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Planning
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School of Civil and Construction Engineering
CE 420/520 Engineering Planning
Lecture 12: Productivity and
Uncertainty
March 4, 2014
Instructor: Dr. H W Chris Lee [email protected]
Activity duration variance
Several factors may affect the duration of activities Production inefficiencies Learning curves Risk
Production inefficiencies
Labor productivity is usually the highest risk component of a construction project.
Various factors may affect labor productivity.
Factors that have been studied include: Working time Increasing workforce
Working time considerations
Worker transportation schedules and distances Time of year/climate enough light? Amount of advance notice needed for hiring Worker morale Safety concerns due to worker fatigue
Extending work day vs. adding a work day Working overtime inefficiency vs.
Mobilization time and project delay
Working overtime
Trades may have overtime productivity tables applicable to their own industries
A general formula for overtime efficiency (relative to efficiency for normal 40-hour work week):
Eff (%) = 100% 5%[(days 5)+ (hours 8)]Where:Eff = Worker efficency based on 100% for a regular 40-hr wkdays = Number of days worked per weekhours = Number of hours worked per day
Relative to the regular 40-hr week, what will be the expected efficiency, if a crew works for 9 hours per day for 6 days per week?
40%$
50%$
60%$
70%$
80%$
90%$
100%$
110%$
8$ 9$ 10$ 11$ 12$ 13$ 14$ 15$ 16$Hours&per&day&
Eciency&by&length&of&work&week&
5$Day$
6$Day$
7$Day$
Working overtime
Increasing workforce
Increasing the workforce on a project may: Tax existing resources Cause crowding in constructed areas Cause trade stacking Hence, result in lower productivity
Formula to calculate efficiency when increasing workforce (relative to a standard 40-hour work week):
Eff (%) = 115%15%(new_workforce / normal _workforce)Where:Eff (%) = Worker efficiency based on 100% for a normal workforce
Relative to the regular 40-hr week, what will be the expected efficiency, if a crew increase its size by 50% from its normal setup?
0.0%$
20.0%$
40.0%$
60.0%$
80.0%$
100.0%$
120.0%$
10%$ 100%$ 200%$ 300%$ 400%$ 500%$Increase$in$work$force$
Produc;vity$
Produc'vity,
Increasing workforce can lead to lower productivity
Inefficiencies other considerations
Increasing number of starting points (multiple work crews working simultaneously) Decreases negative impacts of crowding, but
communications, material deliveries, and keeping crews supplied with the necessary equipment is more complex
Quality and consistency of work among different crews
Type of work/trade, interaction between trades, size of the work area, safety
Learning curves
Projects, by definition, are unique
Although activities among projects may be similar, there are usually enough environmental or design differences that some new learning occurs on each project
The process of learning decreases the inefficiency of production until the learning process is complete
This phenomenon has been studied, and the effect is predicted through a Learning Curve
Learning curves Basically, the observation is that there is a factor which describes
the rate at which effort/unit decreases as more units are produced (in other words, efficiency increases) The factor is based on a constant and the number of units A constant is assumed that describes the learning rate for every
doubling of units Each time the number of units is doubled, the effort/unit decreases by L
The learning curve formula is: Tn = KT *N ^ sWhere:TN = Effort required to complete Nth unitN = Unit numberKT = time for 1st units = slope parameter = Log(L) / Log(2)L = rate of improvement per doubled units
Learning curves example
1st unit of construction completed in 10,000 hours Learning rate of 80% expected on doubled units How much time required to complete the 8th unit?
s = log (0.8) / log (2) = -0.3219 TN = KT x Ns T8 = 10,000 x (8)-0.3219 T8 = 5,120 hours
If the learning rate is 95%, how much time required to complete the 10th unit?
[example from Hinze (2012)]
Learning curves
0.0#
2.0#
4.0#
6.0#
8.0#
10.0#
12.0#
1# 2# 4# 8# 16#
32#
64#
128#
256#
512#
1024
#40
96#
8192
#
Eort#p
er#unit#
Units#produced#
Learning#curves#
70%$
80%$
90%$
95%$
Risk (uncertainty)
Weather Add duration to each activity based on weather data Add an activity, or activities, called weather at the
end of a schedule along the critical path Deliveries / material availability Labor issues Differing site conditions Scope changes Financial challenges
Measuring uncertainty
The risk process begins with identifying the sources of risk and developing a Risk Register
Then, based upon the risks, evaluate how an activitys durations may vary
A common method for estimating variation is to establish optimistic, likely, and pessimistic durations
Often, the deterministic duration is the likely duration
Once established, two common methods are used to determine the effect of risk on the project duration:
PERT, and Monte-Carlo simulation
PERT
The expected value, or mean of this PDF is:
(O + 4L + P) / 6 (32 + 4*38 + 50) / 6 = 39 The standard deviation is:
(P-O) / 6 (50-32) / 6 = 3
Distributions of uncertainty using three points of duration to fit to a special Beta (PERT-Beta) probability density function (PDF) Assume for a roadway sub-base design,
Optimistic = 32 days Likely = 38 days Pessimistic = 50 days
PERT
Now, suppose that the roadway design had three critical-path activities: A. Soils investigation B. Sub-base design C. Base design Key: ES PERT EF
s t
i
0 22,26,52 30
5 30
A
30 32,38,50 69
3 39
B
69 10,16,17 84
2.3 15
C
PERT
These results provide important planning information about the overall project:
The sum of the means tells us what the 50% likely duration is for the project The calculation for total standard deviation (s) provides confidence levels for
completion date
Key: ES PERT EF s t
i
0 22,26,52 30
5 30
A
30 32,38,50 69
3 39
B
69 10,16,17 84
2.3 15
C
Activity Mean duration
Standard deviation (s)
Variance (s2)
A 30 5.0 25.0
B 39 3.0 9.0
C 15 2.3 5.3
Sum 84 39.3
s for the project as a whole, then, is (39.3)1/2 = 6.27
Calculate t
he PERT pr
oject
duration a
long a crit
ical
path
PERT When many activities with different PDFs are included in PERT, it is
acceptable to assume that the project duration is normally distributed.
From the example, the project duration ~ N (84 , 6.272). The probability of completing the project in less than X days
= the shaded area
84 X
=
0 X - 84 6.27
Transforming to the standard normal distribution ~ N (0,1)
PERT What is the likelihood of finishing in 90.3 days or less?
(90.3 84) / 6.27 = 1.00 So, 84.13%
What is the likelihood to finish in 88.7 days or less? What is the likelihood to finish between 82 and 89 days?
Monte Carlo simulation
Some projects are extremely complicated, and some activities may use PDFs other than PERT Like normal, triangular, uniform, and so forth
In these cases, simple mathematical solutions are not available
Activities still get assigned a range of durations, but a computer simulation is used to establish project confidence levels
Monte Carlo simulation
Process: Assign a distribution to each individual
activity in a schedule Run many simulations with a random
duration picked for each activity Accumulate durations for the whole project Overall project duration mean and standard deviation are
calculated using the results
Software: Oracle Crystal Ball, Excel add-in @Risk
Monte Carlo simulation
QUESTIONS?