The document discusses project scheduling and some key concepts related to it. It defines project scheduling as the process of converting a general project plan into a time-based graphic presentation given information on available resources and time constraints. It outlines the basic principles of project scheduling such as compartmentalizing tasks, determining interdependencies, allocating time, and defining responsibilities, outcomes and milestones. It also discusses some basic scheduling terminology like tasks, activities, work products, and events. Finally, it explains common scheduling techniques like network diagrams and bar charts, as well as objectives and applications of network analysis in project scheduling.

1. Chapter-05
PROJECT SCHEDULING
OutlineSyllabus
Network techniques - PERT and CPM - Gantt Charts -Resource Allocation.
5.01 PROJECT SCHEDULING
The project schedule is the core of the project plan. U is used by the project manager to commit
people to the project and show the organization how the work will be performed. It enables the
project manager to identify risk points, understand the proper linkage of events assists in the
resource planning and allows the Project Manager to establish goals for the team and the project.
Before a project schedule can be related, the project manager must have a Work Breakdown
Structure (WBS), an effort estimate for each task, and a source list with availability for each
resource.
Project Scheduling is the process of converting a general or outline plan for a project into a
time-based graphic presentation given information on available resources and time constraints.
Or
Project Scheduling is the process of identifying and organizing the tasks of a project into a
sequence of events ensuring a harmonious completion of the venture. These events are dependent
on the results of their preceding activities, thus interlinking all the activities of the project. This
interdependency provides for a major need of effective project scheduling.
5.02 BASIC PRINCIPLES OF PROJECT SCHEDULE
A number of basic principles guide software project schedule:
1 Compartmentalization: The project must be compartmentalized into a number of manageable
activities and tasks. To accomplish compartmentalization, both the product and the process are
refined.
2. Interdependency: The interdependency of each compartmentalized activity or task must be
determined. Some tasks must occur in sequence, while others can occur in parallel. Some
activities cannot commence until the work product produced by another is available. Other
activity can occur independently.
3. Time allocation: Each task to be scheduled must be allocated some number of work units
(e.g., person-days of effort). In addition, each task must be assigned a star date and a completion
What do you mean by project scheduling?

2. Project Management84
date that is a function of the interdependencies and whether work will be conducted on a full time
basis.
4. Effort validation: Every project has a defined number of people on the software team. As time
allocation occurs, you must ensure that no more than the allocated number of people has been
scheduled at any given time.
5. Defined responsibilities: Every task that is scheduled should be assigned to a specific team
member.
6. Defined outcomes: Every task that is scheduled should have a defined outcome for software
projects; the outcome is normally a work product or a part of a work product. Work products are
often combined in deliverables.
7. Defined milestones: Every tasks or a group of tasks should be associated with a project
milestones. A milestone is accomplished when one or more work products has been reviewed for
quality and has been approved.
3. Activities: Croup of related tasks is called as activities. A project manager assigns a task to
role.
4. Work product: It is a tangible item that results from a task. For example, an objective models
a class diagram, a piece of source code, a document etc.
5. Work package: The specification of work to be accomplished in completing a task or activity
is described in a work package.
6. Event: Something that cause a system or objective to change state. For example, a message
the condition becoming time of completion of an activity.
7. Synchronization points: The points in a project schedule that require the team to synchronize
the contents of products, complete tasks and reduce defects.
8. Thrashing: The performing of unproductive work associated with a software project is known
as thrashing.
9. Task status: The status of a specific task relative to the task goals and completion.
10. Network: A network is a graphical representation of a project plans, showing the interrela-
tionships of various activities.
5.03 SCHEDULING TERMINOLOGY
Some basic terminology related to scheduling is given below:
1. Scheduling: A scheduling is the mapping of task onto time. Each task has a start and an end
lime. We can thus plan the deadlines for individual deliverables.
2. Task: A task is a well defined work assignment for a role.
3. Activity: An activity is defined as a job or a task that consumes time and is represented on a
network diagram by an arrow on a line. It consumes time and resources.
4. Event: An event is a specific accomplishment of an activity in the overall program is normally
represented by a circle on the network diagram and can be a meeting point of two or more
activities. No event can be accomplished until all die preceding activities leading to it are
completed and this must lie at a specific point in time.
What are the basic principlesofproject scheduling?

