1. Project Networks

2. A,4 B,3 C,4 D,6 E,3 H,6 F,5 G,4 I,2 St,0 Fin,0 Example Network - terminology C,t Activity Duration of Activity (ES, LS) Early Start Late Start (ES, LS) LS means Late Start EF means Early Finish EF LS This is the basic model. The forward pass will find the Early Start for each activity and ultimately the overall project duration. The backward pass will find the Late Start times for each activity. Together with Early Starts, slack for each activity can be determined. Activities with 0 slack mean that they are on the critical path. Slack Time is LS-ES ES = EF predecessor EF = ES + t LF = LS successor LS = LF-t Note: The book uses a slightly different notation at each node. By putting the EF and LS times on the arcs, IMHO it is easier to identify ES and LS times for the node. ES EF LSLF

3. A,4 B,3 C,4 D,6 E,3 H,6 F,5 G,4 I,2 St,0 Fin,0 C,t Activity Duration of Activity (ES, LS) Early Start Late Start (0, LS) (4, LS) (9, LS) (4, LS) (10, LS) (15, LS) (17, LS) 0 LS LF LS LF LS Forward Pass (0, LS) 0 14 15 3 4 9 10 17 0 7 0 4 4 4 When you have multiple paths coming into a node, you take the highest EF because the activity can not start until all preceding activities are completed The forward pass shows that the total project duration will be 17 days, weeks, or whatever the unit of time is for the project Remember this is the Early Finish (EF) time. You get this by taking the ES time (in this case 0) and adding the activity duration (4) to get a early finish of the activity C of 4. All EF times are calculated the same way Example Network ES = EF predecessor EF = ES + t

4. A,4 B,3 C,4 D,6 E,3 H,6 F,5 G,4 I,2 St,0 Fin,0 C,t Activity Duration of Activity (ES, LS) Early Start Late Start (0, 1) ( 0, 6) (0, 0) (4, 5) (4, 12) (9, 9) (4, 4) (10, 11) (15, 15) (17, 17) 0 11 9 4 5 12 1 8 5 6 0 15 1 6 0 Backward Pass (0, 0) 0 14 15 3 4 9 10 17 0 7 0 4 4 4 When you have multiple paths coming into a node, you take the smallest LS because if the activity started any later than that, the overall project duration would get larger. By definition, we set the Late Start equal to the Early Start at the finish node. The party can’t start until we are done, but don’t want to wait a minute to start it!! The Critical Path is identified by looking at activities with zero slack time (LS-ES = 0) or in our model the numbers in the parentheses are the same. Remember this is the Late Start (LS) time. You get this by taking the LS time of the next activity (in this case 17) and subtracting the activity duration (2) to get a late start of activity I of 15. All LS times are calculated the same way. If you were to start activity I later than time 15, you would go past the project duration of 17. Example Network LF = LS successor LS = LF- t or LS = LS successor - t Note that the Late Finish of an activity is actually the late start of the successor (next) activity. You get the late start of the activity by subtracting the activity duration from the late start of the next activity. That way you will ensure that your late finish for the activity is no later than the Late Start for the next activity