MAX
1.10 wh/m²
3.00 m²/m³
8.50 wh/t
125.00 kg/m³
0.60 wh/m³
100.00 wh/hr
75.00 %
8.00 hr/d
38,000 m³
7.50 %
1.20 wh/m²
3.20 m²/m³
9.50 wh/t
129.00 kg/m³
0.65 wh/m³
110.00 wh/hr
80.00 %
8.50 hr/d
38,275 m³
10.00 %
1.35 wh/m²
3.50 m²/m³
11.00 wh/t
135.00 kg/m³
0.75 wh/m³
120.00 wh/hr
88.00 %
9.00 hr/d
39,500 m³
12.00 %
2012|Palisade Risk Conference | London
Construction Management
42
Calculation of Construction Costs: Calculation Mode 1
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Calculation of labour consumption rate for reinforced concrete works: MLV
Average labour consumption rate - shuttering works
Average formwork ratio for the entire building
Average labour consumption rate - reinforcement works
Average reinforcement ratio for the entire building
Average labour consumption rate - concrete works
Maximum number of workers
Proportion of the average number of workers
Daily working time
Concrete quantity
Buffer
MIN
MLV
MAX
1.10 wh/m²
3.00 m²/m³
8.50 wh/t
125.00 kg/m³
0.60 wh/m³
100.00 wh/hr
75.00 %
8.00 hr/d
38,000 m³
7.50 %
1.20 wh/m²
3.20 m²/m³
9.50 wh/t
129.00 kg/m³
0.65 wh/m³
110.00 wh/hr
80.00 %
8.50 hr/d
38,275 m³
10.00 %
1.35 wh/m²
3.50 m²/m³
11.00 wh/t
135.00 kg/m³
0.75 wh/m³
120.00 wh/hr
88.00 %
9.00 hr/d
39,500 m³
12.00 %
TCRA, RCW  CRA, FW  FRA, BD  CRA, RW  RRA, BD  CRA,CW
Fitting
Application:
Performing arts centre
Conclusion
TCRA, RCW  1.20 wh / m²  3.20 m² / m³  9.50 wh / t  0.129 t / m³  0.65 wh / m³  5.72 wh / m³
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
43
Calculation of Construction Time: Calculation Mode 1
Analysis of Situation
Objective
Calculation of costs of production for reinforced concrete works: MLV
Reinforced Concrete
Works – Basics
DRCW , BU 
Calculation Mode 1:
Deterministic
Approach
QC
 WRCW WTRCW

 TCRRCW




 BU T , RCW 
 1
100 % 
 

 


 
Average labour consumption rate - shuttering works
Average formwork ratio for the entire building
Average labour consumption rate - reinforcement works
Average reinforcement ratio for the entire building
Average labour consumption rate - concrete works
Maximum number of workers
Proportion of the average number of workers
Daily working time
Concrete quantity
Buffer
MIN
MLV
MAX
1.10 wh/m²
3.00 m²/m³
8.50 wh/t
125.00 kg/m³
0.60 wh/m³
100.00 wh/hr
75.00 %
8.00 hr/d
38,000 m³
7.50 %
1.20 wh/m²
3.20 m²/m³
9.50 wh/t
129.00 kg/m³
0.65 wh/m³
110.00 wh/hr
80.00 %
8.50 hr/d
38,275 m³
10.00 %
1.35 wh/m²
3.50 m²/m³
11.00 wh/t
135.00 kg/m³
0.75 wh/m³
120.00 wh/hr
88.00 %
9.00 hr/d
39,500 m³
12.00 %
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
DRCW , BU
Application:
Performing arts centre




38,275 m³
10
%
  322 d

 1 
100 % 
 88 wh / hr  8.50 hr / d 


 
5.72 wh / m³


 
Conclusion
TCRA, RCW  1.20 wh / m²  3.20 m² / m³  9.50 wh / t  0.129 t / m³  0.65 wh / m³  5.72 wh / m³
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
44
Application
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
?
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
45
Calculation of Labour Consumption Rate: Calculation Mode 3
Analysis of Situation
Objective
The values from this table are used for the input variables to labour consumption
rate for reinforced concrete works (asymmetric triangular distribution).