3. Chapter 5: Project Scheduling 85
5.04 SCHEDULING TECHNIQUES
Scheduling techniques can be broadly divided into two main categories:
1. Network diagram: PERT and CPM.
2. Bar chart: Milestone chart and Gantt charts.
1. Network diagram: Network diagrams play a very important role in the project scheduling.
This is one of the most important scheduling techniques applied in various fields of project
development.
Network analysis/diagrams entails a group of techniques for presenting information relating time
and resources so as to assist in the planning, scheduling and controlling of projects.
The information usually represented by a network includes the sequences, interdependences,
interrelationships and criticality of various activities of the project.
2. Bar chart: Planning is one of the main secrets to successful project implementation, as anyone
who has been involved in relocation or major project knows.
The key to good planning is simply to get the team talking and thinking about what needs to be
done, and then use charts to communicate that to others.
Two simple planning techniques are useful to Project Teams; Milestone Plans and Bar or Gantt
charts shown below.
• Milestone Plans focus mainly on the end-dates by which something needs to be complete or by
which certain objectives need to be achieved.
• Gantt Charts focus more on the activities to be carried out to complete the project.
Both are invaluable in forcing a Project Team to think through the detail of what needs to be
done, what the priorities and linkages are, and then as a means of communicating intentions to
others in a diagram or picture.
5.05 OBJECTIVES OF NETWORK ANALYSIS
The various objectives of network analysis are:
1. Powerful tools for planning, scheduling and control.
2. Minimization of total cost.
3. Minimization of total time.
4. Minimization of cost for a given total time.
5. Minimization of time for a given cost.
6. Minimization of idle resources.
7. To minimize production delays, interruptions and conflicts.
What are the basic terminology,relatedto projectscheduling?
Explainthe schedulingtechniques ofa project.
Explainthe various objectivesofnetwork analysis.

4. Project Management86
5.06 APPLICATIONS OF NETWORK ANALYSIS
Network analysis nowadays can be used in scheduling the projects of almost every field. Some of
its applications are mentioned as follows:
1. Construction of a dam or canal system in a region.
2. Construction of a building or a highway.
3. Maintenance of aero planes or oil refinery.
4. Space flight.
5. Missile development.
6. Assembly line scheduling.
7. Cost control of a project using PERT/CPM.
8. Designing a prototype of a machine.
9. Development of supersonic planes.
10. Research and development.
11. Budget and auditing procedures.
12. Planning of political campaigns.
13. Strategic and tactical military planning.
14. Market penetration programs.
15. Find the best traffic flow pattern in a large city.
16. Preparing inventory plans.
17. Organization of big conferences, public works etc.
18. Shifting of manufacturing plant from one side to another.
5.07 BENEFITS AND DRAWBACKS OF THE NETWORK
APPROACH
Some benefits drawbacks of the networkapproach to project planning are givenbelow:
ADVANTAGES:
1. The network approach makes it easier for the project managers to build a team and create
human network for efficient handling of a multitasked project.
2. The network approach binds the entire team together and motivates the human resources in
timely completion of the tasks in a project.
3. The network approach takes into consideration the requirements well in advance to complete
a project in the most efficient way possible.
4. With help of the network approach the project managers can determine the duration and
estimate exact time and cost of the project. It helps to monitor human resources, and the
direct and indirect costs associated with the project.
Explainthe applicationsof network analysis.

