finish date or the early start date from the late start date. The numbers will be the same. If not, you made a math error.

Total Float = Late Start - Early Start (or Late Finish - Early Finish)

Free float is the number of days an activity can be delayed without taking float away from the next activity. Another way of saying the same thing is that free float is the number of days an activity can be delayed without delaying the early start date of the next activity. To calculate the free float for an activity, you subtract any lag and the early finish for the activity from the early start for the next activity. To calculate the free float for activity 1020 in figure 2-13 you would take the early start for activity 1050, subtract any lag between 1020 and 1050 (zero in this case), and subtract the early finish for activity 1020 (11 - 0 - 10= 1). Free float for activity 1020 is 1 day. You can see that delaying activity 1020 by 1 day will not delay activity 1050 from its early start date. Delaying activity 1020 by 2 days will delay the start of activity 1050 until day 12 and will reduce the float for activity 1050 by 1 day (to zero, in this case). Delaying activity 1020 by more than 2 days will delay the project completion date because 1020 has only 2 days of total float.

Free Float = Early Start (next activity) - Lag (if any) - Early Finish*

Looking at activity 1020 in figure 2-13 you see you could start that activity as early as day 3 or as late as day 5. Now subtract 3 from 5 and enter 2 days as the total float. Where the early start and late start are the same there is no float. No float means you have to start that activity on its early start date. It cannot be delayed without delaying the project completion. Activities with no float are said to be critical. The first and last activities will always be critical and there will be a critical path of activities between them. The critical path in figure 2-13 is 1010-1040-1060-1070. The critical path allows management to focus attention on those activities that cannot slip.

TYPES All examples shown so far have used finish-to- start logic. This logic type requires an activity to finish before the next one can start. There are two other types of logic relationships that are frequently encountered. They are the start-to-start (S/S) and finish-to-finish (F/F). S/S is where the start of the second activity is dependent on the start of the first activity. F/F is where the finish of the second activity is dependent on the finish of the first activity. Finish-to-start logic will give you the longest total project duration and is the most common logic type used in the NCF. The S/S and F/F logic can be used to compress (shorten) the schedule. This compression is often used in the execution phase of the project to catch up. These logic relationships also can be used to plan repetitive work such as roadways or sewer lines. For a sewer line you wouldn't want to excavate the entire ditch before starting to lay pipe.

NOTE: Equations marked with an (*) are changed with different types of logic (S/S or F/F).

Start-to-Start

Forward Pass: Early start + Lag = Early start (next activity)

Backward Pass: Late start - Lag = Late start (preceding activity)

Free Float: Early start (next activity) - Lag - Early start

Finish-to-Finish

Forward Pass: Early finish + Lag = Early finish (next activity)

Backwwd Pass: Late finish - Lag = Late finish (preceding activity)

Free Float: Early finish (next activity) - Lag - Early finish

The general rule to follow with different types of logic is to always follow your logic connectors.

Figure 2-14 is an example of a network with lag times (between activities B and F, C and D, C and E). Figure 2-15 is an example of logic relationships. Using the formulas, work through the calculations.

LEVEL III BARCHARTS

Having determined the construction schedule on the precedence network, you must now transfer that

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