Planning and scheduling Techniques.ppt

Chapter 3
Project Management Techniques
March, 2018
CEng 5204 (Construction Management)

Planning
 Planning is a general term that sets a clear road map that should be
followed to reach a destination.
 Planning aims at formulation of a time based plan of action for
coordinating various activities and resources to achieve specified
objectives.
 Planning can be thought of as the definition and sequencing of the
work packages within a given project. That is:
 Planning = Work Breakdown + Work Sequencing

Planning
 Project planning is the process of identifying all the activities
necessary to successfully complete the project.
 Planning leads to a refinement of the scope of work as established in
the contract documents.
 Planning in it’s broader perspective involves advance thinking as to
what is to be done, what are the activities, how it is to be done, when it
is to be done, where it is to be done, what is needed to do it, who is to
do it, and how to ensure that it is done;
 A good plan reduces uncertainty and improves efficiency.

Planning
 The process involved in construction planning can broadly be divided
into two stages;
 Planning time
• what is to be done?
• what are the activities involved?
• how it is to be done?
• when it is to be done?
• where it is to be done?
 Planning resource
• what is needed to do it?
• who is to do it?

 Proper design of each element of the project
 Procurement of materials well in advance
 Proper arrangement of repair of equipment and machinery
 Employment of trained and experienced staff on the project
 To provide incentive for good workers
 To arrange constant flow of funds for the completion of project
 To provide proper safety measures and ventilation, proper arrangement
of light and water.

Construction Project Planning:
 Activities involved in construction planning
1. Define the scope of work, method statement, and sequence of work.
2. Generate the work breakdown structure (WBS) to produce a complete list
of activities.
3. Develop the organization breakdown structure (OBS) and link it with work
breakdown structure o identify responsibilities.
4. Determine the relationship between activities.
5. Estimate activities time duration, cost expenditure, and resource
requirement.
6. Develop the project network.

Defining the scope of work:
Since all activities involve consumption of different resources to
different extents, it is important that the scope of work involved is
properly and, to the extent possible, completely defined.
Any addition, deletion or modification in the scope could have serious
repercussions in terms of time of completion and cost.
For example if felling trees and leveling the ground is added (at a later
date) to the scope of a contractor awarded a job for construction of
roads, would obviously cause difficulties!!

Identifying activities involved:
This part of planning is very closely linked to defining the scope,
It involves identifying activities in a particular job.
Since different activities involved consume different physical
resources to varying extents, it is crucial that these activities are
exhaustively listed, along with the resources required.
For example, though different agencies may be concerned with
‘environmental impact assessment’ it is important for them to identify
the tools or parameters each will be using so to plan effectively.

Establish project duration:
This can be done only with a clear knowledge of the required resources,
productivities, and inter- relationships.
This information is used to prepare a network and other forms of
representations outlining the schedules.
It may be remembered that the duration required for any activity is related to
the resources committed and it may be possible to reduce the project
duration by increasing the resource commitment, even at additional cost.
Thus a balance between time and project cost is required to arrive at an
optimum level of resource commitment.

Type of Project Plans
Time Plan
Resources Plan
 Manpower Plan
 Material Plan
 Construction Equipment Plan
 Finance Plan

Time planning
Time is the essence of all construction projects, and contracts often have
clauses outlining awards (bonus payments) or penalties (as liquidated
damages) for completing a work ahead or later than a scheduled date.
some of the common reasons for delays could be a sluggish approach
during planning,
 delay in award of contract
 changes during execution
 alterations in scope of work
 delay in payments
 slow decision making
 delay in supply of drawings and materials and
 labor trouble.

Cont’d…
Several reasonably well-established techniques for time planning are
available:
commonly used (or ‘scheduling’) activities are:
 Critical path method (CPM),
 Programme evaluation and review technique (PERT),
 Precedence network analysis (PNA),
 Line of balance technique (LOB),
 Linear Programme chart (LPC) and
 Time scale network (TSN).
The choice of the method to be used in a particular case depends on
the intended objective, nature of the project, target audience, etc.

Resources planning
a resource plan, combines manpower, materials, equipment, budget or
cash flow, is also drawn up for a project to show the overall
requirement of the different resources in the project.
• Such a plan can be prepared only on the basis of the schedule of a
project.
• In a manner of speaking, the relationship between planning for time and
other resource is similar to the relationship between design and
analysis of a structure.

Manpower planning
 This plan focuses on :
• estimating the size of work force,
• division in functional teams and scheduling the deployment of
manpower.
• establishing labor productivity standards,
• providing suitable environment and financial incentives for
optimum productivity, and
• grouping the manpower in suitable functional team in order to get
the optimum utilization.

Material plan
 The material plan involves
• identification of required materials, estimation of required
quantities,
• defining specification and forecasting material requirement besides
identification of appropriate source(s),
• inventory control,
• procurement plans, and
• monitoring the usage of materials.

Construction equipment planning
Modern construction is highly mechanized
The role of heavy equipment in ensuring timely completion of
projects cannot be overemphasized.
Induction of modern equipment could improve productivity and
quality besides reducing cost.
At the same time it should be borne in mind heavy equipment are
very costly and should be optimally utilized in order to be productive.
It is also important that the characteristics of equipment are kept in
mind when drawing up an equipment plan.

Finance plan
 Large construction projects require huge investments, and a long
time to complete, it is obvious that all the money is not required at
any one point in time.
 Contractors fund their projects from their
 Working capital and
 a combination of avenues such as mobilization advance for the
project, advance payments, and credits from suppliers against
work done.

Project costs start slowly, but increase sharply once the project
enters the construction phase
Ability to influence decisions falls off sharply as time on the project
passes
Time-Cost Relationship
Influence/
Project cost
TIME

Projects build up slowly as workers and equipment are brought to the project
and mobilized.
Early on only a few activities may occur, but once mobilization is complete work
proceeds at a rapid pace until the end.
Production Curve (s-curve)
TIME

Definition of Scheduling
 Schedules establish the start, duration and completion date of a
project or task
 Scheduling is the determination of the timing and sequence of
operations in the project and their assembly to give the overall
completion time.
 It is a timetable which formulates the activities that must be
accomplished to reach a certain goal or objective
 The timing and sequence of tasks within a project. A schedule consists
of many tasks, tasks dependencies and time oriented project
information.