5. Chapter 5: Project Scheduling 87
5. The network approach assists the project managers in planning schedules, monitoring tasks,
and helps control the project expenses.
6. The network approach also makes it convenient for the project managers to calculate the time
required to complete the tasks of the project. That helps them to predict completion date of
every phase, anticipate problems along the way, if any, and react accordingly.
7. Charting in a network approach makes it easier to evaluate parallel activities, handle delays
and judge the outcome of a task.
8. It enables the managers to minimize the project length by monitoring the critical path.
9. The network approach chart clearly identifies critical path/s of the project, which assists the
managers in decision making to address the issue quickly. It also enables the project head to
determine if the task is on schedule or needs boost to accelerate the process.
The charting in a network approach also enables the managers to determine start time, end
time, slack time and float time associated with each activity of the project.
DISADVANTAGES:
1. In a big project, a network approach can become extremely complicated and difficult to
fathom for the new recruits to the project team.
2. If the project is far too bulky and lengthy, the network approach requires software to monitor
the plan.
3. Network approach can become ineffective and difficult to manage if it is not well-defined and
stable.
4. It cannot effectively handle sudden changes in the implementation of the plan on ground. It is
very difficult to redraw the entire network approach chart if the plan of the project suddenly
changes midway.
5. The network approach cannot form and control the schedules of the persons involved in the
project.
6. The allocation of resources cannot be properly monitored.
7. The critical path of the network approach of a big project is not always clear. The project
managers have to spend a lot of time to calculate it carefully.
8. The network approach takes longer to identity and to monitor the critical path when the
project is of big dimension.
9. Using network approach, identifying and determining a critical path is difficult when there
are many other similar duration paths in the project.
10. At times, to design a network approach is time consuming. It is also difficult to estimate the
activity completion time in a multidimensional project.
What are some benefits of the network approach to project planning? What are
some drawbacks? BBA (Professional) 2014

6. Project Management88
5.08 CHARACTERISTIC OF THE CRITICAL PATH TIMES
THAT MAKES THEM CRITICAL
There are a number of characteristic of the critical path times that makes them critical. These
include:-
(a) Wrong (b) Right
Fig-5.1: Representation of an activity
1. Each activity is represented by one and only one arrow in the network
2. No two events can be identified by the same end events.
3. The flow of the diagram should be from left to right.
4. Activities are represented by arrows (→) and events are represented by circles (O).
5. Arrows should not cross each other.
6. Arrows should be kept straight and should not be curved or bent.
7. Dangling must be avoided in a network diagram.
8. The dummy activity should be introduced only if it extremely necessary.
9. All events should be numbered in ascending order.
10. No event numbers can be repeated.
11. No event can occur until every activity preceding it has been completed.
12. An activity succeeding an event cannot be started until that event has occurred.
13. The network lies only one starting point (event) and one ending point which is known as
ending/terminal event.
5.09 TERMINOLOGIES IN PROJECT MANAGEMENT
1. ACTIVITY
An individual operation which has an end and a beginning and which utilizes resources is called
activity. An arrow is used to represent an activity with it's head indicating the direction of
progress in project.
The activities are divided into four categories
(a) Predecessor activity: Activities that must be completed immediately prior to the start of
another activity are called as Predecessor Activity.
What characteristic of the critical path times makes them critical?
BBA (Professional) 2014

7. Chapter 5: Project Scheduling 89
(b) Successor activity: Activities that cannot be started until one or more of other activities are
completed, but immediately succeed them are called Successor Activity.
(c) Concurrent activity: Activities which can be accomplished concurrently are known as
concurrent activities.
(d) Dummy activity: In most projects many activities can be performed concurrently or
simultaneously. It is possible that two activities could be drawn by the same beginning and end
events. In such situation when two or more activities can be performed concurrently, the concept
of dummy activity is introduced to resolve this problem. Thus, an activity which does not
consume any kind of resource but merely depicts the technological dependence is termed as
dummy activity.
Dummy Activities is inserted in the network to clarify the activity pattern in the following two
situations:
 To make activities with common starting and finishing points distinguishable.
 To identify and maintain proper precedence relationship between activities those are not
connected by events.
Example: Consider a situation where A and B are concurrent activities C is dependent on A and
D is dependent on both A and B. Such a situation can be handled using a dummy activity as
follows:
2. EVENT
An Event is an instant of time at which an activity starts and finishes. An event is represented by
circle (O) in a network which is known as node or connector. The event can be classified into 3
categories:
(a) Merge event: When more than one activity comes and joins an event such an event is known
as merge event.
(b) Burst event: When more than one activity leaves an event, such event is known as burst
event.
(c) Merge and burst event: An activity may be a merge and burst event at the same time with
respect to some activities it may be a burst event.
Merge event Burst event Merge and burst event
Fig. 5.6: Typos of event
3. FLOAT
Float can be described as the free time associated with an event. Hence, float or slack is that time
by which an activity can be delayed without delaying the entire project. Activities which do not
have any float or slack time are the activities which cannot be delayed without delaying the
Fig.5.5: Example of dummy activity

