critical path method/ program evaluation and review technique
TRANSCRIPT
CPM/ PERTCritical Path Method/ Program Evaluation and Review Technique
Operation Research IIPrepared By: Jomari Gingo
BSIE 4-1
CPM/ PERT
• Network-based methods design to assist planning, scheduling and control of time consuming project.
• Provides analytic mean for scheduling the activities.
• Use to know bottlenecks and critical activities
Phases for Project Planning with CPM/PERT
Define Project
Activities
Time Scheduling
NetworkNetwork
Calculation
Defining Project Activities
• CPM– Assumes deterministic activity duration.
• PERT– Assumes probabilistic duration. The time to
perform each activities appears uncertain and as such thru time estimate is needed as (optimistic, pessimistic and most likely) are used,
Defining Project Activities
• PERT– Optimistic time- denoted as a, which occurs when
execution goes extremely well.– Most Likely time- denoted as m, which occurs
when execution is done under normal condition. – Pessimistic time- denoted as b, which occurs when
execution goes extremely poorly.
Defining Project Activities
• PERT– Expected time• “average” of the time (optimistic, pessimistic, and most
likely
Expected time= (a+4m+b)/6
Defining Project ActivitiesOther Concept1. Critical Path- consist of the sequence of those events and connected activities that
require maximum time in the completion of the project it is that path that takes the longest time. It is critical because it control the completion date of the project.
2. Bottleneck activities-any delay in the completion of one or more of these activities will cause delay in the completion of the activity.
3. Earlier Start Time (ES)- Beginning of the activity.4. Earlier Finish Time (EF)- Sum of the earliest start time and estimated time to
perform the concerned activity.5. Latest Finish Time (LF)- an activity that can finish without delaying the project
beyond its deadline on the assumption that all subsequent activities are performed as planned.
6. Latest Start Time (LS)- is the difference between the latest finished time and the estimated time for the activity to be performed.
Network
Legend for making Network:
Event
ES and EF
LF and LS
Activity
Dummy
NetworkNetwork Representation Rule:Rule 1: Each activity is represented by one, and only one arc.Rule 2: Each activity must be identified by two distinct end nodes.Rule 3: To maintain the correct precedence relationship, the
following questions must be answered as each activity is added to network.
1. What activities must immediately precede the current activity?
2. What activities must follow the current activity?3. What activities must occur concurrently with the current
activity?
Network
Using Dummy:
1 21 3
2
1
1
2
A
B
A
B
C
A
B
C
E
A B
C ED
Network
Important note: In case of multiple activity
In ES and EFChoose the largest value
In LS and LFChoose the smallest value
Example 1: Activity ProjectActivity a b m (a+4m+b)/6
A 1 2 3 2
B 1 2 3 2
C 1 2 3 2
D 1 2 9 3
E 2 3 10 4
F DUMMY 0
G 3 6 15 7
H 2 5 14 6
I 1 4 7 4
J 4 9 20 10
K 1 2 9 3
L 4 4 4 4
Example 1: Network
1
3
2
4
5
6
8
7
9
A=2
B=2
C=2
D=3
E=4 F=0
H=6
J=10
I=4
G=7
K=3
L=4
50
40
00
62
62
22
62
22
1212
1515
1510
159
1515
11
582
72
72 11
6
11
6
11
6
11
6
1212
128
1515
Example 1: Network CalculationActivity ES LS EF LF Slack (LS-
ES or LF-EF)
Critical Path
A 0 5 2 7 5
B 0 4 2 6 4
C 0 0 2 2 0 YES
D 2 8 5 11 6
E 2 7 6 11 5
F DUMMY
G 2 8 9 15 6
H 2 6 8 12 4
I 6 11 10 15 5
J 2 2 12 12 0 YES
K 12 12 15 15 0 YES
L 15 15 19 19 0 YES
Example 1: Network Calculation
Note:LS-ES and LF-EF are always equal and is
called “slack”
Slack with zero values are the critical path
Example 2: Problem
A publisher has a contract with an author to publish a textbook. The simplified activities associated with the production of the text book are given below. The author is required to submit to the publisher a hard copy and a computer file of the manuscript. Develop the associated network for the project.
Example 2: Project ActivitiesActivity Predecessor(s) Duration (weeks)
A: Manuscript proofreading by editor None 3
B: Sample pages preparation None 2
C: Book cover design None 4
D: Artwork preparation None 3
E: Author’s approval of edited manuscript and sample pages
A,B 2
F: Book formatting E 4
G: Author’s review of formatted pages F 2
H: Author’s review of artwork D 1
I: Production of printed plates G,H 2
J: Book production and binding C,I 4
Example 1: Network
1
I=2
70
2 3 4 6
5 7
8 9
A=3
00 6
0
10
11
411
11
15
15
33
33
32
82
33
33
55
55
777
77
99
82
93
99
B=2
K=0
D=2
C=4
E=2 F=2
H=1
G=2
J=4
11
11
Example 2: Network CalculationActivity ES LS EF LF Slack (LS-
ES or LF-EF)
Critical Path
A 0 0 3 3 0 YES
B 0 1 2 3 1
C 0 7 4 11 7
D 0 7 2 8 6
E 3 3 5 5 0 YES
F 5 5 7 7 0 YES
G 7 7 9 9 0 YES
H 2 8 3 9 6
I 9 9 11 11 0 YES
J 11 11 15 15 0 YES
DUMMY K 0 0 0 0 0 YES
ADDITIONAL TOPIC:BASIC TIME SCHEDULING
(CONSTRUCTING TIME SCHEDULE)
Time Scheduling
Constructing Time Schedule Table1.The critical activities (shown by solid lines) must be
stacked one right after the another to ensure that the project is completed within its maximum duration. (In problem 2, its 15 days)
2. The non critical activities (shown by dashed lines) have time spans that are larger than their respective durations, thus allowing slack ( or “leeway”) in scheduling them with in their allotted time intervals.
Example 3: Network
Findings: The critical path is A, D and H. The maximum time is 25
Time Scheduling
Note: Consider time duration and activity predecessor(s).
THANK YOU!