Estimating Project Activity Duration

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ESTIMATING PROJECT ACTIVITY DURATION

Excavate trench —

1.0

Place formwork

Excavate trench

0.5

Place reinforcing Place formwork

0.5

In
most
scheduling
procedures, each work
activity has an associated
time duration. These
durations
are
used
extensively in preparing
a schedule.

Place reinforcing 1.0

TABLE 1: Durations and

Activity

Pour concrete

Predecessor

Duration (Days)

Predecessors for a Four Activity Project Illustration
All formal scheduling procedures rely upon estimates of the durations of the
various project activities as well as the definitions of the predecessor relationships
among tasks. The variability of an activity’s duration may also be considered.
Formally, the probability distribution of an activity’s duration as well as the
expected or most likely duration may be used in scheduling. A probability
distribution indicates the chance that a particular activity duration will occur. In
advance of actually doing a particular task, we cannot be certain exactly how long
the task will require.
A straightforward approach to the estimation of activity durations is to keep
historical records of particular activities and rely on the average durations from this
experience in making new duration estimates. Since the scope of activities are
unlikely to be identical between different projects, unit productivity rates are
typically employed for this purpose. For example, the duration of an activity D ij
such as concrete formwork assembly might be estimated as:
(1)
where Aij is the required formwork area to assemble (in square yards), P ij is the
average productivity of a standard crew in this task (measured in square yards per
hour), and Nij is the number of crews assigned to the task. In some organizations,
unit production time, Tij, is defined as the time required to complete a unit of work
by a standard crew (measured in hours per square yards) is used as a productivity
measure such that Tij is a reciprocal of Pij.
A formula such as Eq. (1) can be used for nearly all construction activities.
Typically, the required quantity of work, Aij is determined from detailed

examination of the final facility design. This quantity-take-off to obtain the
required amounts of materials, volumes, and areas is a very common process in bid
preparation by contractors. In some countries, specialized quantity surveyors
provide the information on required quantities for all potential contractors and the
owner. The number of crews working, Nij, is decided by the planner. In many
cases, the number or amount of resources applied to particular activities may be
modified in light of the resulting project plan and schedule. Finally, some estimate
of the expected work productivity, Pij must be provided to apply Equation (1). As
with cost factors, commercial services can provide average productivity figures for
many standard activities of this sort. Historical records in a firm can also provide
data for estimation of productivities.
The calculation of a duration as in Equation (1) is only an approximation to the
actual activity duration for a number of reasons. First, it is usually the case that
peculiarities of the project make the accomplishment of a particular activity more
or less difficult. For example, access to the forms in a particular location may be
difficult; as a result, the productivity of assembling forms may be lower than the
average value for a particular project. Often, adjustments based on engineering
judgment are made to the calculated durations from Equation (1) for this reason.
In addition, productivity rates may vary in both systematic and random fashions
from the average. An example of systematic variation is the effect of learning on
productivity. As a crew becomes familiar with an activity and the work habits of
the crew, their productivity will typically improve. Figure 1 illustrates the type of
productivity increase that might occur with experience; this curve is called a
learning curve. The result is that productivity Pij is a function of the duration of an
activity or project. A common construction example is that the assembly of floors
in a building might go faster at higher levels due to improved productivity even
though the transportation time up to the active construction area is longer. Again,
historical records or subjective adjustments might be made to represent learning
curve variations in average productivity.

Figure 1 Illustration of Productivity Changes Due to Learning
Random factors will also influence productivity rates and make estimation of
activity durations uncertain. For example, a scheduler will typically not know at
the time of making the initial schedule how skillful the crew and manager will be
that are assigned to a particular project. The productivity of a skilled designer may
be many times that of an unskilled engineer. In the absence of specific knowledge,
the estimator can only use average values of productivity.
Weather effects are often very important and thus deserve particular attention in
estimating durations. Weather has both systematic and random influences on
activity durations. Whether or not a rainstorm will come on a particular day is
certainly a random effect that will influence the productivity of many activities.
However, the likelihood of a rainstorm is likely to vary systematically from one
month or one site to the next. Adjustment factors for inclement weather as well as
meteorological records can be used to incorporate the effects of weather on
durations. As a simple example, an activity might require ten days in perfect
weather, but the activity could not proceed in the rain. Furthermore, suppose that
rain is expected ten percent of the days in a particular month. In this case, the
expected activity duration is eleven days including one expected rain day.
Finally, the use of average productivity factors themselves cause problems in the
calculation presented in Equation (1). The expected value of the multiplicative