Construction Planning
 Essential aspects of construction planning include the generation
of required activities, analysis of the implications of these
activities, and choice among the various alternative means of
performing activities.
 In developing a construction plan, it is common to adopt a primary
emphasis on either cost control or on schedule control.
Alternative Emphases in Construction Planning

One of the first question an owner or project manager wants
answered is “when can the project be completed”?
Schedules identify all the tasks required to be completed on a
project, determine how long each will take and place them in
logical order.
Schedules let people and organizations know in advance when to
expect a certain action to take place.
Schedules start date determines when goods and services need
to be brought to the job site, when a work force needs to be
mobilized and when equipment rental begins
Why Construction scheduling ?

When to Schedule?
Schedules are useful
 Knowing the activities timing and the project completion time.
 Having resources available on site in the correct time.
 Making correction actions if schedule shows that the plan will result
in late completion.
 Assessing the value of penalties on project late completion.
 Determining the project cash flow.
 Evaluating the effect of change orders on the project completion
time.
 Determining the value pf project delay and the responsible parties.

Planning Versus Scheduling
 A plan shows the activities and their logic relationships. The
activities in a plan do not have specific start and end dates.
 A schedule establishes the specific start and end dates for the
activities. It also establishes the total project duration. A schedule
determines what resources are needed when for how long for
which activity

Defining Work Tasks /work breakdown
The Work Breakdown Structure (WBS) is a tool that defines a
project and groups the project’s discrete work elements in a way
that helps organize and define the total work scope of the
project.
WBS is structured in accordance with the way the work will be
performed and reflects the way in which project costs and data
will be summarized and eventually reported.

Methodology of WBS
A project is split to different levels from upper end to lower end.
It should be borne in mind that once the breakdown is
exhaustive, operations such as resource allocation, project
monitoring, etc. become simplified.
An illustrative example of such an exercise is shown
schematically in Figure 1, shows the ‘whole to part’ relation
between the project, sub-projects, tasks, work packages and
activities for the construction of a hospital complex.

Scheduling Techniques
1. Bar (Gantt) charts
2. The networking scheduling technique
• The critical path method (CPM)
• The performance (program or project) evaluation technique (PERT)
• Precedence Diagramming Method (PDM)
4. Applicable Software's:
• Primavera
• MS Project

1. Gantt (bar) charts:
 It is one of the most popular and oldest project planning techniques for
scheduling, reporting, and control overall project.
 This technique present the project schedule plotted to a horizontal line
scale graphically represents the progress of a project versus the time
frame within which it must be completed.
 The bar lines represent the time period allocated to each operation and
the relationship between the commencement and completion of each
can be readily observed.
 They are easy to understand and very useful in reviewing progress.

To prepare a Gantt chart:
1. List each of the discrete project activities or tasks that needs to be
completed.
2. Establish the execution sequence of these activities.
3. Estimate the duration of these activities.
4. List all activities in chronological order and determine those that can be
carried out simultaneously and those that must be carried out
sequentially.
5. Consider the resource requirements and allocations for each activity.

example of the construction of a boundary wall

Cont’d…
Advantages of Bar chart:
Useful to report information to people who are concerned about a
project but may not be involved in day-today management.
A simple format and readily understood at all levels of management.
It can provide a quick, visual overview of a project in convenient way to
monitor job progresses, schedule equipment and crews and record
project advancement.
Disadvantages:
Interdependencies among activities are difficult to show. The bar chart
itself doesn’t provide a basis for ascertaining which activities are critical
and which are floaters.
It is not an adequate planning and scheduling tool because it doesn’t
portray a detailed, integrated and complete plan of operations.

2. The Networking Schedule Technique
Terminology Used in Planning Techniques:
Activity:
Performance of a specific task, operation, job or function which
consumes time and resources and has a definite beginning and end is
called activity.
Event or Milestone:
An instantaneous point in time marking the beginning or the end of one
or more activities is called event.
Unlike an activity, does not consume time or resources .Hence,
expresses a state of being.
Activities take place between events.

Cont’d…
Network:
It is the diagrammatic representation of a work plan showing the
activities step by step, leading to the established goal. It depicts the
inter-dependence between the various activities, (i.e. which activities
can be done together and which activities must precede or succeed
others).
Network Representation:
While drawing a network, certain rules are followed while numbering the
events or nodes. For example
 same node number is not to be used twice in the network;
 tail node number is smaller than the head node;
 numbering starts from left hand top and ends in right hand bottom.

Types of networks
AOA (Activity-on-Arrow) and
AON (Activity-on-Node).
AOA (Activity-on-Arrow): in this system an activity is graphically
represented by an arrow from left to right. The description of the
activity is written above the arrow and the time taken to complete the
activity is written below it.
An event is graphically represented by a number enclosed in a circle.
The beginning of an activity is marked by a ‘tail event’ or preceding
event and the end by a ‘head event’ or succeeding event.

Cont’d…
AON (Activity-on-Node): Here activities are represented on the node,
and arrows are used to show the dependency relationship between the
activity nodes. The time required to complete the activity is also indicated
in the node.
Fig, Network on A-O-N

Types of activities relationships
 Four types of relationships among activities can be defined as
described and illustrated below. Typically, relationships are defined
from the predecessor to the successor activity.
a. Finish to start (FS). The initiation of the successor activity
depends upon the completion of the predecessor activity.
b. Finish to finish (FF). The completion of the successor activity
depends upon the completion of the predecessor activity.
c. Start to start (SS). The initiation of the successor activity depends
upon the initiation of the predecessor activity.
d. Start to finish (SF). The completion of the successor activity
depends upon the initiation of the predecessor activity.

