Solution to Problem 2 Developed by: Alex J. Ruiz-Torres, Ph.D.

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Presentation transcript:

Solution to Problem 2 Developed by: Alex J. Ruiz-Torres, Ph.D.

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T ES EF LS LF ES EF LS LF X ES EF LS LF Z ES EF LS LF U Y W T ES EF LS LF ES EF LS LF

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T 0 7 LS LF ES EF LS LF 7 X ES EF LS LF Z ES EF LS LF U Y W T ES EF LS LF ES EF LS LF

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T 0 7 LS LF ES EF LS LF 7 X ES EF LS LF Z ES EF LS LF U Y W T 0 6 LS LF ES EF LS LF 6

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T 0 7 LS LF 7 13 LS LF 6 7 X ES EF LS LF Z ES EF LS LF U Y W T 0 6 LS LF ES EF LS LF 6

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T 0 7 LS LF 7 13 LS LF 6 7 X ES EF LS LF Z 7 12 LS LF 5 U Y W T 0 6 LS LF ES EF LS LF 6

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T 0 7 LS LF 7 13 LS LF 6 7 X ES EF LS LF Z 7 12 LS LF 5 U Y W T 0 6 LS LF 6 10 LS LF 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T 0 7 LS LF 7 13 LS LF 6 7 X 13 27 LS LF 14 Z 7 12 LS LF 5 U Y W T 0 6 LS LF 6 10 LS LF 6 4

Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 The duration of the project under normal times is 27 weeks 0 7 LS LF 7 13 LS LF 6 7 X 13 27 LS LF 14 Z 7 12 LS LF 5 U Y The cost of this project under normal times is $125K W T 0 6 LS LF 6 10 LS LF 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 LS LF 7 13 LS LF 6 7 X 13 27 14 Z 7 12 LS LF 5 U Y W T 0 6 LS LF 6 10 LS LF 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 LS LF 7 13 LS LF 6 7 X 13 27 14 Z 7 12 LS LF 5 U Y W T 0 6 LS LF 6 10 9 13 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 LS LF 7 13 LS LF 6 7 X 13 27 14 Z 7 12 8 13 5 U Y W T 0 6 LS LF 6 10 9 13 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 LS LF 7 13 6 7 X 13 27 14 Z 7 12 8 13 5 U Y W T 0 6 LS LF 6 10 9 13 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 7 13 6 7 X 13 27 14 Z 7 12 8 13 5 U Y W T 0 6 LS LF 6 10 9 13 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 7 13 6 7 X 13 27 14 Z 7 12 8 13 5 U Y W T 0 6 1 7 6 10 9 13 6 4

X Z U Y W T The critical path is Z-X-U Weeks $K CT NT NC CC Rate Pred Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 7 13 6 7 X 13 27 14 Z 7 12 8 13 The critical path is Z-X-U 5 U Y W T 0 6 1 7 6 10 9 13 6 4

X Z U Y W T The critical path is Z-X-U Weeks $K CT NT NC CC Rate Pred Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 0 7 7 13 6 7 X 13 27 14 Z 7 12 8 13 The critical path is Z-X-U 5 U Y W T 0 6 1 7 6 10 9 13 6 4

Activity Z We will crash the lowest cost in the CP Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 We will crash the lowest cost in the CP Activity Z Crashing Z by one week will result in a project duration of 26 weeks total cost of $125 + $3 = $128

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 7 6 X 14 Z 5 U Y W T 0 6 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 5 U Y W T 0 6 6 10 8 12 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 7 12 5 U Y W T 0 6 6 10 8 12 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 7 12 5 U Y W T 0 6 6 10 8 12 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 7 12 5 U Y W T 0 6 6 10 8 12 6 4

X Z U Y W T The critical paths are Z-X-U W-X-U Weeks $K CT NT NC CC Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 7 12 The critical paths are Z-X-U W-X-U 5 U Y W T 0 6 6 10 8 12 6 4

X Z U Y W T The critical paths are Z-X-U W-X-U Options Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 6 The critical paths are Z-X-U W-X-U Options Crash Z and W: 6.67 Crash X: 3.5 Crash U: 5 0 6 6 12 6 7 6 X 12 26 12 26 14 Z 6 11 7 12 5 U Y W T 0 6 6 10 8 12 6 4

Activity X We will crash the lowest cost in the CP Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 We will crash the lowest cost in the CP Activity X Crashing X by one week will result in a project duration of 25 weeks total cost of $128+ $3 .5= $131.5

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 6 5 0 6 7 6 X 14 Z 5 U Y W T 0 6 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 5 0 6 7 6 X 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 6 11 5 U Y W T 0 6 6 10 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 6 11 5 U Y W T 0 6 6 10 7 11 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 6 11 5 U Y W T 0 6 6 10 7 11 6 4

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 11 6 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 6 11 5 U Y W T 0 6 6 10 7 11 6 4

X Z U Y W T The critical paths are Z-X-U Z-Y-U W-X-U W-Y-U Weeks $K CT Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 The critical paths are Z-X-U Z-Y-U W-X-U W-Y-U 11 6 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 6 11 5 U Y W T 0 6 6 10 7 11 6 4

X Z U Y W T The critical paths are Z-X-U Z-Y-U W-X-U W-Y-U Options Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 6 5 The critical paths are Z-X-U Z-Y-U W-X-U W-Y-U Options Crash Z and W: 6.67 Crash X and Y: 9.5 Crash U: 5 11 6 11 6 5 0 6 7 6 X 11 25 14 Z 6 11 6 11 5 U Y W T 0 6 6 10 7 11 6 4

Activity U We will crash the lowest cost in the CP Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 24 $136.5 6 5 We will crash the lowest cost in the CP Activity U Crashing U by one week will result in a project duration of 24 weeks total cost of $131.5+ $5= $136.5

Done with 3 iterations All crash plan

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 24 $136.5 2 0 5 5 X 12 Z 4 U Y W T 0 3 3 3

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 24 $136.5 5 7 2 0 5 5 X 12 Z 5 9 4 U Y W T 0 3 3 6 3 3

X Z U Y W T Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 24 $136.5 5 7 2 0 5 5 X 9 21 12 Z 5 9 4 U Y W T 0 3 3 6 3 3

Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 24 $136.5 … 21 5 7 2 0 5 5 X 9 21 12 Z The duration of this project under “all crash” times is 21 Weeks 5 9 4 U Y W T 0 3 3 6 3 3

Weeks $K CT NT NC CC Rate Pred Z 5 7 12 18 3.00 W 3 6 23 34 3.67 X 2 32 46 3.50 Z, W Y 4 16 22 6.00 T 24 10.00 U 14 28 5.00 Y, X, T Time Cost 27 $125 26 $128 25 $131.5 24 $136.5 … 21 $182 5 7 2 0 5 5 X 9 21 12 Z The cost of this project under “all crash” times is $182K 5 9 4 U Y W T 0 3 3 6 3 3

Tradeoff plot