Critical Path Method/ Program Evaluation and Review Technique

1. CPM/ PERT Critical Path Method/ Program Evaluation and Review Technique Operation Research II Prepared By: Jomari Gingo BSIE 4-1

2. 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

3. Phases for Project Planning with CPM/PERT Define Project Activities Time Scheduling Network Network Calculation

4. 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,

5. 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.

6. Defining Project Activities PERT Expected time “average” of the time (optimistic, pessimistic, and most likely Expected time= (a+4m+b)/6

7. Defining Project Activities Other Concept 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. Bottleneck activities-any delay in the completion of one or more of these activities will cause delay in the completion of the activity. Earlier Start Time (ES)- Beginning of the activity. Earlier Finish Time (EF)- Sum of the earliest start time and estimated time to perform the concerned activity. 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. Latest Start Time (LS)- is the difference between the latest finished time and the estimated time for the activity to be performed.

8. Network Legend for making Network: Event ES and EF LF and LS Activity Dummy

9. Network Network 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. What activities must immediately precede the current activity? What activities must follow the current activity? What activities must occur concurrently with the current activity?

10. Network Using Dummy: 1 2 1 3 2 1 1 2 A B A B C A B C E A B C E D

11. Network Important note: In case of multiple activity In ES and EF Choose the largest value In LS and LF Choose the smallest value

12. Example 1: Activity Project Activity 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 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

13. 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 5 4 6 2 6 2 2 2 6 2 2 2 12 12 15 15 15 10 15 9 15 15 11 5 8 2 7 2 7 2 11 6 11 6 11 6 11 6 12 12 12 8 15 15

14. Example 1: Network Calculation Activity ES LS EF LF Slack (LS-ES or LF-EF) Critical Path A 5 2 7 5 B 4 2 6 4 C 2 2 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 YES K 12 12 15 15 YES L 15 15 19 19 YES

15. 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

16. 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.

17. Example 2: Project Activities Activity 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

18. Example 1: Network 1 I =2 7 2 3 4 6 5 7 8 9 A=3 6 1 11 4 11 11 15 15 3 3 3 3 3 2 8 2 3 3 3 3 5 5 5 5 77 7 7 7 9 9 8 2 9 3 9 9 B =2 K=0 D =2 C=4 E =2 F =2 H=1 G =2 J=4 11 11

19. Example 2: Network Calculation Activity ES LS EF LF Slack (LS-ES or LF-EF) Critical Path A 3 3 YES B 1 2 3 1 C 7 4 11 7 D 7 2 8 6 E 3 3 5 5 YES F 5 5 7 7 YES G 7 7 9 9 YES H 2 8 3 9 6 I 9 9 11 11 YES J 11 11 15 15 YES DUMMY K YES

20. ADDITIONAL TOPIC: BASIC TIME SCHEDULING (CONSTRUCTING TIME SCHEDULE)

21. Time Scheduling Constructing Time Schedule Table 1. 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.

22. Example 3: Network Findings: The critical path is A, D and H. The maximum time is 25

23. Time Scheduling Note: Consider time duration and activity predecessor(s).

24. THANK YOU!