8. Project Management90
project. These activities are called the critical activities. Hence along the critical path the float or
slack is zero, types of Float
(a) Total float: The amount of time by which the completion of an activity could be delayed
beyond the earliest expected completion time without affecting the overall project duration time.
This float is concerned with overall project duration
(b) Free float: The amount of time by which the completion of an activity could be delayed
beyond the earliest expected completion time without affecting the earliest start of a succeeding
activity. This float is concerned with the commencement of the succeeding activity.
(c) Independent float: The amount of time by which the start of an activity can be delayed
without affecting the earliest start time of any immediately following activities, assuming that the
preceding activity has finished at its latest finish time. This float is concerned with prior and
subsequent activities.
(d) Critical path: Critical path can be defined as "the sequence of critical activities in a
network".
OR
The critical path is the longest path in the network from starting event to ending event and defines
the minimum time required to complete the project.
By the term path we mean a sequence of activities such that it begins at the starting event and end
at the final event. The length of a path is the sum of the individual times of the activities lying on
a path.
If the activities on a critical path are delayed by a day, the project would also be delayed by a day
unless the times of the future activities are reduced by a day by different means. The critical path
is denoted by double or darker lines to make distinctions from other non-critical paths. The
critical path identifies all critical activities of the project.
Features of Critical Path
1. If the project has to be shortened, then some of the activities on that path must also be
shortened.
2. The variation in the actual performance from the expected activity duration time will be
completely reflected in one to one fashion in the anticipated completion of the whole project.
5.10 STEPS IN THE PERT PLANNING PROCESS
PERT planning involves the following steps:
1. Identify the specific activities and milestones.
2. Determine the proper sequence of the activities.
3. Construct a network diagram.
4. Estimate the time required for each activity.
5. Determine the critical path.
6. Update the PERT chart as the project progresses.
Define activity, event, float and critical path?
What are the difference between activity and event? Or Draw the distinction
between activity and event? BBA (Professional) 2009

9. Chapter 5: Project Scheduling 91
1. Identify Activities and Milestones : The activities are the tasks required to complete the
project. The milestones are the events marking the beginning and end of one or more activities. It
is helpful to list the tasks in a table that in later steps can be expanded to include information on
sequence and duration.
2. Determine Activity Sequence: This step may be combined with the activity identification step
since the activity sequence is evident for some tasks. Other tasks may require more analysis to
determine the exact order in which they must be performed.
3. Construct the Network Diagram: Using the activity sequence information, a network
diagram can be drawn showing the sequence of the serial and parallel activities. For the original
activity-on-arc model, the activities are depicted by arrowed lines and milestones are depicted by
circles or "bubbles".
If done manually, several drafts may be required to correctly portray the relationships among
activities. Software packages simplify this step by automatically converting tabular activity
information into a network diagram.
4. Estimate Activity Times: Weeks are a commonly used unit of time for activity completion,
but any consistent unit of time can be used.
A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion
times. For each activity, the model usually includes three time estimates:
♦ Optimistic time - generally the shortest time in which the activity can be completed. It is
common practice to specify optimistic times to be three standard deviations from the mean so
that there is approximately a 1% chance that the activity will be completed within the optimistic
time.
♦ Most likely time - the completion time having the highest probability. Note that this time is
different from the expected time.
♦ Pessimistic time - the longest time that an activity might require. Three standard deviations
from the mean is commonly used for the pessimistic time.
PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the
expected time for each activity can be approximated using the following weighted average:
Expected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6
This expected time may be displayed on the network diagram.
To calculate the variance for each activity completion time, if three standard deviation times were
selected for the optimistic and pessimistic times, then there are six standard deviations between
them, so the variance is given by:
[ ( Pessimistic - Optimistic ) / 6 ]2
5. Determine the Critical Path: The critical path is determined by adding the times for the
activities in each sequence and determining the longest path in the project. The critical path
determines the total calendar time required for the project. If activities outside the critical path
speed up or slow down (within limits), the total project time does not change. The amount of time
that a non-critical path activity can be delayed without delaying the project is referred to as slack
time.