reciprocal of a variable is not exactly equal to the reciprocal of the variable’s
expected value. For example, if productivity on an activity is either six in good
weather (ie., P=6) or two in bad weather (ie., P=2) and good or bad weather is
equally likely, then the expected productivity is P = (6)(0.5) + (2)(0.5) = 4, and the
reciprocal of expected productivity is 1/4. However, the expected reciprocal of
productivity is E[1/P] = (0.5)/6 + (0.5)/2 = 1/3. The reciprocal of expected
productivity is 25% less than the expected value of the reciprocal in this case! By
representing only two possible productivity values, this example represents an
extreme case, but it is always true that the use of average productivity factors in
Equation (1) will result in optimistic estimates of activity durations. The use of
actual averages for the reciprocals of productivity or small adjustment factors may
be used to correct for this non-linearity problem.
The simple duration calculation shown in Equation (1) also assumes an inverse
linear relationship between the number of crews assigned to an activity and the
total duration of work. While this is a reasonable assumption in situations for
which crews can work independently and require no special coordination, it need
not always be true. For example, design tasks may be divided among numerous
architects and engineers, but delays to insure proper coordination and
communication increase as the number of workers increase. As another example,
insuring a smooth flow of material to all crews on a site may be increasingly
difficult as the number of crews increase. In these latter cases, the relationship
between activity duration and the number of crews is unlikely to be inversely
proportional as shown in Equation (1). As a result, adjustments to the estimated
productivity from Equation (1) must be made. Alternatively, more complicated
functional relationships might be estimated between duration and resources used in
the same way that nonlinear preliminary or conceptual cost estimate models are
prepared.
One mechanism to formalize the estimation of activity durations is to employ a
hierarchical estimation framework. This approach decomposes the estimation
problem into component parts in which the higher levels in the hierarchy represent
attributes which depend upon the details of lower level adjustments and
calculations. For example, Figure 2 represents various levels in the estimation of
the duration of masonry construction. At the lowest level, the maximum
productivity for the activity is estimated based upon general work conditions. Table
2 illustrates some possible maximum productivity values that might be employed
in this estimation. At the next higher level, adjustments to these maximum
productivities are made to account for special site conditions and crew
compositions; table 3 illustrates some possible adjustment rules. At the highest
level, adjustments for overall effects such as weather are introduced. Also shown in

Figure 2 are nodes to estimate down or unproductive time associated with the
masonry construction activity. The formalization of the estimation process
illustrated in Figure 2 permits the development of computer aids for the estimation
process or can serve as a conceptual framework for a human estimator.
TABLE 2 Maximum Productivity Estimates for Masonry Work

Masonry
size

unit Condition(s)

Maximum
achievable

productivity

8 inch block

None

400 units/day/mason

6 inch

Wall is "long"

430 units/day/mason

6 inch

Wall is not "long"

370 units/day/mason

12 inch

Labor is nonunion

300 units/day/mason

4 inch

Wall

is

"long" 480 units/day/mason

Weather is "warm and dry"
or high-strength mortar is used
4 inch

Wall

is

not

"long" 430 units/day/mason

Weather is "warm and dry"
or high-strength mortar is used
4 inch

Wall

is

"long" 370 units/day/mason

Weather is not "warm and dry"
or high-strength mortar is not
used
4 inch

Wall

is

not

"long" 320 units/day/mason

Weather is not "warm and dry"

or high-strength mortar is not
used
8 inch

There is support from existing 1,000 units/day/mason
wall

8 inch

There is no support from 750 units/day/mason
existing wall

12 inch

There is support from existing 700 units/day/mason
wall

12 inch

There is no support from 550
existing wall

TABLE 3: Possible Adjustments to Maximum Productivities for Masonry
Construction
Impact

Condition(s)

Adjustment
magnitude
(%
of
maximum)

Crew type

Crew type is nonunion 15%
Job is "large"

Crew type

Crew

type

is

union 10%

Job is "small"
Supporting labor

There are less than two 20%
laborers per crew

Supporting labor

There are more than two 10%
masons/laborers

Elevation

Steel frame building with 10%
masonry
exterior
wall has "insufficient"
support labor

Elevation

Solid masonry building 12%
with work on exterior uses
nonunion labor

Visibility

block is not covered

7%

Temperature

Temperature is below 45o F

15%

Temperature

Temperature is above 45o F

10%

Brick texture

bricks

are

baked

high

Weather is cold or moist

Figure 2 A Hierarchical Estimation Framework for Masonry Construction
In addition to the problem of estimating the expected duration of an activity, some
scheduling procedures explicitly consider the uncertainty in activity duration
estimates by using the probabilistic distribution of activity durations. That is, the
duration of a particular activity is assumed to be a random variable that is
distributed in a particular fashion. For example, an activity duration might be
assumed to be distributed as a normal or a beta distributed random variable as
illustrated in Figure 3. This figure shows the probability or chance of experiencing
a particular activity duration based on a probabilistic distribution. The beta
distribution is often used to characterize activity durations, since it can have an
absolute minimum and an absolute maximum of possible duration times. The
normal distribution is a good approximation to the beta distribution in the center of
the distribution and is easy to work with, so it is often used as an approximation.

Figure 3 Beta and Normally Distributed Activity Durations
If a standard random variable is used to characterize the distribution of activity
durations, then only a few parameters are required to calculate the probability of
any particular duration. Still, the estimation problem is increased considerably
since more than one parameter is required to characterize most of the probabilistic
distribution used to represent activity durations. For the beta distribution, three or
four parameters are required depending on its generality, whereas the normal
distribution requires two parameters.
As an example, the normal distribution is characterized by two parameters, and
representing the average duration and the standard deviation of the duration,
respectively. Alternatively, the variance of the distribution
could be used to
describe or characterize the variability of duration times; the variance is the value
of the standard deviation multiplied by itself. From historical data, these two
parameters can be estimated as:
(2)

(3)

where we assume that n different observations xk of the random variable x are
available. This estimation process might be applied to activity durations directly
(so that xk would be a record of an activity duration D ij on a past project) or to the
estimation of the distribution of productivities (so that xk would be a record of the
productivity in an activity Pi) on a past project) which, in turn, is used to estimate
durations using Equation (4). If more accuracy is desired, the estimation equations
for mean and standard deviation, Equations (2) and (3) would be used to estimate
the mean and standard deviation of the reciprocal of productivity to avoid nonlinear effects. Using estimates of productivities, the standard deviation of activity
duration would be calculated as:

(4)

where
is the estimated standard deviation of the reciprocal of productivity
that is calculated from Equation (3) by substituting 1/P for x.

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