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Average labour consumption rate - shuttering works
Average formwork ratio for the entire building
Average labour consumption rate - reinforcement works
Average reinforcement ratio for the entire building
Average labour consumption rate - concrete works
Maximum number of workers
Proportion of the average number of workers
Daily working time
Concrete quantity
Buffer
Source: Hofstadler
ChristianHOFSTADLER | 2012
MIN
MLV
MAX
1.10 wh/m²
3.00 m²/m³
8.50 wh/t
125.00 kg/m³
0.60 wh/m³
100.00 wh/hr
75.00 %
8.00 hr/d
38,000 m³
7.50 %
1.20 wh/m²
3.20 m²/m³
9.50 wh/t
129.00 kg/m³
0.65 wh/m³
110.00 wh/hr
80.00 %
8.50 hr/d
38,275 m³
10.00 %
1.35 wh/m²
3.50 m²/m³
11.00 wh/t
135.00 kg/m³
0.75 wh/m³
120.00 wh/hr
88.00 %
9.00 hr/d
39,500 m³
12.00 %
2012|Palisade Risk Conference | London
Construction Management
46
Calculation of Labour Consumption Rate: Calculation Mode 3
Selection of distribution functions and input of individual values
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
CRFW
*
FRBD
+
CRRW
*
RRBD
+
CRCW
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
TCRRCW
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
47
Calculation of Labour Consumption Rate: Calculation Mode 3
Analysis of Situation
Objective
Monte Carlo Simulation – Results: Total labour consumption rate for
reinforced concrete works
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Asymmetric
triangular distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
0.734 wh/m³
5.503 wh/m³
Conclusion
6.237 wh/m³
Total labour consumption rates for reinforced concrete works are below 5.503
wh/m³ only in 5% of all cases (X5); they exceed 6.237 wh/m³ in 5% of all cases
(X95). The range between these quantiles amounts to 0.734 wh/m³.
Source: @RISK, Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
48
Calculation of Labour Consumption Rate: Calculation Mode 3
Analysis of Situation
Objective
Monte Carlo Simulation – Results: Total labour consumption rate for
reinforced concrete works
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Asymmetric
triangular distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
28.8%
Fitting
Application:
Performing arts centre
5.72 wh/m³
Conclusion
TCRA, RCW  1.20 wh / m²  3.20 m² / m³  9.50 wh / t  0.129 t / m³  0.65 wh / m³  5.72 wh / m³
For example, the probability that the total labour consumption rate for reinforced
concrete works will be less than 5.72 wh/m³ is 28.8 % whereas the probability that
the labour consumption rate will be higher than this value amounts to 71.2%.
Source: @RISK, Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
49
Calculation of Labour Consumption Rate: Calculation Mode 3
Analysis of Situation
Objective
Monte-Carlo Simulation – Results: Total labour consumption rate for
reinforced concrete works
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Asymmetric
triangular distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
The expected mean value amounts to 5.8540 wh/m³, with a standard deviation
of 0.2224 wh/m³. The distribution of the values is roughly symmetrical (skewness
= 0.1933).
Source: @RISK, Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
50
Change of Distribution Functions
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Consequences
Fitting
Application:
Performing arts centre
?
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
51
Change of Distribution Functions
Isosceles
triangular distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
2.00
1.80
Isosceles triangular distribution
1.60
1.40
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
7.25
7.50
Total labour consumption rate for reinforced concrete works [wh/m³]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
52
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
2.00
1.80
Isosceles triangular distribution
1.60
Asymmetric triangular distribution
1.40
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
7.25
7.50
Total labour consumption rate for reinforced concrete works [wh/m³]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
53
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
2.00
Isosceles triangular distribution
1.80
1.60
Asymmetric triangular distribution
1.40
Uniform distribution
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
7.25
7.50
Total labour consumption rate for reinforced concrete works [wh/m³]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
54
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
2.00
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
1.80
Asymmetric triangular distribution
1.60
Uniform distribution
Calculation Mode 3:
Monte Carlo Method
1.40
Beta distribution
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
7.25
7.50
Total labour consumption rate for reinforced concrete works [wh/m³]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
55
Calculation of Construction Time: Calculation Mode 3
Analysis of Situation
Objective
The values from this table are used for the input variables to construction time for
reinforced concrete works (asymmetric triangular distribution).
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Average labour consumption rate - shuttering works
Average formwork ratio for the entire building
Average labour consumption rate - reinforcement works
Average reinforcement ratio for the entire building
Average labour consumption rate - concrete works
Maximum number of workers
Proportion of the average number of workers
Daily working time
Concrete quantity
Buffer
Source: Hofstadler
ChristianHOFSTADLER | 2012
MIN
MLV
MAX
1.10 wh/m²
3.00 m²/m³
8.50 wh/t
125.00 kg/m³
0.60 wh/m³
100.00 wh/hr
75.00 %
8.00 hr/d
38,000 m³
7.50 %
1.20 wh/m²
3.20 m²/m³
9.50 wh/t
129.00 kg/m³
0.65 wh/m³
110.00 wh/hr
80.00 %
8.50 hr/d
38,275 m³
10.00 %
1.35 wh/m²
3.50 m²/m³
11.00 wh/t
135.00 kg/m³
0.75 wh/m³
120.00 wh/hr
88.00 %
9.00 hr/d
39,500 m³
12.00 %
2012|Palisade Risk Conference | London
Construction Management
56
Calculation of Construction Time: Calculation Mode 3
Selection of distribution functions and input of individual values
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
CRFW
*
FRBD
CRRW
+
*
RRBD
+
CRCW
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
WRCW
WTRCW
*
/
TCRRCW
Expert Survey
Fitting
QC
/
PRRCW
Application:
Performing arts centre
DRCW
Conclusion
+
BUT,RCW
DRCW,BU
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
57
Calculation of Construction Time: Calculation Mode 3
Analysis of Situation
Objective
Monte Carlo Simulation – Results: Construction time (incl. buffer)
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Asymmetric
triangular distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
73.7 d
Conclusion
293.3 d
367.0 d
The construction times of reinforced concrete works are below 293.3 d only in 5%
of all cases (X5); they exceed 367.0 d in 5% of all cases (X95). The range between
these quantiles amounts to 73.7 d.