10. Project Management92
If the critical path is not immediately obvious, it may be helpful to determine the following four
quantities for each activity:
 ES - Earliest Start time
 EF - Earliest Finish time
 LS - Latest Start time
 LF - Latest Finish time
These times are calculated using the expected time for the relevant activities. The earliest start
and finish times of each activity are determined by working forward through the network and
determining the earliest time at which an activity can start and finish considering its predecessor
activities. The latest start and finish times are the latest times that an activity can start and finish
without delaying the project. LS and LF are found by working backward through the network.
The difference in the latest and earliest finish of each activity is that activity's slack. The critical
path then is the path through the network in which none of the activities have slack.
The variance in the project completion time can be calculated by summing the variances in the
completion times of the activities in the critical path. Given this variance, one can calculate the
probability that the project will be completed by a certain date assuming a normal probability
distribution for the critical path. The normal distribution assumption holds if the number of
activities in the path is large enough for the central limit theorem to be applied.
Since the critical path determines the completion date of the project, the project can be
accelerated by adding the resources required to decrease the time for the activities in the critical
path. Such a shortening of the project sometimes is referred to as project crashing.
6. Update as Project Progresses: Make adjustments in the PERT chart as the project progresses.
As the project unfolds, the estimated times can be replaced with actual times. In cases where there
are delays, additional resources may be needed to stay on schedule and the PERT chart may be
modified to reflect the new situation.
What stepsare involvedin PERT analysis?
BBA (Professional) 2008,2010
5.11 PERT VS. CPM
CPM and PERT (Program Evaluation and Review Technique) are most commonly used
methods for project management. There are some similarities and differences between PERT and
CPM. PERT can be applied to any field requiring planned, controlled and integrated work efforts
to accomplish defined objectives. On the other hand, CPM (Critical Path Method) is the method
of project planning consisting of a number of well-defined and clearly recognizable activities.
The differences between CPM and PERT is shown below.
CPM PERT
1. CPM uses activity oriented network. 1. PERT uses event oriented Network.
2. Durations of activity may be estimated with a
fair degree of accuracy.
2. Estimate of time for activities are not so
accurate and definite.
3. It is used extensively in construction projects. 3. It is used mostly in research and
development projects, particularly projects of
non-repetitive nature.
4. Deterministic concept is used. 4. Probabilistic model concept is used.

11. Chapter 5: Project Scheduling 93
5. CPM can control both time and cost when
planning.
5. PERT is basically a tool for planning.
6. In CPM, cost optimization is given prime
importance. The time for the completion of the
project depends upon cost optimization. The
cost is not directly proportioned to time. Thus,
cost is the controlling factor.
6. In PERT, it is assumed that cost varies
directly with time. Attention is therefore given
to minimize the time so that minimum cost
results. Thus in PERT, time is the controlling
factor.
5.12 RESOURCE ALLOCATION
Resource allocation is used to assign the available resources in an economic way. In project
management, resource allocation is the scheduling of activities and the resources required by
those activities while taking into consideration both the resource availability and the project time.
The Key to Effective Project Resource Allocation
 Determine quickly what resource you will need
 Determine who the best people are in that are
 Approach their line manager and check on their availability
 Assuming they are available put their name down against the relevant tasks in your
project plan
 Get your project plan into the PMO and get it base lined as soon as possible
5.13 ASSUMPTIONS UNDERLYING CPM ANALYSIS
The usual assumptions underlying CPM analysis are:
1. The costs associated with a project can be divided into two components: direct costs and indirect costs.
Direct
costs are incurred on direct material and direct labour. Indirect costs consist of overhead items like indirect
supplies, rent, insurance, managerial services, etc.
2. Activities of the project can be expedited by crashing which involves employing more resources.
3. Crashing reduces time but enhances direct costs because of factors like overtime payments, extra
payments,
and wastage. The relationship between time and direct activity cost can be reasonably approximated by a
downward sloping straight line.
What is the basic difference between PERTand CPM?
BBA (Professional) 2008,2011,212,2013, 2014
What do you mean by resource allocation?
What are the usual assumptions underlyingCPManalysis?
BBA (Professional) 2014

