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PROGRAM EVALUATION
AND REVIEW TECHNIQUE
(PERT)
CRITICAL PATH METHOD
(CPM)
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• PERT
was developed by the Navy
Special
Project
Office
in
cooperation with Booz, Allen, and
Hamilton.
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• It was specifically directed at
planning and controlling the Polaris
missile program, a massive project
which had 250 prime contractors
and 9,000 subcontractors.
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Dummy activity - an activity which
requires no time and which is used to
establish a precedence relation of a
network.
Immediate predecessors – the activities that
must
immediately precede a given activity
in a project.
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ACTIVITY TIME IN A PERT
NETWORK
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CHARACTERISTIC OF THE DISTRIBUTION
USED TO EXPRESS THE VARIATION OF TIME
1. A small probability (1 in 100) of reaching the
most optimistic time (shortest time), symbolized a
2. A small probability (1 in 100) of reaching the
most pessimistic time (longest time), symbolized b
3. One and only one most likely time, symbolized m,
which would be free to move between the two
extremes mentioned in 1 and 2 above
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The earliest-start-time rule
The earliest time for an activity leaving any
node is equal to the largest earliest finish time of
all activities entering that same node.
The earliest start time for activities D and E is 2, the
earliest finish time for activity A.
9 Critical path - the longest path through the network
A path is defined as a sequence of connected activities that
leads from the beginning of the project to the end of the project. Earliest finish time = earliest start time + expected time
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The latest-finish-time rule
The second step in finding the critical path is to
compute a latest start time and latest finish time for
each activity.
Latest finish time is simply the latest time at
which an activity can be completed without
extending the completion time of the network.
The latest time start is the latest time at
which an activity can begin without extending the
completion time on the project
11 Activity Description
Develop the advertising plan (a detailed plan of project radio, television, and newspaper advertising)
Develop the promotion and training materials plan (a detailed study of the materials that will be required for training the store manager for the final in-store introduction)
Develop the training plan (the design of the training program that the store manager will undertake prior to the final in-store introduction)
Schedule the radio, television, and newspaper advertisements that will appear prior to the final introduction
Develop the advertising copy that will be required
A “dummy” activity (one that takes no time) which lets us draw networks using only straight line or which establishes precedence relationships (What activities precede each other)
Prepare promotion materials which will be used during the in-store introduction
Prepare materials which will be used in the training program for the store managers
Conduct the pre-introduction advertising campaign in the media
Screen and select the store managers who will undergo training
Conduct the training program
The final in-store introduction of the Response 1000
12 Activity Description
Develop the advertising plan (a detailed plan of project radio, television, and newspaper advertising)
Develop the promotion and training materials plan (a detailed study of the materials that will be required for training the store manager for the final in-store introduction)
Develop the training plan (the design of the training program that the store manager will undertake prior to the final in-store introduction)
Schedule the radio, television, and newspaper advertisements that will appear prior to the final introduction
Develop the advertising copy that will be required
A “dummy” activity (one that takes no time) which lets us draw networks using only straight line or which establishes precedence relationships (What activities precede each other)
Prepare promotion materials which will be used during the in-store introduction
Prepare materials which will be used in the training program for the store managers
Conduct the pre-introduction advertising campaign in the media
Screen and select the store managers who will undergo training
Conduct the training program
The final in-store introduction of the Response 1000
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Slack is the length of time we can delay an activity
without interfering with the project completion.
Slack = LF – EF or
LS – ES
LF – EF for activity A = 7 – 2 = 5
LS – ES for activity A = 5 – 0 = 5
Latest-finish-time rule would be that the latest
finish time for an activity entering any node is
equal to the smallest latest start time for all
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Example 1. From the following table of information,
(a) Draw a precedence diagram, (b) Find the critical
path, (c) determine the expected duration of the
project
Activity Precedes Expected Time (days)
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SOLUTION
1. Use pencil in constructing precedence diagram;
2. Activities without predecessors are placed at the start of the network (left side);
3. Activities with multiple predecessors are located at path intersections;
4. Start with a single node and end with a single node; 5. Avoid having paths that cross with each other;
6. Number nodes from left to right;
7. Activities should go from left to right;
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Activities without predecessors:
A precedes C, B
E precedes F
20 A = 4 E = 3 G = 1 C = 12 B = 5 F = 8 H = 3 D = 2 I = 12 K = 15 J = 9 Path: A, C, D, I, J = 4 + 12 + 2 + 12 + 9 = 39* A, B, I, J = 4 + 5 + 12 + 9 = 30 E, F, J = 3 + 8 + 9 = 20 G, H, K = 1 + 3 + 15 = 19
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Example 2. From the following network diagram,
determine the following:
a. The early start (ES) in days
b. The early finish (EF) in days
c. The latest start (LS) in days
d. The latest finish (LF) in days
22 1 2 3 4 5 5 2 4 3 4 3 5 2 2 5 5 6 8 9 8 11
Numbers inside the blue box is the Early Finish Time of the activity Numbers inside the red box is the Early Start Time of the activity The project duration is 11 days
To determine the Early Start (ES) and Early
Finish (EF) Time
23 1 2 3 4 5 5 2 4 3 4 3 5 4 4 5 7 8 8 8 11
Numbers inside the blue box is the Latest Finish Time of the activity Numbers inside the red box is the Latest Start Time of the activity The project duration is 11 days
To determine the Latest Start (LS) and Latest
Finish (LF) Time
0
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To compute the slack time using LS – ES or LF - EF
Activity LS ES SLACKS LF EF SLACKS
1-2
0
0
0
5
5
0
1-3
2
0
2
4
2
2
2-4
5
5
0
8
8
0
2-5
7
5
2
11
9
2
3-4
4
2
2
8
6
2
4-5
8
8
0
11
11
0
The activities with zero slack time indicate the critical path.