Source: @RISK, Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
58
Calculation of Construction Time: Calculation Mode 3
Analysis of Situation
Objective
Monte Carlo Simulation – Results: Construction time (incl. buffer)
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Asymmetric
triangular distribution
Calculation Mode 3:
Monte Carlo Method
40.2%
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
DRCW , BU




38,275 m³
10 % 


 1
 322 d
 88 wh / hr  8.50 hr / d   100 % 


 
5.72 wh / m³


 
322 d
For example, the probability that construction time will be less than 322 d is 40.2%
whereas the probability that the time is longer amounts to 59.8%.
Source: @RISK, Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
59
Calculation of Construction Time: Calculation Mode 3
Analysis of Situation
Objective
Monte Carlo Simulation – Results: Construction time (incl. buffer)
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Asymmetric
triangular distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
The expected mean value amounts to 328.6 d, with a standard deviation of
22.45 d. The distribution of the values is roughly symmetrical (skewness = 0.2223).
Source: @RISK, Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
60
Change of Distribution Functions
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Consequences
Fitting
Application:
Performing arts centre
?
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
61
Change of Distribution Functions
Isosceles
triangular distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
0.020
Calculation Mode 1:
Deterministic
Approach
0.018
Calculation Mode 3:
Monte Carlo Method
0.014
Isosceles triangular distribution
0.016
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
62
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
0.020
0.018
Isosceles triangular distribution
0.016
Asymmetric triangular distribution
0.014
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
63
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
0.020
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
0.018
Asymmetric triangular distribution
0.016
Uniform distribution
0.014
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
64
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
0.020
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
0.018
Asymmetric triangular distribution
Uniform distribution
0.016
Beta distribution
Calculation Mode 3:
Monte Carlo Method
0.014
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
65
Expert Survey
Analysis of Situation
Objective
Expert surveys were conducted at Graz University of Technology to derive the
distribution function for labour consumption rates for shuttering works.
Reinforced Concrete
Works – Basics
Using a structured interview design, 19 experts from construction contractors were
personally interviewed to obtain labour consumption rates for floor shuttering
works.
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Labour consumption rates for seven different floor layouts were collected
(separately for formwork placement and stripping). Experts received information
on the dimensions and quality of the components (columns, walls, floors).
Expert Survey
Fitting
Application:
Performing arts centre
Simple
Medium
Complex
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
66
Expert Survey
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Simple
Calculation Mode 1:
Deterministic
Approach
Medium
Complex
The experts then provided their labour consumption estimates for the individual
layouts.
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
67
Expert Survey
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Survey outcomes: Labour consumption rates for formwork placement and stripping
G1
Labour Consumption Rate
[wh/m²]
G2
Labour Consumption Rate
[wh/m²]
G3
Calculation Mode 3:
Monte Carlo Method
Labour Consumption Rate
[wh/m²]
G4
Expert Survey
Labour Consumption Rate
[wh/m²]
G5
Fitting
Labour Consumption Rate
[wh/m²]
G6
Application:
Performing arts centre
Labour Consumption Rate
[wh/m²]
G7
Conclusion
Labour Consumption Rate
[wh/m²]
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.55 0.60 0.56 0.70 0.55 0.60 0.55 0.60 0.60 0.45 0.48 0.45 0.50 0.45 0.65 0.55 0.65 0.95 0.45
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.55 0.65 0.56 0.75 0.60 0.60 0.60 0.60 0.60 0.50 0.50 0.50 0.50 0.50 0.65 0.55 0.80 1.05 0.45
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.55 0.65 0.58 0.80 0.70 0.65 0.60 0.65 0.60 0.50 0.55 0.55 0.55 0.60 0.70 0.60 1.00 1.10 0.45
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.65 0.70 0.66 0.75 0.70 0.75 0.70 0.70 0.60 0.60 0.62 0.60 0.60 0.65 0.70 0.65 1.00 1.10 0.55
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.65 0.70 0.66 0.90 0.80 0.85 0.80 0.80 0.65 0.70 0.67 0.70 0.70 0.70 0.75 0.75 1.15 1.30 0.55
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.65 0.80 0.66 0.95 0.85 1.05 0.85 0.85 0.70 1.50 0.72 0.75 0.80 0.75 0.75 0.90 1.15 1.30 0.55
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.85 0.80 0.79 1.00 0.95 1.05 1.10 0.85 0.80 1.80 0.77 1.00 1.10 0.75 0.75 0.90 1.15 1.30 0.60
The survey aimed to derive distribution functions from the interview results.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
68
Expert Survey
Analysis of Situation
Objective
Layout classes were derived from the results of the expert survey in order to
determine a general representation of results for the individual floor layouts.
