Critical Path Method

Samantha Manawadu
 Introduction
 Managers have been planning, scheduling, monitoring, and
controlling large scale projects for hundred years, but it has
only been in the last 50 years that management science
techniques have been applied to major projects.
 In 1957, the Critical Path Method (CPM) was developed by
Kelly and Walker to assist in building and maintenance of
chemical plants.
 In 1958, the special projects office of the US navy
developed the Program Evaluation and Review Technique
(PERT) to plan and control the Polaris missile program.
 In the recent time, PERT and CPM are two popular
management science techniques that help mangers plan,
schedule, monitor, and control large scale and complex
projects
 PERT/CPM
 PERT stands for Program Evaluation and Review Technique.
 CPM stands for Critical Path Method.
 PERT/CPM is used to plan the scheduling of individual activities
that make up a project.
 PERT/CPM can be used to determine the earliest/latest start and
finish times for each activity, the entire project completion time
and the slack time for each activity.
 PERT and CPM are similar in their basic approach, they do differ
in the way activity times are estimated.
 For each PERT activity three times (optimistic, pessimistic and
most likely times) are combined to determine the expected
activity completion time and its variance. Thus, PERT is a
probabilistic technique: it allows us to find the probability of the
entire project being completed by any given date.
 CPM, on the other hand, is called a deterministic approach. It
uses two time estimate, the normal time and the crash time, for
each activity
 Importance of PERT/CPM
By using PERT and CPM analysis you will be able to answer questions such
as:
1. When will the entire project be completed?
2. What are the critical activities or tasks in the project, that is, the ones that
will delay the entire project if they are late?
3. Which are the noncritical activities, that is, the ones that can run late
without delaying the whole project’s completion time?
4. What is the probability that the project will be completed by a specific
date?
5. At any particular date, is the project on schedule, behind schedule, or a
head of the schedule?
6. On any given date, is the money spent equal to, less than, or greater
than the budgeted amount?
7. Are there enough resources available to finish the project on time?
8. If the project is to be finished in a shorter amount of time, what is the
best way to accomplish this at the least cost? (crash analysis)
CPM
 Finding the critical path is a major part of
controlling a project.
 The activities on the critical path represent
tasks that will delay the entire project if they
are delayed.
 Manager gain flexibility by identifying
noncritical activities and re-planning,
rescheduling, and reallocating resources
such as personnel and finances
Critical Path
 The path (or paths) in the network diagram,
from start to finish, on which all the activities
have zero total and free floats, is called
Critical Path.
 It is the longest path (or paths) from start to
finish in a net work diagram.
 It gives minimum normal time (shortest time)
to complete a project.
 It is usually marked by double lined arrows in
a network diagram.
 Determining the Critical Path
 Step 1: Make a forward pass through the network
as follows: For each activity beginning at the Start
node, compute:
 Earliest Start Time (ES) = the maximum of the earliest
finish times of all activities immediately preceding activity
i. (This is 0 for an activity with no predecessors.). This is
the earliest time an activity can begin without violation of
immediate predecessor requirements.
 Earliest Finish Time (EF) = (Earliest Start Time) + (Time
to complete activity . This represent the earliest time at
which an activity can end. ( EF = ES + D)
The project completion time is the maximum of the
Earliest Finish Times at the Finish node.
 Determining the Critical Path
 Step 2: Make a backwards pass through the network
as follows: Move sequentially backwards from the
Finish node to the Start node. At a given node, j,
consider all activities ending at node j. For each of
these activities, (i,j), compute:
 Latest Finish Time (LF) = the minimum of the latest
start times beginning at node j. (For node N, this is
the project completion time.). This is the latest time
an activity can end without delaying the entire
project.
 Latest Start Time (LS) = (Latest Finish Time) - (Time
to complete activity (i,j)). This is the latest time an
activity can begin without delaying the entire project.
(LS = LF – D)
 The purpose of backward pass is to find the float.
 Float is the amount of time an activity can be
delayed or lengthened. Also called slack.
 Total float: the amount of time an activity can be
delayed or extended without extending the overall
project’s completion time. On a critical path, the
total float is zero.
Total Float = LS - ES or
Total Float = LF - EF
 Free float : is the amount of time that an activity
can be delayed without delaying the Early Start of
its successor activity.
Free Float = ES of Successor - EF
Determining the Critical Path
 Step 3: Calculate the slack time for each
activity by:
Slack = (Latest Start) - (Earliest
Start), or
= (Latest Finish) - (Earliest
Finish).
A critical path is a path of activities, from the
Start node to the Finish node, with 0 slack
times.
Detailed Illustration of Arrow
Diagramme
 AON ES,EF

A, d B, d

LS,LF

 AOA
ES EF
F
LS LF

A, d B, d
Example: ABC Associates
 Consider the following project:
Immediate
Activity Predecessor time (days)
A -- 6
B -- 4
C A 3
D A 5
E A 1
F B,C 4
G B,C 2
H E,F 6
I E,F 5
J D,H 3
K G,I,J 5
Example: network
Earliest/Latest Times

Activity Time IP ES EF LS LF TS FS
TF FF

EF = ES + t A 6 --- 0 6 0 6 0* 0
LS = LF – t B 4 --- 0 4 5 9 5 5
Where t is the C 3 A 6 9 6 9 0* 0
Activity time D 5 A 6 11 15 20 9 8
E 1 A 6 7 12 13 6 6
Total Slack
= LF – EF F 4 B.C 9 13 9 13 0* 0
= LS - ES G 2 B,C 9 11 16 18 7 7

Free Slack H 6 E,F 13 19 14 20 1 0

= ES (s) – EF
I 5 E,F 13 18 13 18 0* 0
J 3 D,H 19 22 20 23 1 4
K 5 G.I,J 18 23 18 23 0* 0

The estimated project completion time = 23

 Importance of Float (Slack) and Critical Path
1. Slack or Float shows how much allowance each activity
has, i.e how long it can be delayed without affecting
completion date of project

2. Critical path is a sequence of activities from start to finish

with zero slack. Critical activities are activities on the
critical path.

3. Critical path identifies the minimum time to complete

project

4. If any activity on the critical path is shortened or

extended, project time will be shortened or extended
accordingly
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 Importance of Float (Slack) and Critical Path (cont)
5. So, a lot of effort should be put in trying to control activities
along this path, so that project can meet due date. If any activity
is lengthened, be aware that project will not meet deadline and
some action needs to be taken.

6. If can spend resources to speed up some activity, do so only for

critical activities.

7. Don’t waste resources on non-critical activity, it will not shorten

the project time.

8. If resources can be saved by lengthening some activities, do so

for non-critical activities, up to limit of float.

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