Types of activities relationships
Figure: Types of activities relationships

Rules for developing Networks:
Rule 1
No activity can commence until all preceding activities have been
completed.
From the above figure, Concrete foundation can commence only after
‘procure cement’, ‘procure aggregate’ and ‘Install concrete mixer’ are all
completed.

Cont’d…
Rule 2
A dummy activity is introduced in the network either to show
dependency or to avoid duplicate numbering on activities.
A dummy activity: is an artificial activity shown by a dotted line
and used to define interdependence between activities and
included in a network for logical and mathematical reasons..
This activity does not involve consumption of resources, and
therefore does not need any time to be ‘completed.’

Cont’d…
From the above figure, ‘erect beam’ can be taken up only when
both ‘concrete pier’ and ‘Precast beams’ are completed.
Dummy activity 2-3 shows this dependency and also avoids
duplicated numbering of ‘concrete pier’ and ‘Precast beam’.

Cont’d…
Rule 3
 The logical placement of an activity in the network is governed by the
following three considerations.
• Which activity must be completed before this activity can commence?
(precedence)
• Which activity can be carried out along with this activity? (Concurrence).
• Which activity can not commence until this activity is completed?
(Subsequence).
 Consider the following activities pertaining to the construction of mass
concrete foundation:
Excavation : 3 days
Prepare shuttering : 2 days
Fix shuttering : 1 day
Concrete foundation : 1 day

Cont’d…
The placement of various activities in the network is shown
below.

Cont’d…
Rule 4
No activity should lead to previous event i.e. there must not be any
‘looping’
For example, if activity A precedes activity B, activity B precedes activity C,
and activity C precedes activity A, then the project can never be started or
completed! Something is wrong with the logic or thinking.

Cont’d…
Rule 5
In any network there must be one start and one finish (with any number of
activities in between) i.e. no activity should be left dangling.
(a) Incorrect network as activity 2-3 & 2-4 are left dangling

Cont’d…
(b) Correct form of the network with one start and one finish

Preparation of Network Diagram
Creating a network diagram involves:
Preparing a work breakdown structure for the project.
Determining the interdependency among the activities,
Estimating the duration for each activity and
Finally drawing the network.

Preparing the work breakdown structure:
This involves defining the constitute activities of the project.
For example works requiring similar labor, similar plant and
equipment, etc. may be classified in same group.
Each activity under different divisions of work breakdown structure
should be in manageable unit of work .
Resources should be considered while defining the activities, and
their requirement estimated.

Inter dependence of activity:
For each activity the planner must know which activity precedes or
succeeds a particular activity and which activity can be taken up
concurrently with this particular activity.
The answer to these questions will furnish the dependency
relationships between the activity in question and its immediately
following activities.
Such considerations define certain logic for the network and the
plan of construction of the project.

Estimating duration for an activity:
In most scheduling procedures, each work activity has associated
time duration.
These durations are used extensively in preparing a schedule.
The time required to complete an activity should depend not only
on the quantum of work to be executed (Q) but also the resources
allocated (R) and the (unit) productivity of the resources (P).

Cont’d…
 Simply put, the time required (T) to complete an activity
can be calculated using the following relationship:
T = Q / (RxP)
Where T= the time required to complete an activity.
Q= the quantum of work to be executed.
R= resources allocated
P= the unit productivity of the resources.

Cont’d…
The duration for an activity can be estimated using several approaches:
-Time study approach
-Previous project data
-Guesstimating approach
-Range estimates
-Estimates from vendors and subcontractors

Cont’d…
Time study approach:
In this approach the time T=Q/(p x n),
where Q= Total quantity of work,
p= productivity factor,
n= normal size of crew.
 It can be noticed that Q, p, and n are all dependent on the
availability of the information or data and at the time of estimate,
the information all the three variables would be difficult to get.

CPM and PERT
Critical Path Method (CPM)
 developed by Du Pont in 1957 for construction of new
chemical plant and maintenance shut-down
 handles deterministic task times
 good for jobs having repetitive nature. E.g. Construction
Project Evaluation and Review Technique (PERT)
 developed by U.S. Navy (1958) for missile program
 handles multiple task time estimates (probabilistic nature)
 especially good for non-repetitive jobs (R & D work)

Both PERT and CPM are important quantitative tools to
 determine the critical path
 establish the most likely time estimated for individual tasks by
applying statistical models
 calculate boundary time (window) for a particular task
Normally, both techniques(PERT and CPM) are driven by
information already developed in the project planning step like:
 Estimates of efforts
 Decomposition of tasks
CPM and PERT

CPM and PERT
CPM/PERT can answer the following important questions:
 How long will the entire project take to be completed? What
are the risks involved?
 Which are the critical activities or tasks in the project which
could delay the entire project if they were not completed on
time?
 Is the project on schedule, behind schedule or ahead of
schedule?
 If the project has to be finished earlier than planned, what is
the best way to do this at the least cost?

CPM and PERT – simple steps
1. Identify activities
2. Determine sequence
3. Create network/develop network diagram
4. Determine activity times
5. Find the critical path based on:
 Earliest & latest start times
 Earliest & latest finish times
 Slack

Important Terminologies in CPM/PERT
In PERT and CPM, the greatest amount of management
attention is focused on activities on the critical path.
 A path is a route through a network that begins at the first
activity and ends at the last activity.
 The length of a path is the sum of times for the activities on
the path.
 The critical path is the longest path in a network (path with
highest length)

Activity
– A task or a certain amount of work to be done in the project
– Requires time to complete
– Usually represented by an arrow in a network diagram
Event
 Signals the beginning or ending of an activity
 Designates a point in time
 Usually represented by a circle (node) in a network diagram
Network
 Shows the sequential relationships among activities using
nodes and arrows
Important Terminologies in CPM/PERT

Application Area of CPM
CPM is commonly used with all forms of projects, including
 construction,
 software development,
 research projects,
 product development, and
 engineering, etc.
Any project with interdependent activities can apply this method of
mathematical analysis.