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
The seven different layouts were categorised according to their degree of
complexity and grouped into three different classes.
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Class 0
Class 1
Class 2
Einfache
Grundrissformen
Medium layouts
Complex layouts
Simple layouts
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
69
Expert Survey: Merging of datasets
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Class 0
Simple
Einfache
layouts
Grundrissformen
Class 1
Medium layouts
Class 2
Complex
layouts
Although the derived distribution functions do not have greater accuracy, they
provide a greater degree of certainty with respect to variations and uncertainties
resulting from the expert survey.
An expert survey dataset includes the labour consumption rate estimates provided
by several experts for a certain layout.
Indirect use of this data is enabled if the distribution of expert opinions is evaluated
and a distribution function fitted on this basis.
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
70
Expert Survey: Merging of datasets
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Grouping into classes is achieved by merging the expert survey datasets.
The expert survey datasets are skewed as a result of the varying degree of
complexity of the layouts. This skewness needs to be corrected in the merging
process.
Three classes Cc (c = 0, 1, 2) are defined:
• simple C0
• medium C1
• complex C2
These classes are derived from the layout-related datasets as follows:
• C0 comprises layout shapes G1 and G2
• C1 comprises layout shapes G3, G4 and G5
• C2 comprises layout shapes G6 and G7
Conclusion
Each layout shape i is represented by 19 expert values j (Ei,j).
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
71
Expert Survey: Merging of datasets
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Class 0
Class 1
Class 2
Simple
Einfache
layouts
Grundrissformen
Medium layouts
Complex
layouts
C0
C1
C2
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
72
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
1.) In the first step, the average minimum value is calculated from the expert
values of the associated layouts of class Cc (c = 0, 1, 2).
min Cc 
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
 iC minGi 
Number of layouts of class
2.) Calculation of the spread of the expert values within the individual layouts of
the respective class (i Є C).
sGi  maxGi   minGi 
Expert Survey
Fitting
3.) Calculation of the average spread of class Cc.
Application:
Performing arts centre
sc 
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
 iC sG
i
Number of layouts of class
2012|Palisade Risk Conference | London
Construction Management
73
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
4.) Scaling of expert values Ei,j for the jth expert of the ith layout within the cth class.
Reinforced Concrete
Works – Basics
Ei , jnew 
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Ei , j  minGi 
sGi
 sc  min Cc
An average spread has been established for the expert values Ei,jnew grouped into
classes.
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
74
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
An example of the medium class should illustrate the approach:
Reinforced Concrete
Works – Basics
Datasets of layouts G3, G4 and G5 are used for class C1.
Calculation Mode 1:
Deterministic
Approach
Class 1
Calculation Mode 3:
Monte Carlo Method
Medium layouts
Expert Survey
G3
Fitting
Application:
Performing arts centre
Conclusion
E1
Labour Consumption Rate
[wh/m²]
G4
G5
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.65 0.70 0.66 0.75 0.70 0.75 0.70 0.70 0.60 0.60 0.62 0.60 0.60 0.65 0.70 0.65 1.00 1.10 0.55
E1
Labour Consumption Rate
[wh/m²]
E3
0.55 0.65 0.58 0.80 0.70 0.65 0.60 0.65 0.60 0.50 0.55 0.55 0.55 0.60 0.70 0.60 1.00 1.10 0.45
E1
Labour Consumption Rate
[wh/m²]
E2
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.65 0.70 0.66 0.90 0.80 0.85 0.80 0.80 0.65 0.70 0.67 0.70 0.70 0.70 0.75 0.75 1.15 1.30 0.55
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
75
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
The minimum expert values for each layout are applied [min(Gi)], added up and
divided by the number of layouts included in the calculation (in this case, three).
