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 hw.chris.lee@oregonstate.edu

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?