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CRASHING AND COST PLAN
1. Reducing Time and Cost
Purpose:
•To avoid penalties for not completing the project on time.
•To take advantage of monetary incentives for completing the project on or before the target date.
•To free the resources such as, money, equipment and men for use on other projects.
•Reduce indirect costs associated with the project such as: 1.Facilities and equipment
2.Supervision cost 3.Labor Cost
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CRASHING AND COST PLAN
1. Reducing Time and Cost
The following information should be
needed:
Regular time and crash time estimates.
Regular cost and crash estimate for
each activity.
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CRASHING AND COST PLAN
2. Procedure in Crashing Project Time
Obtain an estimate of regular and crash
time plus the costs of each activity.
Determine the length of all paths and their
float/slack time.
Determine which activities are on the
critical path.
Crash the critical activities in the order of
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Example 3. From the following data, perform
crashing the project.
Activity Time in Weeks Cost Cost
Per Week
Normal Crash Normal Crash
29 1 2 4 6 3 5 7 A B C D E F G H I 6 8 7 12 7 3 5 11 10
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Path Duration in Weeks
A-C-F-I B-E-H B-D-F-I B-E-G-I 6 + 7 + 3 + 10 = 26 8 + 7 + 11 = 26 8 + 12 + 3 + 10 = 33* 8 + 7 + 5 + 10 = 30
Step 1. Determine the different lengths and identify the critical path.
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Activity Time in Weeks Cost Cost
Per Week
Normal Crash Normal Crash
A 6 2 2,000.00 10,000.00 2,000.00 B 8 3 4,000.00 7,000.00 600.00 C 7 4 2,000.00 3,200.00 400.00 D 12 8 8,000.00 10,000.00 500.00 E 7 3 2,000.00 5,200.00 800.00 F 3 1 10,000.00 14,000.00 2,000.00 G 5 2 6,000.00 8,100.00 700.00 H 11 7 6,000.00 9,600.00 900.00 I 10 6 4,000.00 8,000.00 1,000.00 Total 33 18 44,000.00 75,100.00
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Step 2. Starting from path with 33 weeks time duration Along this path the least expensive activity is with P500.00
cost per week.
Crash this activity to its minimum time of 8 weeks. Subtract: 12 – 8 = 4 weeks
Crash Cost = 4 weeks x P500.00 per week = P2,000.00
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Step 2. Starting from path B-D-F-I with 33 weeks time duration Along this path the least expensive activity is D with P500.00
cost per week.
Crash this activity to its minimum time of 8 weeks. Subtract: 12 – 8 = 4 weeks
Crash Cost = 4 weeks x P500.00 per week = P2,000.00
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Step 3. Next path is with 30 weeks time duration
Along this path the least expensive activity is with P600.00 cost per week.
Crash this activity to its minimum time of 3 weeks. Subtract: 8 – 3 = 5 weeks
Crash Cost = 5 weeks x P600.00 per week = P3,000.00
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Step 4. Next path is with 29 weeks time duration
Along this path the least expensive activity is with P1,000.00 cost per week.
Crash this activity to its minimum time of 6 weeks. Subtract: 10 – 6 = 4 weeks
Crash Cost = 4 weeks x P1,000.00 per week = P4,000.00
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Step 5. Next path is with 26 weeks time duration
Along this path the least expensive activity is with P400.00 cost per week.
Crash this activity to its minimum time of 4 weeks. Subtract: 7 – 4 = 3 weeks
Crash Cost = 3 weeks x P400.00 per week = P1,200.00
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Step 6. Next path is with 26 weeks time duration
Along this path the least expensive activity is with P800.00 cost per week.
Crash this activity to its minimum time of 3 weeks. Subtract: 7 – 3 = 4 weeks
Crash Cost = 4 weeks x P800.00 per week = P3,200.00
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Step 7. Next path is with 25 weeks time duration
Along this path the least expensive activity is with P700.00 cost per week.
Crash this activity to its minimum time of 2 weeks. Subtract: 5 – 2 = 3 weeks
Crash Cost = 3 weeks x P700.00 per week = P2,100.00
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Step 8. Next path is with 20 weeks time duration
Along this path the least expensive activity is with P2,000.00 cost per week.
Crash this activity to its minimum time of 1 weeks. Subtract: 3 – 1 = 2 weeks
Crash Cost = 2 weeks x P2,000.00 per week = P4,000.00
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Step 9. Next path is with 19 weeks time duration
Along this path the least expensive activity is with P2,000.00 cost per week.
Crash this activity to its minimum time of 2 weeks. Subtract: 6 – 2 = 4 weeks
Crash Cost = 4 weeks x P2,000.00 per week = P8,000.00
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Step 10. Next path is with 17 weeks time duration
Along this path the least expensive activity is with P900.00 cost per week.
Crash this activity to its minimum time of 7 weeks. Subtract: 11 – 7 = 4 weeks
Crash Cost = 4 weeks x P900.00 per week = P3,600.00
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Therefore;
Total Crash Cost =
Total Crash Cost = 31,100.00
Total Cost = Normal Cost + Total Crash Cost = 44,000.00 + 31,100.00
Total Cost = 75,100.00
Length of Time per Path; A-C-F-I =
B-E-H =