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
min C1 
Calculation Mode 3:
Monte Carlo Method
minG3   minG4   minG5 
3
min C1 
0.45  0.55  0.55
3
Expert Survey
min C1  0.517
Fitting
wh
m²
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
76
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
In the next step, the spreads of the expert values are calculated for each layout:
sG3  maxG3   minG3 
Reinforced Concrete
Works – Basics
sG3  1.10  0.45
Calculation Mode 1:
Deterministic
Approach
sG3  0.65
Calculation Mode 3:
Monte Carlo Method
wh
m²
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
sG4  maxG4   minG4 
sG5  maxG5   minG5 
sG4  1.10  0.55
sG5  1.30  0.55
sG4  0.55
wh
m²
Source: Hofstadler
ChristianHOFSTADLER | 2012
sG5  0.75
wh
m²
2012|Palisade Risk Conference | London
Construction Management
77
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
Step 3 includes the calculation of the average spread for class C1, as follows:
Reinforced Concrete
Works – Basics
s1 
Calculation Mode 1:
Deterministic
Approach
s1 
Calculation Mode 3:
Monte Carlo Method
sG3  sG4  sG 5
3
0.65  0.55  0.75
3
s1  0.65
Expert Survey
wh
m²
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
78
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
In the final step, all expert values Ei,j of class C1 are scaled in order to create a new
dataset that can be used for subsequent fitting. The following example illustrates
the scaling of one of these values:
Calculation Mode 1:
Deterministic
Approach
Ei , jnew 
Calculation Mode 3:
Monte Carlo Method
E3,1new 
Ei , j  minGi 
sGi
E3,1  minG3 
sG3
Expert Survey
E3,1new 
Fitting
 s1  min C1
0.55  0.45
 0.65  0.517
0.65
E3,1new  0.617
Application:
Performing arts centre
 sc  min Cc
wh
m²
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
79
Preparation of fitting: Merging of datasets
Analysis of Situation
Objective
Original dataset for C1:
G3
Reinforced Concrete
Works – Basics
E1
Labour Consumption Rate
[wh/m²]
G4
Calculation Mode 1:
Deterministic
Approach
Expert Survey
E2
E4
E5
E3
E4
E5
E2
E3
E4
E5
G3
Labour Consumption Rate
[wh/m²]
Application:
Performing arts centre
G4
Labour Consumption Rate
[wh/m²]
Conclusion
G5
Labour Consumption Rate
[wh/m²]
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.65 0.70 0.66 0.90 0.80 0.85 0.80 0.80 0.65 0.70 0.67 0.70 0.70 0.70 0.75 0.75 1.15 1.30 0.55
E3,1new 
Scaled dataset for C1:
Fitting
E6
0.65 0.70 0.66 0.75 0.70 0.75 0.70 0.70 0.60 0.60 0.62 0.60 0.60 0.65 0.70 0.65 1.00 1.10 0.55
E1
Labour Consumption Rate
[wh/m²]
E3
0.55 0.65 0.58 0.80 0.70 0.65 0.60 0.65 0.60 0.50 0.55 0.55 0.55 0.60 0.70 0.60 1.00 1.10 0.45
E1
Labour Consumption Rate
[wh/m²]
G5
Calculation Mode 3:
Monte Carlo Method
E2
E1
E2
E3
E4
E5
E6
E7
0.55  0.45
wh
 0.65  0.517  0.617
0.65
m²
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.62 0.72 0.65 0.87 0.77 0.72 0.67 0.72 0.67 0.57 0.62 0.62 0.62 0.67 0.77 0.67 1.07 1.17 0.52
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.63 0.69 0.65 0.75 0.69 0.75 0.69 0.69 0.58 0.58 0.60 0.58 0.58 0.64 0.69 0.63 1.05 1.17 0.52
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
0.60 0.65 0.61 0.82 0.73 0.78 0.73 0.73 0.60 0.65 0.62 0.65 0.65 0.65 0.69 0.69 1.04 1.17 0.52
These scaled datasets can be used for subsequent fitting with the @Risk software.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
80
Fitting
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
The results of the expert survey served to identify the most appropriate distribution
function using the @RISK software.
For fitting purposes, both the datasets of the individual layouts and the scaled
datasets of the three classes (simple, medium, complex) were analysed.
The LogLogistic distribution was found to be most appropriate in almost all cases.
Compared to other distribution functions, this function gives the smallest error in
the Kolmogorov-Smirnov, Anderson-Darling and Chi-square tests.
For x > 0, the probability density of the LogLogistic distribution is defined as:
β 1
 β x
  
α
α
f x       2
  x β 
1    
  α  
Application:
Performing arts centre
Conclusion
In this equation, α > 0 and β > 0 are distribution parameters.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
81
Fitting
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Fitting aims to numerically determine the parameters (offset and form parameters)
of a distribution function in order for the distribution to represent the collected raw
data as accurately as possible.