Critical Path Method (CPM)
CPM is a network diagramming technique used to predict total
project duration based on critical path.
 A critical path for a project is the series of activities that
determines the earliest time by which the project can be
completed.
 The critical path is the longest path through the network
diagram and has the least amount of slack or float.
 Slack or float is the amount of time an activity can be delayed
without delaying a succeeding activity or the project finish
date.

Characteristics of CPM
CPM does not incorporate uncertainties in job times,
 It is mostly suitable for the jobs of repetitive in nature where the
activity time estimates can be predicted with considerable
certainty due to the existence of past experience.
Example: construction type projects
CPM assumes that activity time is proportional to the resources
allocated to it (within a certain limit).
The objective of using CPM is to determine Critical path that
results in minimum project duration while floats available with each
activity.

Activity Resource Estimating
Before estimating activity durations, you must have a good idea of
the quantity and type of resources that will be assigned to each
activity.
Consider important issues in estimating resources:
 How difficult will it be to complete specific activities on this
project?
 What is the organization’s history in doing similar activities?
 Are the required resources available?
People doing the work should help create estimates, and an expert
should review them.

Inputs:
 Activities from work breakdown structure
 Precedence relationships among activities
(what activities must be completed before other activities can
be started)
 One time estimate for each activity (how long does it take to
do the activity?)
Outputs:
 Project completion time
 Start and end times for each activity
 Critical path: activities that must be finished on time so that
the project will be completed on time
CPM – Inputs and Outputs

Consider the following project network. Find the critical path.
Critical Path Analysis – Simple Example 1

List of all possible sequences (chain/path) of activities (Enumeration
method):

Critical Path Analysis – Structured Approach
Critical path calculations involve TWO passes
 Forward Pass (Early start schedule): the process of
calculating the earliest event time in a forward direction. (left
to right)
 Backward Pass (Late start schedule): the process of
calculating the latest event time in a backward direction.
(right to left)
Note:
 If two/more activities enter to one activity, TE will be the max, of
the two in forward pass.
 If two/more activities enter to one activity, TL will be the min, of the
two in backward pass.

Critical path Analysis- Forward Pass
Start at the beginning of CPM network to determine the earliest
activity times.
 Earliest Start Time (ES)
 The earliest possible time at which the activity can
start
ES = maximum EF of immediate predecessors
 Earliest finish time (EF)
 The earliest possible time at which the activity can
finish.
EF= ES + t
Where, t = duration of the activity

Critical Path Analysis- Backward Pass
Determines latest activity times by starting at the end of CPM
network and moving back.
 Latest Start Time (LS)
 The latest time at which the activity can start without
causing the project to finish after its earliest finish time.
 LS= LF – t
 Latest finish time (LF)
 The latest time at which the activity can finish without
causing the project to finish after its earliest finish time.
 LF = minimum LS of immediate successors

Critical Path - Float/Slack
Float is the maximum amount of time that an activity can be
delayed before it becomes a critical activity, i.e., delays completion
of the project.
Float/Slack = LS – ES = LF – EF
Activities on the critical path have zero slack.
Non-critical activities have positive slack.
Slack could be:
 Free slack or free float is the amount of time an activity can be
delayed from its early start without delaying the early start of
any immediately following activities.
 Total slack or total float is the amount of time an activity can be
delayed from its early start without delaying the planned project
finish date.

Steps in CPM Analysis
Draw the CPM network
Analyze the paths through the network
Determine the float for each activity
 Compute the activity’s float
Float = LS - ES = LF - EF
Find the critical path, (that is, the sequence of activities and
events where there is no “slack” or Zero slack)
Find the project duration – the minimum project completion time.
Find activities starting and finishing time.

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
CPM Network example 1

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
0 6
0 8
0 5
ES and EF Times

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
0 6
6 21
6 23
0 8
0 5
8 21
5 14
ES and EF Times

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
0 6
6 21
6 23
23 29
21 30
0 8
0 5
8 21
5 14
21 33
ES and EF Times
Project’s EF = 33

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
21
LS and LF Times
21 33
21 33
21
21 30
24 33
21
21 29
27 33
21
6 23
21
0 6
21
6 21
21
0 8
21
5 14
21
8 21
21
0 5

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
21
LS and LF Times
21 33
21 33
21
21 30
24 33
21
21 29
27 33
21
6 23
10 27
21
0 6
21
6 21
9 24
21
0 8
21
5 14
12 21
21
8 21
8 21
21
0 5

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
21
LS and LF Times
21 33
21 33
21
21 30
24 33
21
21 29
27 33
21
6 23
10 27
21
0 6
3 9
21
6 21
9 24
21
0 8
0 8
21
5 14
12 21
21
8 21
8 21
21
0 5
7 12

a, 6
f, 15
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9
i, 6
j, 12
21
LS and LF Times
21 33
21 33
21
21 30
24 33
21
23 29
27 33
21
6 23
10 27
21
0 6
3 9
21
6 21
9 24
21
0 8
0 8
21
5 14
12 21
21
8 21
8 21
21
0 5
7 12
0
0 0
3
3
4
4
3
7
7

7
6
5
4
3
2
1
te =11
te =12
te =7
te =7
te =13
te =10
te =8
te =11
te =10
te =4

7
6
5
4
3
2
1
te =11
te =12
te =7
te =7
te =13
te =10
te =8
te =11
te =10
te =4
12/19
42/52
0/11
12/16 18/31
11/18
Legend: ES/EF
11/21
18/26
0/12 31/42

Example Flow Diagram with Critical Path
7
6
5
4
3
2
1
t1-3=11
0|0|11|11
t1-2=12
0|2|12|14
t3-4=7
11|11|18|18
t2-5=7
12|24|19|31
t4-5=13
18|18|31|31
t3-6=10
11|32|21|42
t4-6=8
18|34 |26|42
t5-6=11
31|31|42|42
t6-7=10
42|42|52|52
t2-4=4
12|14|16|18
ES|LS|EF|LF

