Appendix IV: The Forward and Backward Pass
Early and late activity dates are determined by the logical sequence of effort that planners lay out. Network logic calculates activity dates that define both when an activity may start and finish and when an activity must start and finish to meet a specified program completion date.
Suppose house construction and exterior finishing have been completed, and the necessary electrical, gas, and water inspections are complete. Several activities remain before the owner can occupy the house—specifically, utility systems must be started up and tested. Workers must
set the electricity meter,
start up and test the electrical system,
set the gas meter,
start up and test the furnace and air conditioner,
set the water meter, and
start up and test the plumbing fixtures.
Once these activities are completed, then the start-up and testing phase is completed and the owner can occupy the house. These activities must happen in a specified order:
The electricity, gas, and water meters cannot be set until the inspections are completed.
The electrical system cannot be tested until the meter is set.
The furnace and air conditioner cannot be tested until the gas and electricity meters are set.
The plumbing fixtures cannot be tested until the gas and water meters are set.
The start-up and test phase is complete when the electrical system, furnace, air conditioner, and plumbing fixtures are tested.
Table 9 shows the expected durations of each activity, given the estimated resources.
Table 9: Expected Durations and Estimated Resources in House Construction
| Activity | Resource name | Resource units | Work hours | Duration in days |
|---|---|---|---|---|
| Set electricity meter | Electrician | 2 | 16 | 1 |
| Electrical service technician | 1 | 8 |
|
|
| Start up and test electrical system | Electrician | 1 | 16 | 2 |
| Set gas meter | Gas service technician | 2 | 16 | 1 |
| Start up and test furnace and air conditioner | HVAC technician | 1 | 8 | 1 |
| Set water meter | Water service technician | 2 | 16 | 1 |
| Start up and test plumbing fixtures | Plumber | 2 | 32 | 2 |
Source: GAO. | GAO-16-89G
Assuming the inspections are completed by Monday, January 26, the electricity, gas, and water meters can be set on January 27. Then, assuming that all succeeding activities are related by finish-to-start relationships, the start-up and testing network will appear as in figure 51.
Figure 51: Start-Up and Testing Network
The activities in figure 51 are planned according to forward scheduling; that is, activities begin as soon as possible according to their logic relationships. For example, once the electricity meter is set, starting up and testing the electrical system can begin. Calculating the earliest dates when activities can start and finish—given their predecessor and successor logic and durations—is known as the forward pass. In the forward pass, durations are added successively through the network.
If inspections complete at the end of the business day on Monday, January 26, then the work associated with setting the electricity, gas, and water meters can begin on Tuesday, January 27. This is the early start (ES) for these activities and is noted in a box in the upper left corner of the text box representing each activity in figure 52. To calculate the early finish (EF) of each activity, the duration is added to the ES. One day must be subtracted to account for the full day of work available between the early start and early finish. That is,
EF = ES + duration - 1
The EF is noted in the upper right corner of the activity’s text box. The durations are noted between the ES and EF boxes. In these simple cases of 1-day activities, the early start and early finish dates are the same day. The numbers above the date boxes represent the cumulative duration of the project as work progresses along those dates.
Figure 52: Early Start and Early Finish Calculations
Early starts of successor activities are calculated according to the logic of the network. For a single finish-to-start relationship, the early start of the successor activity is simply the predecessor’s early finish plus 1 day. The “start up and test electrical system” activity can begin the day after “set electricity meter” finishes, as shown in figure 53. The EF for “start up and test electrical system” is its ES (January 28) plus its 2 days of duration (January 30) and minus 1 day (January 29).
Figure 53: Successive Early Start and Early Finish Calculations
When an activity has two or more predecessor activities, the ES is calculated with the latest EF of its predecessor activities. That is, an activity cannot begin until the latest predecessor finishes. In figure 54, “start up and test furnace and AC” cannot begin until both the electricity meter and the gas meter are set. Setting the meters takes a day for each one, but they happen concurrently so they both finish on January 27. Therefore, starting up and testing the furnace and AC can start as early as January 28. Likewise, plumbing fixtures testing cannot begin until the gas meter and the water meter are set. But because these are both 1 day long and occur on the same day, testing plumbing fixtures can begin as early as January 28.
Figure 54: Complete Early Start and Early Finish Calculations
Note that testing plumbing fixtures is expected to take 2 days as well. Its EF is calculated as its ES (January 28) plus 2 days (January 30) minus 1 day (January 29). Finally, the ES of the “start up and test complete” milestone is calculated with the latest EF of its three predecessors. Both “start up and test plumbing fixtures” and “start up and test electrical system” have EF dates of January 29. Therefore, the earliest when “start up and test complete” could possibly occur is January 29 (milestones have no duration and therefore occur immediately after their latest predecessor).
As can be concluded by these calculations, the ES and EF dates are the earliest dates when an activity may start and finish. We are also interested in the latest dates when an activity must start or finish. That is, what are the latest dates when activities must start and finish to finish a project by a given date? These dates are calculated by the backward pass. Once the forward pass has been calculated, the backward pass determines the latest possible start and finish dates for activities.
The backward pass essentially calculates how long activities can wait to start or finish with the project still completing on time. The backward pass begins with the EF of the project. In the house construction set-up and test example, each of the three testing activities has a late finish (LF) of January 29. This is equal to the latest EF of the testing activities and, likewise, the date of the completion milestone. In figure 55, the LF is noted in the bottom right corner of each activity. To calculate an activity’s late start (LS), the duration is subtracted from its LF, and 1 day is added to account for the full day of work between the two dates:
LS = LF - duration + 1The LS is noted in the bottom left corner of the activity’s text box in figure 55.
Figure 55: Late Start and Late Finish Calculations
In general, an activity’s LF is equal to its successor’s LS minus 1 day:
LF = LS - 1When an activity has two or more successor activities, its LF is derived from the earliest LS of its successors. Stated another way, an activity does not need to finish until its successor must start; in the case of multiple successors, the earliest successor start date drives the activity’s LF. In the following example, “set gas meter” has two successors: “start up and test furnace and AC” and “start up and test plumbing fixtures.” The late start for testing plumbing fixtures is January 28, and the late start for testing the furnace and AC is January 29. The LF for “set gas meter” uses the earliest LS of its successors, which in this case is January 28 for “start up and test plumbing fixtures.”
The successors for “set electricity meter”—“start up and test electrical system” and “start up and test furnace and AC”—also have different LS dates (January 28 and 29). Its LF is therefore January 27, 1 day before the earliest LS date. The complete forward pass and backward pass calculations are shown in figure 56.
Figure 56: Early and Late Dates of a Start-Up and Testing Network