The used @Risk software applies the Levenberg-Marquardt method, which uses
the following (simplified) algorithm:
1. Calculate the "first guess" of all parameters
Calculation Mode 3:
Monte Carlo Method
2. Find the goodness-of-fit of the input data to the function using these parameters
Expert Survey
3. Vary the parameters by an amount proportional to a factor λ
Fitting
4. Measure the goodness-of-fit with the modified parameters
Application:
Performing arts centre
5. If the modified parameters produce a better fit, update the parameters with these
values and decrease the value of λ by an order of magnitude
Conclusion
6. If the modified values produce a worse fit, do not update the parameters and
increase the value of λ by an order of magnitude
7. Return to step 3
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
82
Fitting
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
The algorithm ends if the error changes by only a very small margin.
Obviously, there is still a residual error after this process, which can be quantified
using various statistical tests.
Amongst others, these include the Chi-square, Kolmogorov-Smirnov and
Anderson-Darling tests.
For the statistical tests, all potential distribution functions available in @Risk were
considered.
The distribution giving the smallest error is then used for the subsequent
computation steps; it replaces the previously applied triangular distributions.
Application:
Performing arts centre
Conclusion
For the expert survey analysis, the error was determined in the KolmogorovSmirnov test because this test is best suited to treating only a small amount of data.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
83
Fitting
Analysis of Situation
Objective
The scaled values and the fitting with @RISK result in the following LogLogistic
distribution as the distribution function for Class 1:
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
84
Fitting
Analysis of Situation
Objective
The steepness of the LogLogistic functions is due to the fact that the majority of
experts estimated labour consumption rates in a narrower range.
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
However, upward outliers are not excluded but their likelihood of occurrence is
much smaller than in the case of downward outliers.
If a triangular instead of the LogLogistic distribution were used in the present case,
a higher likelihood of occurrence would be assigned to the values in the maximum
range, which would contradict the expert survey results completely.
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
85
Fitting
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Chau also analysed the validity of triangular distributions for the purpose of
calculating construction costs using the Monte Carlo method.
In this case, the costs of electrical installations were estimated by seven senior
experts.
One of the distinctive characteristics of this analysis was that the expected value
was located closer to the minimum than to the maximum in most cases.
This is explained by the fact that there is a theoretical lower construction cost limit
determined by the minimum degree of resource utilisation. No upper limit exists,
though.
As a result, each of the experts adopted a different view with regard to the potential
maximum cost depending on his personal background and experience.
This suggests that the triangular distribution of the input values would result in an
excessive distortion towards the maximum values.
Chau indicates a right-skewed distribution as the form of the distribution function.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
86
Fitting
Analysis of Situation
Objective
Comparison: LogLogistic distribution and triangular distribution
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
87
Verification of Results
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Chau also analysed the validity of triangular distributions for the purpose of
calculating construction costs using the Monte Carlo method.
In this case, the costs of electrical installations were estimated by seven senior
experts.
Chau indicates a right-skewed distribution as the form of the distribution function.
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler.,Chau
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
88
Verification of Results
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
The comparison of the distribution function according to Chau with the
LogLogistic distribution function derived from the expert survey shows a strong
correlation.
Distribution function according to Chau
New distribution function
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
This finding permits the conclusion that right-skewed distribution functions are
particularly well-suited to representing labour consumption rates.
Conclusion
More specifically, the LogLogistic distribution is proposed for labour consumption
rates for shuttering works.
The LogLogistic distribution is also believed to be most appropriate for labour
consumption rates of other works, such as reinforcing or concrete placement.
Source: Hofstadler, Chau
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
89
Fitting
Analysis of Situation
Objective
The two parameters determining the form and the offset of the distribution (α, β)
need to be entered in order to define a LogLogistic distribution for a calculation.
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
However, this is not in line with the previously applied approach according to
which minimum, expected and maximum input values were specified for the
triangular distributions.
Since α and β are very difficult to estimate, further considerations are necessary to
retain the LogLogistic form of the distribution whilst also facilitating data entry.
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Another argument supporting the view that the general form of the LogLogistic
distribution is not practical is the fact that users (cost surveyors, work schedulers,
risk managers etc.) are unable to identify the values to be used for α und β.
For this reason, further investigations were carried out in order to identify an option
for retaining the characteristics of the LogLogistic distribution whilst facilitating
data entry (making it suitable for practical applications).
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
90
Optimised Distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
The solution lies in the polygonal approximation of the LogLogistic distribution.
The fitted distribution is approximated by connected straight lines.
In @Risk, the distribution function is approximated using the so-called “General
Distribution” feature.
Distribution obtained by fitting
Distribution after polygonal
approximation
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
91
Optimised Distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Polygonal approximation:
Y
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Area = 1
Conclusion
X
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
92
Optimised Distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
The approximated distribution is defined by x and y values. If specific limits for
input values are selected, the x values need to be converted in order to retain the
form of the distribution function.