CPM - Exercise 1
Consider the following network diagram. Applying
CPM, find:
 the project period
 activities ES and EF, LS and LF
 float for each activity
 the critical path

Pause
PERT – Concept and Analysis

PERT is a model for project management designed to analyze the
tasks involved in completing a given project.
It is used more in projects where time, rather than cost, is the major
factor.
Unlike CPM, PERT is suitable for Non-repetitive projects (eg. R & D
work), where job-times are not estimable with certainty a priori.
Thus, PERT takes uncertainty of activity durations in a project into
account
PERT
91

Project evaluation and review technique (PERT) – inputs
 Activities from work breakdown structure
 Precedence relationships among activities
 3 time estimates for each activity
Project evaluation and review technique (PERT) – outputs
 Estimated start and end dates for each activity
 Normal distribution for project completion date
 Probability of finishing the project by the mean date = 50%
 Standard deviation
 Can compute probability of finishing project by the due date.
92
PERT

PERT - Three Point Estimates
PERT is based on the assumption that an activity’s duration
follows a probability distribution instead of being a single value.
Three time estimates are required to compute the parameters of an
activity’s duration distribution:
 Pessimistic time (b) - the time the activity would take if things
did not go well. (E.g. likely occur 1 in 20)
 Most likely time (m) - the consensus best estimate of the
activity’s duration. (E.g. Modal value)
 Optimistic time (a ) - the time the activity would take if things
did go well. (E.g. Would be exceeded only one time in 20)
93

Assumptions in PERT :
1. The activity durations are independent. i.e. the duration of one
doesn’t affect another.
2. The activity durations follow Beta – distribution.
Therefore, in PERT analysis
Activity Mean Time Estimate, te = (a + 4m + b)/6
Activity Standard Deviation, e = (b – a) /6
Activity Variance Estimate, 2
e = (b – a)2 /36
94
PERT - Three Point Estimates

Application of te and 2
e :
 Use of te and 2
e allows one to make probabilistic estimates
of completion dates.
 By summing the te’s of the activities on the critical path
you can estimate the duration of the entire project.
 By summing the Variance (2
e) of the activities on the
critical path, you can estimate the total variance of the
critical path and make one-sided interval estimates of
project completion times.
95
PERT - Time Estimates

Example 1. If the optimistic time, the most likely time and pessimistic
time of completing a project are 8 days, 10days and 24 days,
respectively, find the expected time that the project can be completed.
Activity mean time = 8 workdays + 4 X 10 workdays + 24 workdays
6
= 12 days
The answer is 12 days.
96
PERT - Time Estimates

PERT - Example Network Flow Diagram
7
6
5
4
3
2
1
B
A
E
C
D
G
F
H
I
J
Example 2. Find the critical path and the expected time of
completion of a project given the following network diagram and
three probabilistic duration of activities.
7:58 AM
97

PERT - Example Activity Characteristics
A 1-2 10 12 14
B 1-3 9 11 13
C 2-4 1 3 11
D 2-5 1 8 9
E 3-4 1 7 13
F 3-6 5 10 15
G 4-5 8 13 18
H 4-6 1 7 19
I 5-6 6 10 20
J 6-7 6 10 14
Activity a m b
98

A 1-2 10 12 14 12 2/3
B 1-3 9 11 13 11 2/3
C 2-4 1 3 11 4 5/3
D 2-5 1 8 9 7 4/3
E 3-4 1 7 13 7 6/3
F 3-6 5 10 15 10 5/3
G 4-5 8 13 18 13 5/3
H 4-6 1 7 19 8 9/3
I 5-6 6 10 20 11 7/3
J 6-7 6 10 14 10 4/3
Activity a m b te e
99
PERT - Example Activity Characteristics

7
6
5
4
3
2
1
te =11
te =12
te =7
te =7
te =13
te =10
te =8
te =11
te =10
te =4
100

7
6
5
4
3
2
1
te =11
te =12
te =7
te =7
te =13
te =10
te =8
te =11
te =10
te =4
ES=18
ES=0
Find ES, EF, LS and LF times
ES=12
ES=52
ES=42
ES=31
ES=11
101

1-2 10 12 14 12 2/3 0 2 12 14
1-3 9 11 13 11 2/3 0 0 11 11
2-4 1 3 11 4 5/3 12 14 16 18
2-5 1 8 9 7 4/3 12 24 19 31
3-4 1 7 13 7 6/3 11 11 18 18
3-6 5 10 15 10 5/3 11 32 21 42
4-5 8 13 18 13 5/3 18 18 31 31
4-6 1 7 19 8 9/3 18 34 26 42
5-6 6 10 20 11 7/3 31 31 42 42
6-7 6 10 14 10 4/3 42 42 52 52
a m b te e ES EF LF
LS
102

PERT – Network Diagram with Critical Path
7
6
5
4
3
2
1
t1-3=11
0|0|11|11
t1-2=12
0|2|12|14
t3-4=7
11|11|18|18
t2-5=7
12|24|19|31
t4-5=13
18|18|31|31
t3-6=10
11|32|21|42
t4-6=8
18|34 |26|42
t5-6=11
31|31|42|42
t6-7=10
42|42|52|52
t2-4=4
12|14|16|18
ES|LS|EF|LF
103

1. Draw the project network.
2. Compute the expected duration of each activity, te
3. Analyze the paths through the network (ES/EF/LS/LF) and find
the critical path.
The length of the critical path is the mean of the project duration
probability distribution which is assumed to be normal.
4. Find the standard deviation of the project duration probability
distribution by adding the variances of the critical activities (all
of the activities that make up the critical path) and taking the
square root of that sum.
5. Probability computations can now be made using the normal
distribution table.
2
2
2
2
1 ... en
e
e
cp 


