Project Scheduling

Infrastructure Management
Dr. Mark Hsu
 The Basis of a Project Plan - The Project Charter

❑ The multiple elements in the Project Charter:

1. Purpose: Why the organization is undertaking the project?
2. Objectives: What is the project’s scope?
3. Overview: What is the description of the project and its deliverables
with a list of milestones?
4. Schedule: Includes summary of schedules and milestones – Work
Breakdown Structure (WBS).
5. Resource requirements: Estimates of project expenses, both capital
and operating.
6. Personnel and stakeholders: Possible members of the project team.
7. Risk management: Attempt to remedy the damages.
8. Evaluation methods: Describes all project evaluation procedures
and quality standards.

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 The Planning Process
1. Develop and evaluate the concept of the project. Describe what
it is you wish to develop, including its basic performance
characteristics, and decide if getting such a deliverable is
worthwhile. If so, continue.
2. Carefully identify and spell out the actual capabilities that the
project’s deliverable must have to be successful. Design a
system (product or service) that will have the requisite
capabilities.
3. Create such a system (product or service), which is to say, build
a prototype deliverable.
4. Test the prototype to see if it does, in fact, have the desired
capabilities. If necessary, cycle back to step 3 to modify the
prototype and retest it. Continue until the deliverable meets the
preset requirements.

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 The Planning Process
5. Integrate the deliverable into the system for which it was designed.
In other words, install the deliverable in its required setting.
6. Validate the deliverable—which answers the question, “Now that we
have installed the deliverable, does it still work properly?”
7. If the deliverable has been validated, let the client test it. Can the
client operate the system? If not, instruct the client.
8. If the client can operate (and accepts) the deliverable, make sure
that the client understands all standard operating and maintenance
requirements. Then shake the client’s hand, present the client with a
written copy of maintenance and operating instructions, give the
client the bill, and leave.

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 Work Breakdown Structure (WBS)

❑ The work breakdown structure provides a common

framework for the natural development of the overall
planning and control of a contract and is the basis for
dividing work into definable increments from which
the statement of work can be developed and technical,
schedule, cost, and labor hour reporting can be
established.

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 Work Breakdown Structure (WBS)
❑ To use this process, one must start with the project’s
objective(s).
❑ The planner, often the PM, makes a list of the major
activities that must be completed to achieve the
objective(s). The list may be as short as two or three
activities, or as large as 20. Usually the number is
between 5 and 15. We call these Level 1 activities.
❑ The planner now takes each Level 1 activity and
delegates it to an individual or functional group. (The PM
might delegate one or more Level 1 tasks to him- or
herself.)

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 Work Breakdown Structure (WBS)
❑ The delegatee deals with the task as if it is itself a project
and makes a plan to accomplish it; that is, he or she lists
a specific set of Level 2 tasks required to complete each
Level 1 task.
❑ Again, the breakdown typically runs between 5 and 15
tasks, but a few more or less does not matter. The
process continues.
❑ For each Level 2 task, someone or some group is
delegated responsibility to prepare an action plan of
Level 3 subtasks.

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 Work Breakdown Structure (WBS)

❑ The procedure of successively decomposing larger

tasks into their component parts continues until the
lowest level subtasks are sufficiently understood so that
there is no reason to continue.
❑ As a rule of thumb, the lowest level tasks in a typical
project will have a duration of a few hours to a few days.
If the team is quite familiar with the work, longer
durations are acceptable for the lowest level tasks.

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 Work Breakdown Structure (WBS)
❑ Another simple approach to creating the WBS begins by
gathering the project team together and providing each
member with a pad of sticky-notes.
❑ After defining the project’s objectives, and Level 1 tasks,
team members then write on the sticky-notes all the
tasks they can think of that are required to complete the
project.
❑ Provides the entire team with a better understanding of
the work needed to complete the project.

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Work Breakdown Structure (WBS)

A partial WBS for an Annual Tribute Dinner project

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 Work Breakdown Structure (WBS)
❑ In doing hierarchical planning, only
one rule appears to be mandatory.
At any given level, the “generality” or
“degree of detail” of the tasks should
be roughly at the same level.
❑ When producing a painting or
drawing, an artist first sketches-in
the main compositional lines in the
scene. The artist then adds detail,
bit by bit, over the whole drawing,
continuing this process until the
work is completed.

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 Construction WBS
❑ https://www.smartsheet.com/content/constru
ction-work-breakdown-
structure#:~:text=Structures%20with%20Sma
rtsheet-
,What%20Is%20a%20Work%20Breakdown%2
0Structure%20in%20Construction%3F,chunk
s%20known%20as%20work%20packages.

