Project Management CPM Method Tutorial-p2 Objectives and Information Step 1. Developing the Network Step 2. Determining the Duration Step 3. Determining the Critical Path (s) Developed by: Alex J. Ruiz-Torres, Ph.D.
Step 3. Determining the Critical Path(s)
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y 3S10 LS LF 10 16 LS LF U X 0 3 LS LF 19 23 LS 23 Z A For the activity with largest EF. Let LF = EF R Y 3S 8 LS LF 10 19 LS LF
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y 3S10 LS LF 10 16 LS LF U X 0 3 LS LF 19 23 ES EF LS LF Z A Calculate Late Start LS = LF – Activity Time LS = 23 – 4 = 19 R Y 3S 8 LS LF 10 19 LS LF
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y 3S10 LS LF 10 16 LS LF U X 0 3 LS LF 19 23 ES EF LS LF Z A We ‘MOVE’ to the LEFT R Y 3S 8 LS LF 10 19 LS LF
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y When only one relationship, then LF = LS of predecessor ES EF LS LF 3S10 LS LF 10 16 LS L19 U X 0 3 LS LF 19 23 Z A R Y 3S 8 LS LF 10 19 LS LF
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y When only one relationship, then LF = LS of predecessor 3S10 LS LF 10 16 LS L19 U X 0 3 LS LF 19 23 Z A R Y 3S 8 LS LF 10 19 LS L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y LS = LF – Activity Time = 19 – 6 = 13 3S10 LS LF 10 16 13L19 U X 0 3 LS LF 19 23 Z A R Y LS = LF – Activity Time = 19 – 9 = 10 3S 8 LS LF 10 19 10 L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y When an Activity precedes two or more, the minimum LS becomes its LF Min (13, 10) = 10 3S10 LS 10 10 16 13L19 U X 0 3 LS LF 19 23 Z A R Y 3S 8 LS LF 10 19 10 L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y When an Activity precedes two or more, the minimum LS becomes its LF Min (13, 10) = 10 3S10 LS 10 10 16 13L19 U X 0 3 LS LF 19 23 Z A R Y 3S 8 LS 10 10 19 10 L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y LS = LF – Activity Time = 10 – 7 = 3 3S10 3S 10 10 16 13L19 U X 0 3 LS LF 19 23 Z A LS = LF – Activity Time = 10 – 5 = 5 R Y 3S 8 5S 10 10 19 10 L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y LF of Z = Min of LS from U and R = Min (3, 5) = 3 3S10 3 10 10 16 13L19 U X 0 3 LS 3 19 23 Z A R Y 3S 8 5S 10 10 19 10 L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y LS = LF – Activity Time LS = 3 – 3 = 0 3S10 3 10 10 16 13L19 U X 0 3 0S 3 19 23 Z A R Y 3S 8 5S 10 10 19 10 L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y We now determine the SLACK of each Activity. SLACK = LF – EF 3S10 3 10 10 16 13L19 U X 0 3 0S 3 19 23 Z A R Y 3S 8 5S 10 10 19 10 L19
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y SLACK = LF – EF S = 0 3S10 3 10 10 16 13L19 S = 3 U X 0 3 0S 3 19 23 S = 0 S = 0 Z A R Y S = 2 3S 8 5S 10 10 19 10 L19 S = 0
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y All Activities with a Slack = 0 are part of a Critical Path. A Critical Path is a sequence of activities from “start” to “end” with activities with 0 Slack. 3S10 3 10 10 16 13L19 S = 0 S = 3 U X 0 3 0S 3 19 23 S = 0 S = 0 Z A R Y S = 2 3S 8 5S 10 10 19 10 L19 S = 0
Step 3. Determining the Critical Path(s) Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y CP = Z – U – Y – A Activity X has 3 weeks of slack Activity R has 2 weeks of slack 3S10 3 10 10 16 13L19 S = 0 S = 3 U X 0 3 0S 3 19 23 S = 0 S = 0 Z A R Y S = 2 3S 8 5S 10 10 19 10 L19 S = 0