12. Project Management94
5.14 PROBLEMS
BBA (Professional) 2009
Problem 1. Construct a suitable network diagram from the information given below:
Activity Time
Weeks
Precedence
A
B
C
D
E
F
G
H
3
5
14
5
4
7
8
5
None
None
A
A
B
B
D,E
G,F
Requirements:
(i) Draw the PERT Network and find the critical path.
(ii) From where would you suggest transferring resources and to what activities so that the original target
date may be maintained.
Solution:
i) Network showing the Critical Path.
So the time and alternative path are
1. (A- C) = (3+14) = 17 weeks
2. (A-D-G-H) = (3+5+8+5) = 21 weeks
3. (B-E-G-H) = (5+4+8+5) = 22 weeks
4. (B-F-H) = (5+7+5) = 22 weeks
Ans. Critical Path is B→ D→F =22 weeks
Project completion time =22 weeks
(ii) Activity C is ideal. So I would suggest transferring resources C. We shall transfer resources C to
resources H. For these activities the original target date may be maintained, which is shown in the
following diagram.

13. Chapter 5: Project Scheduling 95
BBA (Professional) 2010
Problem 2. Construct the PERT network from the information given:
Activity Events Time Estimate
Optimistic Most Likely Pessimistic
A
B
C
D
E
F
(1-2)
(1-3)
(2-4)
(3-4)
(2-5)
(4-5)
10
20
4
2
8
8
22
20
10
14
8
14
22
20
16
32
20
20
Requirements:
(i) Calculate the Expected Time. (ii) Find the critical path and project completion time.
(iii) Find out the Activity and Event Slacks. (iv) Calculate the LFT and EST.
Solution:
a. Calculation for the Expected Time.
Activities Events Optimistic
Time
(a)
Most Likely
Time
(b)
Pessimistic
Time
(c)
Expected Time (ET)
𝑎 + 4 × 𝑏 + 𝑐
6
ET
A (1-2) 10 22 22 10 + 4 × 22 + 22
6
20
B (1-3) 20 20 20 20 + 4 × 20 + 20
6
20
C (2-4) 4 10 16 4 + 4 × 10 + 16
6
10
D (3-4) 2 14 32 2 + 4 × 14 + 32
6
15
E (2-5) 8 8 20 8 + 4 × 8 + 20
6
10
F (4-5) 8 14 20 8 + 4 × 14 + 20
6
14
b) Network showing the Critical Path.

14. Project Management96
So the time and alternative path are
5. (A- E) = (20+10) = 30 days
6. (A-C-F) = (20+10+14) = 44 days
7. (B-D-F) = (20+15+14) = 49 days
Ans. Critical Path is B→ D→F =49 days
Project completion time =49 days
c) Table showing Activity and Event Slacks
Activity LOT EOT Slack = LOT-EOT
A 25 20 5
B 20 20 0
C 35 30 5
D 35 35 0
E 35 30 5
F 49 49 0
d) Table showing LFT and EFT
Activity LFT EFT
A 25 20
B 20 20
C 35 30
D 35 35
E 35 30
F 49 49
BBA (Professional) 2011, 2013 (ADAPTED)
Problem3. Consider the following project (times given in days):
Activity to tm tP Predecessors
a 1 4 7 -
b 2 2 2 -
c 2 5 8 a
d 3 4 5 a
e 4 6 8 c,b
f 0 0 6 c,b
g 3 6 9 d,e
Find:
(i) The network.
(ii) All expected activity times, variances and slacks.
(iii) The critical path and expected completion time.
(iv) The probability the project will be done in 23 days.
(v) Time corresponding to 95% probability.
(vi) Find the standard deviation of critical path duration.

