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CPM (Deterministic) Problem: A company is bringing a new product on line to be manufactured in their current facility in some existing space. The owners have identified 11 activities and their precedence relationships. Develop an AON for the project.
Activity Description
Immediate
Predecessor
Duration
(weeks)
A Develop product specifications None 4
B Design manufacturing process A 6
C Source & purchase materials A 3
D Source & purchase tooling & equipment B 6
E Receive & install tooling & equipment D 14
F Receive materials C 5
G Pilot production run E & F 2
H Evaluate product design G 2
I Evaluate process performance G 3
J Write documentation report H & I 4
K Transition to manufacturing J 2
© WILEY 2010
CPM (Activity on Node) Diagram © WILEY 2010
Path Completion Times The longest path (ABDEGIJK) limits the project’s duration (project cannot finish in less time than its longest path) ABDEGIJK is the project’s critical path Paths Path duration ABDEGHJK 40 ABDEGIJK 41 ACFGHJK 22 ACFGIJK 23 © WILEY 2010
PERT: Using Probabilistic Time Estimates for the previous problem
Activity Description
Optimistic
time
Most likely
time
Pessimistic
time
A Develop product specifications 2 4 6
B Design manufacturing process 3 7 10
C Source & purchase materials 2 3 5
D Source & purchase tooling & equipment 4 7 9
E Receive & install tooling & equipment 12 16 20
F Receive materials 2 5 8
G Pilot production run 2 2 2
H Evaluate product design 2 3 4
I Evaluate process performance 2 3 5
J Write documentation report 2 4 6
K Transition to manufacturing 2 2 2
Calculating Expected Task Times Activity Optimistic time Most likely time Pessimistic time Expected time A 2 4 6 4 B 3 7 10 6. C 2 3 5 3. D 4 7 9 6. E 12 16 20 16 F 2 5 8 5 G 2 2 2 2 H 2 3 4 3 I 2 3 5 3. J 2 4 6 4 K 2 2 2 2 6 optimistic 4 most likely pessimistic Expected time
Network Diagram with
Expected Activity Times
Project Activity Variances Activity Optimistic Most Likely Pessimisti c Variance A 2 4 6 0. B 3 7 10 1. C 2 3 5 0. D 4 7 9 0. E 12 16 20 1. F 2 5 8 1. G 2 2 2 0. H 2 3 4 0. I 2 3 5 0. J 2 4 6 0. K 2 © WILEY 2010 2 2 0.
Critical Activity Variances Activity Optimistic Most Likely Pessimisti c Variance A 2 4 6 0. B 3 7 10 1. C 2 3 5 0. D 4 7 9 0. E 12 16 20 1. F 2 5 8 1. G 2 2 2 0. H 2 3 4 0. I 2 3 5 0. J 2 4 6 0. K 2 2 2 0. Critical activities highlighted Sum over critical = 4.