 



104
PERT – Analysis Procedure

Probability Computation: the probability that a project is
completed within specified time.
Z =
x - 
e
Where,
 = te = project mean time
e = project standard deviation from the mean
x = (proposed ) specified time
105
PERT – Analysis

Example 1. A 40km asphalt road project has an expected completion
time of 40 weeks, with a standard deviation of 5 weeks. What is the
probability of finishing the project in 50 weeks or less?
Solution:
Assume project completion time follows a normal distribution.
106
PERT Analysis - Examples

Normal Distribution
Standardized
Normal Distribution
0
.
2
5
40
50





e
e
t
X
Z

107

Standardized Normal Probability Table (Portion)
Z - Table
Answer: The probability of completing the project in 50days or less is 0.98 or
98%.
108

1-3 9 11 13 11 2/3 4/9
3-4 1 7 13 7 6/3 36/9
4-5 8 13 18 13 5/3 25/9
5-6 6 10 20 11 7/3 49/9
6-7 6 10 14 10 4/3 16/9
a m b te  e ( e)2
The sum of te’s (Expected time of completing the project) = 52 days
Variance = 130/9 = 14.4
Std Dev = 3.8
The probability that the Project duration is less than 60 days = P(X<60)
Same as the Probability that Z < (60-52)/3.8 = 2.1
Therefore: P(X<60) = Pr(Z<2.1) = 0.98214 or 98.2% (from z-Table)
Example 2: Given the following critical path of a project, find the
probability that the project be completed in less than 60days
109

Example 3. Consider the following PERT network.
a. Find the critical path and project due date
b. What is the probability that the project can be completed in
24 days?
c. What due date has about 90% of the project work be
completed?
110

Activity Precedence a (hr.) m(hr.) b(hr.)
A -- 4 6 8
B -- 1 4.5 5
C A 3 3 3
D A 4 5 6
E A 0.5 1 1.5
F B,C 3 4 5
G B,C 1 1.5 5
H E,F 5 6 7
I E,F 2 5 8
J D,H 2.5 2.75 4.5
K G,I 3 5 7
111

Activity Precedence a (hr.) m(hr.) b(hr.) te (hr.) Var.
A -- 4 6 8 6 4/9
B -- 1 4.5 5 4 4/9
C A 3 3 3 3 0
D A 4 5 6 5 1/9
E A 0.5 1 1.5 1 1/36
F B,C 3 4 5 4 1/9
G B,C 1 1.5 5 2 4/9
H E,F 5 6 7 6 1/9
I E,F 2 5 8 5 1
J D,H 2.5 2.75 4.5 3 1/9
K G,I 3 5 7 5 4/9
b) Critical Path and project due date
112

Activity Prece. a (hr.) m(hr.) b(hr.) te (hr.) Var. ES EF LS LF
A -- 4 6 8 6 4/9 0 6 0 6
B -- 1 4.5 5 4 4/9 0 4 5 9
C A 3 3 3 3 0 6 9 6 9
D A 4 5 6 5 1/9 6 11 15 20
E A 0.5 1 1.5 1 1/36 6 7 12 13
F B,C 3 4 5 4 1/9 9 13 9 13
G B,C 1 1.5 5 2 4/9 9 11 16 18
H E,F 5 6 7 6 1/9 13 19 14 20
I E,F 2 5 8 5 1 13 18 13 18
J D,H 2.5 2.75 4.5 3 1/9 19 22 20 23
K G,I 3 5 7 5 4/9 18 23 18 23
Project due date = 23 113

Varpath = VarA + VarC + VarF + VarI + VarK
= 4/9 + 0 + 1/9 + 1 + 4/9
= 2
And, path = 1.414
b) Z = (X - )/(24 - 23)/(24-23)/1.414 = 0.71
From the standard normal distribution table:
P(z < 0.71) = 0.5 + 0.2612 = 0.7612 or 76%
c) For 90% probability, Z = 1.28 (from Z-table). Therefore,
Z = (X - )/1.28  (X - 23)/1.4141.28
X = 23+1.414*1.28 = 24.81hrs
114

Example 4. The activity times, expected value and variance of a project
is given below. Find
a. What is the probability that the project takes at least 10days?
b. What is the probability that the project takes less than 7days?
Activity a m b te Var.
A 4 5 6 5 4/36
B 4 5 12 6 64/36
C 1 4 7 4 36/36
D 1 2 3 2 4/36
115

Solution:
a. The probability that the project takes at least 10days?
    1711
.
0
8289
.
0
1
95
.
0
1
95
.
0
36
/
40
9
10
)
10
( 












 


 Z
P
Z
P
Z
P
t
P
Answer: The probability that the project at least 10days = 0.17 or 17%
116

Solution:
b. The probability that the project takes less than 7days?
  0287
.
0
90
.
1
36
/
40
9
7
)
7
( 








 


 Z
P
Z
P
t
P
Answer: The probability that the project takes less than 7days = 0.029 or 2.9%
117

Advantages
 Accounts for uncertainty
Disadvantages
 Time and labor intensive
 Assumption of unlimited resources is big issue
 Assumption that duration is most probable value is not
accurate
 Mostly used only on large, complex project
118
PERT – Advantage and Limitations

Pause
PERT – Cost Consideration

• Project crashing is a method of reducing project time
by expending additional resources.
• The goal of crashing is to reduce project duration at
minimum cost. i.e. Least cost schedule.
• No need to crash all jobs to get a project done faster
but only the critical activities.
• Least cost schedule indicate which critical activities
are to be crashed and by how much so as to get
optimum duration.
120
PERT – Project Crashing

 For the time-only CPM project schedule, we typically assume
that activity duration is fixed at its NORMAL TIME, or the
duration with the lowest direct activity cost (i.e., NORMAL
COST).
 However, some activities may be expedited if higher resource
levels are available. The shortest activity duration is called
CRASH TIME. The cost to complete an activity in that amount
of time is called CRASH COST.
121
Time & Costs: Normal vs. Crash

