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## N E T W O R K C O N S T R U C T I O N –

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**N E T W O R K C O N S T R U C T I O N –**C R I T I C A L P A T H M E T H OD**Activity List**You’ll recall from the earlier section in the Module concerning the steps for developing a schedule that you must first produce a list of all the activities in the project, place them in the sequence in which they will occur, and estimate the duration of each. The table below contains the activity list with the estimated duration for each activity and the activities that must be complete before each activity can begin (predecessors). Activity Duration Predecessors A 2 None B 10 A C 13 A D 12 A E 12 B F 7 B G 10 D H 16 D I 6 F J 12 C, G K 5 I L 8 E, K M 5 H N 3 J, L, M**Activity “A” is the first activity in the network. Once**it is complete, its successor activities can begin. A 2**Activities “B”, “C”, and “D” can all begin once**“A” is finished. B 10 C 13 A 2 D 12**E**12 F 7 Once Activity “B” is finished, activities “E” and “F” can begin. After “D” is finished, both activities “G and “H” can start. B 10 C 13 A 2 D 12 G 10 H 16**E**12 F 7 Activity “I” can start when “F” is completed. Activity “J” can begin after “C” and “G” have finished. B 10 I 6 C 13 J 12 A 2 D 12 G 10 H 16**E**12 K 5 F 7 B 10 Activity “K” can begin once “I” is finished. I 6 C 13 J 12 A 2 D 12 G 10 H 16**E**12 K 5 F 7 Activity “L” can start after “E” and “K” are finished. L 8 B 10 I 6 C 13 J 12 A 2 D 12 G 10 M 5 Activity “M” can begin when “H” is completed. H 16**E**12 K 5 F 7 L 8 B 10 I 6 C 13 J 12 A 2 N 3 D 12 G 10 M 5 Finally, activity “N” can begin after “J”, “L” and “M” are completed. H 16**Critical Path**At this point, it is possible to calculate a critical path for the network. Add the time durations of all the activities for each of the paths in the network. The critical path is the path with the greatest sum of activity time durations (i.e., the longest path through the network). In this example: A – B – E – L – N = 2 + 10 + 12 + 8 + 3 = 35 A – B – F – I – K – L – N = 2 + 10 + 7 + 6 + 5 + 8 + 3 = 41 A – C – J – N = 2 + 13 + 12 + 3 = 30 A – D – G – J – N = 2 + 12 + 10 + 12 + 3 = 39 A – D – H – M – N = 2 + 12 + 16 + 5 + 3 = 38 Path A – B – F – I – K – L – N is the longest path and hence the critical path. The next chart shows the critical path in the network.**E**12 K 5 F 7 L 8 B 10 I 6 C 13 J 12 A 2 N 3 D 12 G 10 M 5 H 16**Forward Pass**Next a “forward pass” is made through the network using the estimated durations. Begin with the earliest activity (“A” in this example), and work through to the end, to determine the earliest start and finish times for each activity. In this example, activity “A” starts at time “0”, and adding the duration (2), results in finishing at time “2”. Then, activities “B”, “C”, and “D” can all begin at time “2”, and the corresponding durations are applied to each to determine the earliest finish times (“12”, “15”, and “14” respectively). When there is more than one predecessor activity (e.g., activity “J” which can’t begin until both “C” and “G” are finished), the earliest start time for the successor activity (“J”) will be the latest of the early finish times for its preceding activities (in this example, the “24” for “G”). The next chart shows the complete forward pass and resulting early start and finish times.**Forward Pass**E (12, 24) 12 F (12, 19) 7 K (25, 30) 5 L (30, 38) 8 B (2, 12) 10 I (19, 25) 6 C (2, 15) 13 J (24, 36) 12 A (0, 2) 2 N (38, 41) 3 D (2, 14) 12 G (14, 24) 10 M (30, 35) 5 H (14, 30) 16 Legend: Activity (Earliest Start, Earliest Finish) Duration**Backward Pass**The next step is to complete a “backward pass,” beginning with the final activity and working backward through the network to determine the latest start and finish times. Use the earliest finish time for the final activity from the forward pass as the total time to complete the project. So the latest finish time is the same as the earliest finish time for the final activity. Since the duration remains the same, the earliest and latest start times will also be the same for the final activity. The latest start time of the final activity then becomes the latest finish time of each immediately preceding activity. Subtract the duration of each immediately preceding activity from its latest finish time to determine its latest start time. In this example, the latest start time for activity “N” is time “38” (same as the earliest start time from the preceding chart), so the latest finish times for activities “L” and “M” become time “38”. Subtracting the duration of activity “L” (8) from the latest finish for “L” results in a latest start date of “30”. Likewise, subtracting the duration of “5” for activity “M” from its latest finish results in a latest start of time “33”.**Backward Pass**Continue backward through the network logic to determine the latest start and finish times for all the remaining activities. When an activity has more than one successor activity, (e.g., activity “B”, which must be complete before activities “E” and “F” can begin), the latest finish time for the preceding activity will be the earliest of the late start times for the subsequent activities (in this example, time “12” for Activity “F”). The next chart shows the complete forward and backward passes and resulting early and late start and finish times.**Backward Pass**E (12, 24) 12 (18, 30) F (12, 19) 7 (12, 19) K (25, 30) 5 (25, 30) B (2, 12) 10 (2, 12) L (30, 38) 8 (30, 38) I (19, 25) 6 (19, 25) C (2, 15) 13 (13, 26) J (24, 36) 12 (26, 38) A (0, 2) 2 (0, 2) N (38, 41) 3 (38, 41) D (2, 14) 12 (4, 16) G (14, 24) 10 (16, 26) M (30, 35) 5 (33, 38) H (14, 30) 16 (17, 33) Legend: Activity (Earliest Start, Earliest Finish) Duration (Latest Start, Latest Finish**Slack**Activities where the latest start and finish times are later than the earliest start and finish times have “slack.” Activities where the latest start and finish times are the same as the earliest start and finish times do not have “slack.” To determine the slack for an activity, subtract the earliest start or finish time from the latest start or finish time (e.g., LS – ES or LF – EF). The next chart shows the project’s critical path for this example (the path with activities “A-B-F-I-K-L-N”). Notice there is no slack in any of the activities on the critical path. Except under unusual circumstances, this will always be the case. You can see that activity “E” has 6 time units of slack (using the formulas above, 18-12 or 30-24). While it can start as early as time “12”, it can start as late as time “18” and not delay the overall project.**Slack = Late Start (LS) – Early Start (ES) = Late Finish**(FS) – Early Finish EF) E (12, 24) 12 (18, 30) F (12, 19) 7 (12, 19) K (25, 30) 5 (25, 30) L (30, 38) 8 (30, 38) B (2, 12) 10 (2, 12) I (19, 25) 6 (19, 25) C (2, 15) 13 (13, 26) J (24, 36) 12 (26, 38) A (0, 2) 2 (0, 2) N (38, 41) 3 (38, 41) D (2, 14) 12 (4, 16) G (14, 24) 10 (16, 26) M (30, 35) 5 (33, 38) H (14, 30) 16 (17, 33) Legend: Activity (Earliest Start, Earliest Finish) Duration (Latest Start, Latest Finish