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Extensions of the Everyday WBS

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 Scheduling the Project
❑ The project schedule is simply the project plan in
an altered format. It is a convenient form for
monitoring and controlling project activities.
❑ Schedule can be prepared in several formats.
The most common formats: Gantt charts and
PERT/CPM networks
❑ How to convert a project plan or WBS into these
formats?

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 Network Calculation
❑ The objectives of scheduling in Critical Path
Method (CPM):
▪ Early start time of an activity
▪ Early finish time of an activity
▪ Late start time of an activity
▪ Late finish time of an activity
▪ Total duration of the project
▪ Total float of an activity
▪ Free float of an activity
▪ Critical path of the project

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 Activity and Network
❑ Activity: the performance of a task required
to complete the project
▪ eg: design of foundations, review of design,
excavation of a trench, or paving of a parking lot
▪ An activity requires time, cost or both time and
cost
❑ Network: a diagram to represent the
relationship of activities to complete the
project

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 Network Diagrams
❑ Arrow Network ❑ Node Network

More commonly used!

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AON Network – Easy to Draw

Stage 1
Stage 2

Stage 3

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AOA Network – More Difficult to Draw

Stage 1 Stage 2

Stage 3 Stage 4 (showing a dummy task; Dummy

task require no19time and no resources!)
 Duration (D)
❑ The estimated time required to perform an
activity
❑ The time should include all resources that
are assigned to the activity.

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 Early Start and Early Finish
❑ Early start (ES): the earliest time an activity
can be started
❑ Early finish (EF): the earliest time an activity
can be finished
❑ EF = ES + D

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 Late Finish and Late Start
❑ Late Finish (LF): the latest time on which you
can finish an activity without affecting the
total duration of the project.
❑ Late Start (LS): the latest time on which you
can start an activity without affecting the
total duration of the project.
❑ LS = LF - D

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 Total Float (Slack)
❑ Total Float (TF) or Slack: the amount of time
an activity may be delayed without delaying
the completion date of the project
❑ TF or Slack = LF – EF = LS - ES

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 Free Float
❑ Free Float (FF): the amount of time an
activity may be delayed without delaying the
ES of the immediately following activity
❑ FFi = ESj – EFi
▪ i represents the preceding activity;
▪ j represents the following activity.

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 Critical Path
❑ Critical Path (CP): the path through the
network diagram, with each activity having
zero free and total float time.
❑ It determines the minimum time to complete
the project.

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 Network Calculation
❑ For the forward path, ES and EF of each
activity is established
▪ ES = Max(EF’s of all of its predecessors + lag)
▪ EF = ES + D
❑ For the backward path, LF and LS of each
activity is established
▪ LF = Min(LS’s of all of its successors - lag)
▪ LS = LF - D

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Finding the Critical Path and Time

Stage 1

Stage 2

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Finding the Critical Path and Time

Information contents in an
AON node

Critical Path: A-E-H-J

The critical path and time for sample project

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 More Node Format: Activity Box

Early Start Duration Early Finish

Task Name

Late Start Total Float Late Finish

Different computer programs have different representations.

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 Calculating Activity Slack
Activity Predecessor Duration Slack
a - 5 0
b - 4 7
c a 3 3
d a 4 2
e a 6 0
f b,c 4 3
g d 5 3
h d,e 6 0
i f 6 3
j g,h 4 0

The critical path and time for sample30project

 Managerial Implications
❑ The PM’s primary attention must be paid to activities on
the critical path.
❑ If anything delays one of these activities, the project will
be late.
❑ At the start of the project, the PM correctly notes that
activity a is on the critical path and b is not.
Can any resources reserved for
use on b be borrowed for a few
days to work on a and thereby
shorten its duration?

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 Exercise 1
Early Start Duration Early Finish

Task Name

Late Start Total Float Late Finish

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 Project Risk Management
❑ Calculating Probabilistic Activity Times
Pessimistic: b, greater less than 1 percent of the time
Optimistic: a, lower less than 1 percent of the time
(These estimates are often referred to as “at the .99 or the 99 percent
level” or at the “almost never level”)
Most likely (normal): m, which is the mode of the distribution.
𝑇𝐸 , the mean of this distribution, also referred to as the “expected time,”
can easily be found as:

𝑇𝐸 = (𝑎 + 4𝑚 + 𝑏)/6

The statistical distribution of all possible

34 times for an activity
 Calculating Probabilistic Activity Times
❑ This calculation gives an approximation of the mean of a beta
distribution. The beta distribution is used because it is far more
flexible than the more common normal distribution and because it
more accurately reflects actual time and cost outcomes.
❑ We can also approximate the standard deviation, σ, of the beta
distribution as:
𝜎 = (𝑏 − 𝑎)/6
❑ In this case, the “6” is not a weighted average but rather an
assumption that the range of the distribution covers six standard
deviations (6σ). It follows that the variance of this distribution is
estimated as:
2
(𝑏 − 𝑎) 2
𝑉𝑎𝑟 = 𝜎 = ( )
6

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 Calculating Probabilistic Activity Times

For example, to find 𝑇𝐸 and Var for activity a:

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Calculating Probabilistic Activity Times

An AON network with uncertainty information

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The Probability of Completing the Project on Time
❑ How would you respond if your boss said, “The client
just called and wants to know if we can deliver the
project on April 30, 51 working days from today. I’ve
checked, and we can start tomorrow morning.”

What is the probability that the project will

be completed in 50 days or less?

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 The Probability of Completing the Project on Time

❑ To begin, let’s evaluate the probability that path a-b-d-g-h,

which is the critical path, will be completed on or before 50
days? We can find the probability by finding Z in the following
equation:
D− μ
Z=
𝜎𝜇2
D = the desired project completion time.
μ = the sum of the 𝑇𝐸 activities on the path being investigated.
𝜎𝜇2 = the variance of the path being considered (the sum of the variances of
the activities on the path)

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 The Probability of Completing the Project on Time

❑ The exact nature of Z will become clear shortly. Using the

problem at hand, μ = 47 days, D=50 days, and
𝜎𝜇2 =1.78+.25+.00+4.00+1.36=7.39 days. (The square root
of 7.39 = 2.719.)
❑ Using these numbers, we find

Z = (50 − 47)/2.719 = 1.10

The probability is .8643 (based on the Table 5-7)
❑ This would include all possibilities from a combination of
all optimistic times to a combination of all pessimistic times
and everything in between.

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41
 The Probability of Completing the Project on Time

❑ Because of uncertainty, other paths may turn out to be critical,

possibly delay the project.
❑ Therefore, calculating the probability that the entire project is
completed by some specified date requires calculating the
probability that comprise the project are finished by the
specified time.
❑ Similar calculations are next done for paths: a-b-c-f, a-b-e-h,
and a-b-d-f. The probability of each of these paths being
completed by day 50 are 98.5%, 97.8%, and virtually 100%,
respectively.
❑ Based on this, the probability that the entire project is
completed by day 50 is calculated as:
.864* .985* .978* .1.000 = .832 or 83.2%
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 Selecting Risk and Finding D
❑ Assume that a client is very important, very demanding. The
client insists on a firm date. How sure do you wish to be about
being on time? (Don’t say 100%!)
❑ Carefully considering the matter, you decide that you want a
95% probability of meeting your promised completion date.
When should you tell the client to expect delivery?
❑ Referring to Table 5-7, for a .95 probability, Z will have a value
of 1.645. Therefore:

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 Selecting Risk and Finding D
❑ Note, this result indicates that there is a 95% chance
of completing path a-b-d-g-h in 51.5 days. Remember
that this does not mean that there is a 95% chance of
completing the entire project in 51.5 days.
❑ We can arrive at the same answer using the Excel
NORMINV function. The syntax of this function is
= NORMINV(probability, 𝜇 , 𝜎𝜇 )
In our example, this function would be used as:
= NORMINV(.95, 47, 2.719)

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 The Gantt Chart

A Gantt Chart

A Gantt Chart
showing critical
path

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 The Gantt Chart

A Gantt Chart showing expected durations, critical

path, milestone, and resource requirements

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 The Gantt Chart

A progress report showing actual progress vs. baseline

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 The Gantt Chart
❑ The major advantage of the Gantt chart is that it is easy
to read! (Such charts commonly decorate the walls of
the project office.)
❑ It can contain a considerable amount of information and
is an excellent communication device about the state of
a project.
❑ Its major weakness is that it does not easily expose the
project’s technology, that is, the technical relationship
between a project’s many activities.
❑ PERT/CPM networks are often used as complements
to Gantt charts.

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 Precedence Diagramming

Finish to Start: Activity 2 must not start before Activity 1 has been completed. (2 days after)
Start to Start: Activity 5 cannot begin until Activity 4 has been underway for at least 2 days.
Finish to Finish: Activity 7 must be complete at least one day before Activity 8 is completed.
Start to Finish: Activity 11 cannot be completed before 7 days after the start of Activity 10.

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