@Risk automatically standardises the area under the curve to 1.
Such an approximation is performed for all three classes (simple, medium and
complex). As a result, different distribution functions can be used for individual
layouts in order to determine labour consumption rates.
Provided a class is selected, a minimum and an expected value are chosen for the
labour consumption rates.
Therefore the user needs to enter only two values.
An appropriate conversion factor must be identified in order to retain the form of
the expert survey distribution function for the relevant class.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
93
Optimised Distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Expert Survey
Fitting
Minimum from fitting
Calculation Mode 3:
Monte Carlo Method
Minimum from data
Calculation Mode 1:
Deterministic
Approach
Expected value from fitting
Application:
Performing arts centre
Conclusion
t
r
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
94
Optimised Distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
The difference between the minimum of the class distribution and the expected
value obtained from fitting is used to determine the conversion factor f.
In this regard, it should be noted that the fitting minimum is not equivalent to the
minimum derived from the expert data, which is due to the fact that the fitted curve
is superimposed on the gathered data.
The distribution minimum is thus lower than the minimum value obtained from the
data. The difference between the two values is referred to as t.
Another parameter relevant to the conversion is the difference between the
minimum of the data and the expected value obtained from fitting, which is
referred to as r.
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
95
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
As a result, the conversion factor f can be determined as
follows:
Expected valueEntry  MinimumEntry
f 
r
A new t needs to be determined to be able to calculate the x
values of the new distribution:
Calculation Mode 3:
Monte Carlo Method
Minimum from fitting
Analysis of Situation
Objective
Minimum from data
Optimised Distribution
Expected value from fitting
tnew  f  t
t
r
Expert Survey
The new x values are then calculated as follows:
Fitting
xnew  MinimumEntry  x  MinimumFitting f  tnew
Application:
Performing arts centre
Conclusion
This scaling results in a function that has exactly the same form as the distribution
originally fitted and approximated for the relevant class (similar to a LogLogistic
distribution) whilst adhering to the selected input values.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
96
Optimised Distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
When establishing the polygonal distributions, any input value is possible for the
minimum and expected values. The form of the function is always retained; the
only parameter changing is the spread of the distribution.
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
97
Performing Arts Centre – Musiktheater Linz - Key Details
Analysis of Situation
Objective
Input values to calculate construction time:
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Average labour consumption rate - shuttering works
Average formwork ratio for the entire building
Average labour consumption rate - reinforcement works
Average reinforcement ratio for the entire building
Average labour consumption rate - concrete works
Maximum number of workers
Proportion of the average number of workers
Daily working time
Concrete quantity
Buffer
Source: Hofstadler
ChristianHOFSTADLER | 2012
MIN
MLV
MAX
1.10 wh/m²
3.00 m²/m³
8.50 wh/t
125.00 kg/m³
0.60 wh/m³
100.00 wh/hr
75.00 %
8.00 hr/d
38,000 m³
7.50 %
1.20 wh/m²
3.20 m²/m³
9.50 wh/t
129.00 kg/m³
0.65 wh/m³
110.00 wh/hr
80.00 %
8.50 hr/d
38,275 m³
10.00 %
1.35 wh/m²
3.50 m²/m³
11.00 wh/t
135.00 kg/m³
0.75 wh/m³
120.00 wh/hr
88.00 %
9.00 hr/d
39,500 m³
12.00 %
2012|Palisade Risk Conference | London
Construction Management
98
Calculation of Construction Time: Calculation Mode 3
Selection of distribution functions and input of individual values
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
CRFW
*
FRBD
CRRW
+
*
RRBD
+
CRCW
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
WRCW
WTRCW
*
/
TCRRCW
Expert Survey
Fitting
QC
/
PRRCW
Application:
Performing arts centre
DRCW
Conclusion
+
BUT,RCW
DRCW,BU
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management
99
Change of Distribution Functions
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
LogLogistic
distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Consequences
Fitting
Application:
Performing arts centre
?
