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!