Lecture 14 - Today's Lecture CVEN 349: Civil Engineering...

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LECTURE # 14 Fall 2009 Dr. Ivan Damnjanovic CVEN 349: Civil Engineering CVEN 349: Civil Engineering Project Management Project Management Today Today ’s Lecture s Lecture ± Critical Path ± Forward Pass algorithm ± Backward Pass algorithm ± Float ± Example Finding the Critical Path Finding the Critical Path The critical path is the set of events that cannot be delayed without causing an extension of the project Notation Notation ± EST(I): Early start time of activity I ± EFT(I): Early finish time of activity I ± LST(I): Late start time of activity I ± LFT(I): Late finish time of activity I
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Example of Notation Example of Notation 2 4 2 6 2 6 EST EFT LST LFT Duration Label Forward Pass Calculations Forward Pass Calculations ± Need two equations now: 1. EFT(I)=EST(I)+DUR(I) 2. EST(J)=max[EFT(I)] (maximum over all I that precede J) Example Example 2 4 3 6 6 8 5 2 4 5 1 2 Step 1: Beginning EST = 0, Find Task 1 EFT Step 1: Beginning EST = 0, Find Task 1 EFT 2 4 3 6 6 8 5 2 4 5 1 2 0 2 EFT(1) = EST(1)+DUR(1) =0+2 = 2
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Step 2: Calculate EST(2), EFT(2) Step 2: Calculate EST(2), EFT(2) 2 4 3 6 6 8 5 2 4 5 1 2 0 2 EST(2) = max{EFT(1)} = 2 2 EFT(2) = 2 + 4 =6 6 Step 3: Calculate EST(3), EFT(3) Step 3: Calculate EST(3), EFT(3) 2 4 3 6 6 8 5 2 4 5 1 2 0 2 EST(3) = max{EFT(2)} = 6 2 EFT(3) = 6 + 6 = 12 6 6 12 Step 4: Calculate EST(4), EFT(4) Step 4: Calculate EST(4), EFT(4) 2 4 3 6 6 8 5 2 4 5 1 2 0 2 EST(4) = max{EFT(1)} = 2 2 EFT(4) = 2 + 5 = 7 6 6 12 2 7 Step 5: Calculate EST(5), EFT(5) Step 5: Calculate EST(5), EFT(5) 2 4 3 6 6 8 5 2 4 5 1 2 0 2 EST(5) = max{EFT(4),EFT(2)} = max(6,7) = 7 2 EFT(5) = 7+2 = 9 6 6 12 2 7 7 9
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Step 6: Calculate EST(6), EFT(6) Step 6: Calculate EST(6), EFT(6) 2 4 3 6 6 8 5 2 4 5 1 2 0 2 EST(6) = max{EFT(3),EFT(5)} = max(12,9) = 12
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Lecture 14 - Today's Lecture CVEN 349: Civil Engineering...

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