PERT and CPM are project scheduling techniques. PERT was developed by the U.S. Navy for complex projects with uncertain times, while CPM was developed by DuPont and Remington Rand for industrial projects with known times. An example project schedule is provided showing activities, predecessors, times, earliest and latest start and finish times, slack, and identifying the critical path.

1. Scheduling

2. PERT/CPM
• PERT
• PROGRAM EVALUATION AND REVIEW TECHNIQUE
• DEVELOPED BY U.S. NAVY FOR POLARIS MISSILE PROJECT
• DEVELOPED TO HANDLE UNCERTAIN ACTIVITY TIMES
• CPM
• CRITICAL PATH METHOD
• DEVELOPED BY DU PONT & REMINGTON RAND
• DEVELOPED FOR INDUSTRIAL PROJECTS FOR WHICH ACTIVITY
TIMES GENERALLY WERE KNOWN.

3. EXAMPLE:21
IMMEDIATE COMPLETION
ACTIVITY PREDECESSORS TIME(DAYS)
A ------ 2
B ------ 4
C ------ 3
D A 3
E A 5
F C 6
G C 4
H D 4
I D 8
J B,E,F,I 2
L B,E,F,G,I 3

4. start
A 0 2
2 0 2
B 0 4
4 9 1
3
C 0 3
3 4 7
E 2 7
5 8 1
3
D 2 5
3 2 5
F 3 9
6 7 1
3
G 3 7
4 9 1
3
L 1
3
1
6
3 1
3
1
6
I 5 1
3
8 5 1
3J 13 15
2 13 15
H 5 9
4 1
2
16
End

5. A. THE ES AND LS FOR EACH ACTIVITY
A B C
ES=0 ES=0 ES=0
LS=0 LS=9 LS=4
B. THE EARLIEST TIME IS 16 DAYS.

6. C. THE SLACK ACTIVITY
ACTIVITY ES EF LS LF SLACK
A 0 2 0 2 0
(CRIT.)
B 0 4 9 13 9
C 0 3 4 7 4
D 2 5 2 5 0
(CRIT.)
E 2 7 8 13 5
F 3 9 7 13 6
G 3 7 9 13 4
H 5 9 16 12 4
I 5 13 13 5 0
(CRIT.)
J 13 15 14 16 2

7. D. CRITICAL ACTIVITY
2 – 3– 8– 3
E. THE CRITICAL PATH
A – D – I – L