1. Start D finish A B C E I G H F J KL N M 2 0 4 10 64 7 7 5 9 2 8 45 6 0 ActivityDescription AExcavate BFoundation CRough wall DRoof EExterior plumbing FInterior plumbing GExterior siding HExterior painting IElectrical work JWallboard KFlooring LInterior painting MExterior fixtures NInterior fixtures House Construction – Example 1 CRITICAL PATH METHOD Activities on Nodes Source: Hillier and Lieberman, Chapter 10

2. Forward Pass: The earliest start of an activity is equal to the largest of the earliest finish times of its immediate predecessors. Start D finish A B C E I G H F J KL N M 2 0 4 10 64 7 7 5 9 2 8 45 6 0 ES = EARLIEST START EF = EARLIEST FINISH = ES + DURATION (0,2) (2,6) (6,16) (16,22) (16,20) (16,23) (22,29) (29,38) (38,40) (20,25) (25,33) (33,38) (38,44) (44,44) (0,0)

3. Start D finish A B C E I G H F J KL N M 2 0 4 10 64 7 7 5 9 2 8 45 6 0 Backward Pass: The latest finish time of an activity is equal to the smallest of the latest start times of its immediate successors. FROM THE FORWARD PASS, SET LF = EF (0,2) (2,6) (6,16) (20,26) (16,20) (18,25) (26,33) (33,42) (42,44) (20,25) (25,33) (33,38) (34,38) (38,44) (44,44)

4. Start D finish A B C E I G H F J KL N M 2 0 4 10 64 7 7 5 9 2 8 45 6 0 Calculate the Slack. Zero Slack = on the critical path Slack = LS – ES or LF - EF Any delay in an activity on the critical path will delay the entire project. SLACKS ALONG A CHAIN ARE NOT INDEPENDENT: Chain D – G – H – M has 4 days slack; not 4+4+4+4 = 16

5. GANTT CHART

6. Hydroelectric Project (Dam, Power station, transmission lines)

7. Start 6 finish 12 3 17 2 25 11 5 8 9 10 14 12 200 4 13 6 7 7 7 109 18 6 3 5 1 1 34 416 15 Hydroelectric project (durations in months) Activities on Nodes

8. FORWARD PASS Start 6 finish 12 3 17 2 25 11 5 8 9 10 14 12 200 4 13 6 7 7 7 109 18 6 3 5 1 1 34 416 15

9. BACKWARD PASS Start 6 finish 12 3 17 2 25 11 5 8 9 10 14 12 200 4 13 6 7 7 7 109 18 6 3 5 1 1 34 416 15

10. BACKWARD PASS Start 6 finish 12 3 17 2 25 11 5 8 9 10 14 12 200 4 13 6 7 7 7 109 18 6 3 5 1 1 34 416 15