Conclusion
Labour Consumption Rate
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 100
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
2.00
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
1.80
Asymmetric triangular distribution
1.60
Uniform distribution
Calculation Mode 3:
Monte Carlo Method
1.40
Beta distribution
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
7.25
7.50
Total labour consumption rate for reinforced concrete works [wh/m³]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 101
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Beta distribution
Uniform distribution
LogLogistic
distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
2.00
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
1.80
Asymmetric triangular distribution
Uniform distribution
1.60
Beta distribution
Calculation Mode 3:
Monte Carlo Method
1.40
LogLogistic distribution 0
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
7.25
7.50
Total labour consumption rate for reinforced concrete works [wh/m³]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 102
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
LogLogistic
distribution
Beta distribution
Uniform distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
2.00
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
1.80
Asymmetric triangular distribution
Uniform distribution
1.60
Beta distribution
LogLogistic distribution 0
1.40
LogLogistic distribution 1
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
Total labour consumption rate for reinforced concrete works
Source: Hofstadler
ChristianHOFSTADLER | 2012
6.75
7.00
7.25
7.50
[wh/m³]
2012|Palisade Risk Conference | London
Construction Management 103
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
LogLogistic
distribution
Beta distribution
Uniform distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
2.00
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
1.80
Asymmetric triangular distribution
Uniform distribution
Beta distribution
1.60
LogLogistic distribution 0
Calculation Mode 3:
Monte Carlo Method
LogLogistic distribution 1
1.40
LogLogistic distribution 2
1.20
Expert Survey
1.00
Fitting
Application:
Performing arts centre
0.80
0.60
0.40
Conclusion
0.20
0.00
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
Total labour consumption rate for reinforced concrete works
Source: Hofstadler
ChristianHOFSTADLER | 2012
6.75
7.00
7.25
7.50
[wh/m³]
2012|Palisade Risk Conference | London
Construction Management 104
Change of Distribution Functions
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
LogLogistic
distribution
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Consequences
Fitting
Application:
Performing arts centre
?
Conclusion
Construction Time
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 105
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
0.020
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
0.018
Asymmetric triangular distribution
Uniform distribution
0.016
Beta distribution
Calculation Mode 3:
Monte Carlo Method
0.014
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 106
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
LogLogistic
distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
0.020
Isosceles triangular distribution
Calculation Mode 1:
Deterministic
Approach
Asymmetric triangular distribution
0.018
Uniform distribution
Beta distribution
0.016
LogLogistic distribution 0
Calculation Mode 3:
Monte Carlo Method
0.014
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 107
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
LogLogistic
distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
0.020
Isosceles triangular distribution
Asymmetric triangular distribution
Uniform distribution
Beta distribution
LogLogistic distribution 0
LogLogistic distribution 1
0.018
0.016
0.014
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 108
Change of Distribution Functions
Isosceles
triangular distribution
Asymmetric
triangular distribution
Uniform distribution
Beta distribution
LogLogistic
distribution
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
0.020
Calculation Mode 1:
Deterministic
Approach
0.018
Calculation Mode 3:
Monte Carlo Method
0.014
Isosceles triangular distribution
Asymmetric triangular distribution
Uniform distribution
Beta distribution
LogLogistic distribution 0
LogLogistic distribution 1
LogLogistic distribution 2
0.016
0.012
Expert Survey
0.010
Fitting
Application:
Performing arts centre
0.008
0.006
0.004
Conclusion
0.002
0.000
220
240
260
280
300
320
340
360
380
400
420
440
Construction time, incl. contingencies [d]
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 109
Application of the Monte Carlo Method: Fitting with @RISK
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Labour consumption rates are very important for construction management and
economics.
Both clients and contractors can use this parameter in the individual project phases
(e.g. for costing, review of bids, construction scheduling and logistics, or
actual/budget comparisons).
Estimating labour consumption rates is associated with chances and risks.
Calculation Mode 3:
Monte Carlo Method
Expert Survey
Chances exist because actual values can be lower than the estimates in the
construction process; risks are posed by potential overruns.
Fitting
Various distribution functions are available to describe the distribution of values.
Application:
Performing arts centre
Conclusion
Expert surveys were conducted at Graz University of Technology in order to arrive
at a conclusion regarding the most appropriate distribution function for floor
shuttering works.
19 experts provided labour consumption rates for a range of simple to complex
layouts.
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 110
Application of the Monte Carlo Method: Fitting with @RISK
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
The results were then merged and analysed for the individual layouts.
The @RISK software was used to identify the most appropriate distribution
function.
The analysis showed that the LogLogistic distribution best described the
characteristics of the labour consumption rates.
The use of the outcomes of the analysis should result in improvements in
forecasting construction time, construction cost, productivity etc.
Expert Survey
Fitting
Application:
Performing arts centre
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 111
CASE STUDY
Analysis of Situation
Objective
Reinforced Concrete
Works – Basics
Calculation Mode 1:
Deterministic
Approach
Calculation Mode 3:
Monte Carlo Method
Assoc.Prof. Dipl.-Ing. Dr.techn.
Expert Survey
Fitting
Application:
Performing arts centre
Christian Hofstadler
Associate Professor
Institute of Construction Management and Economics
Graz University of Technology, Austria
hofstadler@tugraz.at
www.christianhofstadler.at
Conclusion
Source: Hofstadler
ChristianHOFSTADLER | 2012
2012|Palisade Risk Conference | London
Construction Management 112