Note the time –cost relationship in crashing:
 Crashing costs increase as project duration decreases.
 Whereas, indirect costs decrease as project duration decreases.
 Therefore, reduce project length as long as crashing costs are less than
indirect costs.
122
Activity Crashing

time
Direct cost
Indirect
cost
Total project cost
Min. total cost =
optimal project
time
123
Time – Cost Tradeoff

1. Draw the project network
2. Determine the critical path and the normal duration.
3. Identify the critical activities
4. Find the total normal cost and the normal duration of the project
5. Compute the cost slope by:
Cost slope = Crash cost-Normal cost
Normal Duration-Crash duration
6. Crash the critical activity of least cost slope first to the
maximum extent possible so that the project duration is really
reduced. Why?
7. Calculate the new total cost by cumulatively adding the cost of
the crashing to the current direct cost.
Total cost = New direct cost + Current indirect cost
124
Least Cost Schedule - Procedure

8. When critical activities are crashed and the duration is reduced
other paths may also become critical. Such critical paths are
called parallel critical paths.
When there is more than one critical path in a network, project
duration can be reduced only when either the duration of a
critical activity common to all critical paths is reduced or the
durations of different suitable activities on different critical
paths are simultaneously reduced.
9. Stop when the total cost is minimum. This gives optimum(least
cost) schedule called optimum duration.
Note: Least or minimum duration does not mean optimum (least cost)
duration.
125
Least Cost Schedule - Procedure

Remember again:
 As a result of reduction in an activity’s time, a new
critical path may be created.
 When there is more than one critical path, each of the
critical paths must be reduced.
 If the length of the project needs to be reduced further,
the process is repeated.
126
PERT – Cost Consideration in Scheduling

Example 1. Consider the following time-cost relationship data for a project.
Find the least cost schedule (optimum duration) if the indirect cost is 100birr
per day.
Activity Normal
time
Normal
cost, Birr
Crash
time,
Days
Crash cost,
Birr
1-2
1-3
2-4
2-5
3-4
4-5
8
4
2
10
5
3
100
150
50
100
100
80
6
2
1
5
1
1
200
350
90
400
200
100
580 1340
127
Project Crashing - Examples

Activity Normal
time
Normal
cost, Birr
Crash
time,
Days
Crash
cost,
Birr
Cost
slope
1-2
1-3
2-4
2-5
3-4
4-5
8
4
2
10
5
3
100
150
50
100
100
80
6
2
1
5
1
1
200
350
90
400
200
100
50
100
40
60
25
10
580 1340
Solution:
The critical path = 1 – 2 – 5. Normal duration = 18days
Total cost = Indirect cost + direct cost = 18*100 + 580 = 2380 birr
128

1
2
3
5
4
8
3
2
5
4
10
Normal critical path
129

Stage 1.
1 – 2 is the critical activity of least cost slope
Crash 1-2 by 2 days.
Current Duration = 18-2 = 16days
Current critical path: 1-2-5
Current Total cost = 16*100 + 580 + 100 = 2280 birr
1
2
3
5
4
6
3
2
5
4
10
Stage 1
130

Stage 2.
1 – 2 and 2 – 5 are critical activities.
Now, crash 2 - 5 by 4 days only since the duration of the path 1-3-4-5
is 12 days.
Current critical paths: i) 1-2-5 and ii) 1-3-4-5
Current Total cost = 12*100 + 680 + 240 (=4*300/5) = 2120 birr
Stage 2
1
2
3
5
4
6
3
2
5
4
6 131

Stage 3.
Critical activities: 1 – 2, 1-3, 2-5, 3-4, 4-5
Crash 2-5 by 1 day and Crash 4-5 by 1 day each (since the duration of the path
1-2-4-5 is 11 days and also the activity 2-5 can be crashed only by one day).
Current critical paths: i) 1-2-5 and ii) 1-3-4-5
Current Total cost = 11*100+920+60 +10 =2090 birr
Stage 3
1
2
3
5
4
6
2
2
5
4
5 132

No further crushing is possible (since all the activities on the critical path
1-2-5 have been crashed to the maximum extent).
Answer: Hence the optimum duration is 11 days and the least cost is
2090birr
Stage Crash Current
duration
Direct
cost
Indirect
cost
Total cost
0 0 18 580 1800 2380
1 1-2 by 2days 16 680 1600 2280
2 2-5 by 4days 12 920 1200 2120
3 2-5 and 4-5
by 1 day each
11 990 1100 2090
Table : Crashing schedule
133

 Any activity that is on the critical path
 Activities with relatively long durations
 Bottleneck activities (that appear on multiple critical
paths)
 Activities with relatively low costs to crash
 Activities that are not likely to cause quality problems if
crashed
 Activities that occur relatively early in the schedule and
are labor intensive
134
Which Activities are the Best Candidates for
Crashing?

Pause
Scheduling with Limited Resources

 The problem of scheduling project with limited resources
is usually large and complex.
 Due to such complexity people employ a rule of thumb
arising from experience, expertise and commonsense.
 But rule of thumb is not sufficient for solving resource
associated problems in a project.
 Under such condition, Heuristic programs for resource
scheduling are used.
 Heuristic programs for resource scheduling include:
A. Resource Levelling Program
B. Resource Allocation Program
136

Resource Leveling Program:
 It is trying usually to reduce peak human resource
requirements and smooth out period to period assignments.
 It is concerned with the efficient use of the required human
resources when the project duration cannot be altered.
 Steps for resource Levelling:
1) Draw the project PERT/CPM network diagram
2) Identify the critical path
3) From step 2, draw the early start schedule graph
4) Identify the Non- critical activities with slack
5) Adjust the activities identified in step 4 to level the peak
resource requirements
137