15. Chapter 5: Project Scheduling 97
Solution
(i) The network.
(ii) All expected activity times, variances and slacks.
Activity Expected activity
times
Variance Slacks
a 4 1.00 0
b 2 0 7
c 5 1.00 0
d 4 0.11 7
e 6 0.44 0
f 1 1 11
g 6 1 0
(iii) The critical path is a – c – e – g and expected completion time= 21 days
(iv)The probability the project will be done in 23 days.
z=(23-21)/√3.44=1.078 for a probability of 85.9%
(v) Time corresponding to 95% probability
P=0.95corresponds to z=1.65 =(T-21)/1.855, or T=24.06 days
(vi) Calculation of Standard Deviation of Critical Path Duration
Activity tP to Standard Deviation
𝜎𝑖 =
𝑡 𝑃 − 𝑡 𝑂
6
a 7 1
𝜎𝑎 =
7 − 1
6
= 1
c 8 2
𝜎𝑐 =
8 − 2
6
= 1
ES EF
21
LS LF
21
Legend:

16. Project Management98
e 8 4
𝜎𝑒 =
8 − 4
6
= 0.67
g 9 3
𝜎𝑔 =
9 − 3
6
= 1
BBA (Professional) 2012
Problem 4. Construct the PERT Network from (he information given below
Activity Events Time Estimate
Optimistic(tO) Most Likely(tM) Pessimistic(tP)
A (1-2) 10 22 22
B (1-3) 20 20 20
C (2-4) 4 10 16
D (3-4) 2 14 32
E (2-5) 8 8 20
F (4-5) 8 14 20
(i) Draw the network diagram.
(ii) Determine the critical path.
(iii) Calculate the activity slack.
(iv) Find the standard deviation of critical path duration.
(v) Compute the probability of completing the project in 45 days.
Solution
(i) The network
(ii) So the time and alternative path are
1. (A- F) = (20+10) = 30 days

17. Chapter 5: Project Scheduling 99
2. (A-C-E) = (20+10+14) = 44 days
3. (B-D-F) = (20+15+14) = 49 days
Ans. Critical Path is B→ D→F =49 days
(iii) Table showing Activity and Event Slacks
Activity LOT EOT Slack = LOT-EOT
A 25 20 5
B 20 20 0
C 35 30 5
D 35 35 0
E 35 30 5
F 49 49 0
(iv) Calculation of Standard Deviation of Critical Path Duration
Activity tP to Standard Deviation
𝜎𝑖 =
𝑡 𝑃 − 𝑡 𝑂
6
B 20 20 𝜎 𝐵 =
20 − 20
6
= 0
D 32 2 𝜎 𝐷 =
32 − 2
6
= 5
F 20 8 𝜎𝐹 =
20 − 8
6
= 2
(v)The probability the project will be done in 45 days.
z=(45-49)/√5.38= -0.7435 for a probability of 77.04%
BBA (Professional) 2014
Problem 5. The events of the project below arc designated as 1. 2 and so on.
(a) Draw the network.
(b) Find the critical path.
(c) Find the slacks on all the activities.
Activity Prec.
Evt.
Sue.
Evt
TE (weeks) Prec. Aciiv.
a 1 2 3 None
b 1 3 6 None
c 1 4 8 None
d 2 5 7 a
e 3 5 5 b
f 4 5 10 c
g 4 6 4 c

18. Project Management100
h 5 7 5 d,e.f
i 6 7 6 G
Solution
(a) Network Diagram:
(b) Critical path:
Start c f h End
8 + 10 + 5 + 0 = 23 weeks
(c) The slacks on all the activities.
Activities Calculation Slacks
a 23-5-7-3 8 weeks
b 23-5-5-6 7 weeks
c 23-5-10-8 0 weeks
d 23-5-10 8 weeks
e 23-5-11 7 weeks
f 23-5-18 0 weeks
g 23-6-12 5 weeks
h 23-23 0 weeks
i 23-18 5 weeks