Example 1. The early start schedule graph of a project is given
below. The manpower requirement for each activity is indicated in
the parenthesis. Using resource leveling programming reduce the
peak resource requirements.
138
1 4 5 6 7 8
2 3 10
9
Time in Weeks
A
B E G
C
F
H
D
(6)
(7)
(17)
(15)
(5) (3)
(15)
(13)
Fig. 1. Early start schedule
graph

139
1 4 5 6 7 8
2 3 10
9
Time in Weeks
10
20
30
40
50
Manpower
Requirement
(43)
(47)
(30)
(20)
(5) (3)
Fig. 2. Manpower Loading
chart

Stage 1.
 B, E, G, H are on the critical path.
 Peak manpower requirement in the 3rd week =47
 D and F activities have slack of 7 and 2 weeks, respectively.
 Since D has maximum slack, reduce peak resource requirement
using this slack.
 Thus, delay the start of activity D by 7 weeks.
140
1 4 5 6 7 8
2 3 10
9
Time in Weeks
A
B E G
C
F
H
D
(6)
(17)
(15)
(5) (3)
(7)
(15)
(13)
Fig. 3. Early start schedule
graph

141
1 4 5 6 7 8
2 3 10
9
Time in Weeks
10
20
30
40
50
Manpower
Requirement
(26)
(30)
(20)
(5)
(20) Fig. 4. Manpower Loading
chart

Stage 2.
 Shift the start of activity F by 2 weeks
 Delay the start of activity A by 2 weeks
142
1 4 5 6 7 8
2 3 10
9
Time in Weeks
A
B E G
C F
H
D
(6)
(17)
(15)
(5) (3)
(7)
(15)
(13) Fig. 5. Early start schedule
graph

143
Fig. 6. Manpower Loading
chart
1 4 5 6 7 8
2 3 10
9
Time in Weeks
10
20
30
40
50
Manpower
Requirement
(20) (21) (20)
Levelling Further is impossible

Resource Allocation Program:
 It is trying to allocate the available limited resources when
two or more activities compete for the same resource such
as machine, material, etc.
 Steps for resource allocation:
1) Allocate resources serially in time
2) If several jobs compete for the same resources, give
preference to the jobs with the smallest slack. Why?
3) Reschedule non-critical jobs, if possible, so as to make
available the needed resources for rescheduling
critical jobs. Why?
144

Example 1. A project has the following characteristics:
145
Activity: 1-2
(A)
1-4
(B)
1-7
(C)
2 -3
(D)
3-6
(H)
4-5
(E)
Duration: 2 2 1 4 1 5
Activity: 4-8
(F)
5-6
(I)
6-9
(J)
7-8
(G)
8-9
(K)
Duration: 8 4 3 3 5
a) Construct a network diagram and find the critical path and the
project duration.
b) Activities 2-3 (D), 4-5(E), 6-9 (J) each requires one unit of the
same key equipment to complete it. Do you think availability of
one unit of the equipment in the organization is sufficient for
completing the project without delaying it; if so what is the
schedule of these activities?

Critical path: 1-4-8-9;
Project Duration = 15 days
146
1
7
2
9
6
C 8
3
4
5
G
K
J
H
A
D
B
F
E
I
2
1
2
5 4
5
3
8
4
1
3

147
Fig. 1. Early start schedule graph
1 4 5 6 7 8
2 3 10
9
Time, days
B F
C
K
8
1
2
12 13 15
14
11
A
5
G
3
2
D
4
E
5
H
1 I
4
J
3

Stage 1.
 Start D after 7 weeks and start J after 12 weeks.
 No change in the start and other activities, as shown in the
following schedule graph on time scale
148
1 4 5 6 7 8
2 3 10
9
Time, days
B F
C
K
2
Fig. 2. Early start schedule graph
12 13 15
14
11
A
G
E
I
D H
J

Resource Leveling (Smoothing)
The problem of resource fluctuation appears after the initial
scheduling of the project without considering the resources.
 The peaks and valleys in the resource profile indicate high day-
to-day variation in the resource demand.
Resource smoothing is the process that attempts to determine a
resource requirement that is "smooth" and where peaks and valleys
are eliminated.

Unconstrained resource scheduling (Constrained time)
Resource Leveling
• Resource unconstrained (No limits on resources)
• Time (Project completion) constrained; project duration
not be delayed
• Reduce the difference between the peaks and the valleys
• Average resource usage
• The objective is to smooth the use of the resources to
avoid the resource fluctuation

Heuristic Method Procedure
 Prepare a complete activity schedule
 Draw a bar chart based on ES timings
 Draw the FF as dashed line beside the upper side of the bar and
the TF beside the lower side
 Put the resource usage in each bar of the related activity
 Critical activities to be drawn first (do not move them)
 Aggregate the resources in each time period

Heuristic Method Procedure
 Calculate the total usage of resources = Σ unit period usage
 Calculate the average resource usage = Σ usage / utilization period
 Shift non-critical activities within their FF first, then their TF to
decrease the peaks and raise the valleys
 Revise the activities float
 Aggregate the resources in each time period

Resource leveling heuristics shift non-critical activities within their
float times so as to move resources from the peak periods (high
usage) to the valley periods (low usage), without delaying the
project.

Resource Leveling (Example)
Activity Activity Duration
(Weeks)
Predecessors Resource
(units/week)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
2
5
3
2
6
6
6
4
2
7
3
2
2
-
1
1
1
2
2
3
4
4
5, 6
6, 7
2, 8
2, 8, 9
10, 11, 12, 13
0
0
2
2
1
2
3
1
0
4
2
2
4
0

Determine minimum level of the resource required to complete
the project.

Resource Leveling (Example)
Activity ES EF FF TF
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
0
0
0
2
2
5
3
3
8
11
9
9
18
0
2
5
3
4
8
11
9
7
10
18
12
11
20
0
0
0
0
4
0
0
0
2
8
0
6
7
0
0
3
0
6
12
3
0
6
9
8
0
6
7
0

Planning and scheduling Techniques.ppt

Planning and scheduling Techniques.ppt

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