Project Network Schedules

Ref#:21A

FORMULAS, EQUATIONS, AND RULES

1. Project Network Schedules

Network schedules are created after duration estimates and the relationships between the work packages have been determined. Following a path(s) from left to right makes a forward pass.

Forward pass

o Yields early start (ES) and early finish (EF) dates

o Early finish = early start + duration

o RULE: If there are multiple predecessors, use LATEST EF to determine successor ES

After all paths have been given their forward path, they are traversed from right to left to make a backward pass.

o Backward pass

Yields late start (LS) and late finish (LF) dates

Late start = late finish – duration

RULE: If there are multiple successors, use EARLIEST LS to determine predecessor LF

Once the forward and backward passes have been completed, the total float for the node can be calculated by:

Total float = late finish – early finish

2. Normal Distribution

The normal distribution, commonly known as the bell curve, is a symmetrical distribution, as shown inFigure 1-1. Each normal curve can be distinctly described using the mean and sum of the values. The possibility of achieving the project objective in the mean time or cost is 0%, with a 50% chance of falling below the mean and a 50% chance of exceeding the mean. Adding one or more standard deviations (σ) to the mean increases the chances of falling within the range. The probability of falling within 1σ, 2σ, or 3σ from the mean is:

1σ = 68.27% 
2σ = 95.45%
3σ = 99.73%

4. Weighted-Average or Beta/PERT Distribution

The beta distribution is like the triangular distribution except more weight is given to the most likely estimate. This may result in either a symmetrical or an asymmetrical (skewed right or skewed left) graph. An asymmetrical graph is shown in Figure 1-3.

Where O = optimistic estimate, ML = most likely estimate, and P = pessimistic estimate, variance for a task (V) is:

                                         V = σ2

Mean (μ)

(μ) = (O + 4ML + P) ÷ 6

Standard deviation (σ)

σ = (P – O) ÷ 6

5. Statistical Sums

o The project mean is the sum of the means of the individual tasks: μp = μ1 + μ2 + . . . + μn

o The project variance is the sum of the variances of the individual tasks: Vp = V1 + V2 + . . . + Vn

o  The project standard deviation is the square root of the project variance:

6. Earned Value Management

Earned value management is used to monitor the progress of a project and is an analytical technique. It uses three independent variables:

Planned value (PV): the budget or the portion of the approved cost estimate planned to be spent during a given period

Actual cost (AC): the total of direct and indirect costs incurred in accomplishing work during a given period

Earned value (EV): the budget for the work accomplished in a given period

These three values are used in combination to provide measures of whether or not work is proceeding as planned. They combine to yield the following important formulas:

Cost variance (CV) = EV – AC

Schedule variance (SV) = EV – PV

Cost performance index (CPI) = EV ÷ AC

Schedule performance index (SPI) = EV ÷ PV

Negative CV indicates cost overrun. Negative SV indicates a project is behind schedule.

A CPI greater than 1.0 indicates costs are below budget. An SPI greater than 1.0 indicates a project is ahead of schedule.

A CPI less than 1.0 indicates costs are over budget. An SPI less than 1.0 indicates a project is behind schedule.

7. Estimate at Completion

An estimate at completion (EAC) is the amount we expect the total project to cost on completion

and as of the “data date” (time now). There are four methods listed in the PMBOK® Guide for computing EAC. Three of these methods use a formula to calculate EAC. Each of these starts with AC, or actual costs to date, and uses a different technique to estimate the work remaining to be completed, or ETC. The question of which to use depends on the individual situation and the credibility of the actual work performed compared to the budget up to that point.

A new estimate is most applicable when the actual performance to date shows that the original estimates were fundamentally flawed or when they are no longer accurate because of changes in conditions relating to the project:

EAC = AC + New Estimate for Remaining Work

The original estimate formula is most applicable when actual variances to date are seen as being the exception, and the expectations for the future are that the original estimates are more reliable than the actual work effort efficiency to date:

EAC = AC + (BAC – EV)

The performance estimate low formula is most applicable when future variances are projected to approximate the same level as current variances:

AC = AC + (BAC – EV) ÷ CPI A shortcut version of this formula is:

EAC = BAC ÷ CPI

The performance estimate high formula is used when the project is over budget and the schedule impacts the work remaining to be completed:

EAC = AC + (BAC – EV) ÷ (CPI)(SPI)

Formulas to be used with Figure 1-4 above include:

CPI = EV ÷ AC

SPI = EV ÷ PV

8. Remaining Budget

RB = Remaining PV

or

RB = BAC – EV

9. Budget at Completion

BAC = the total budgeted cost of all approved activities

10. Estimate to Complete

The estimate to complete (ETC) is the estimate for completing the remaining work for a scheduled activity. Like the EAC formulas above, there are three variations:

o ETC = an entirely new estimate

o ETC = (BAC – EV) when past variances are considered to be atypical

o ETC = (BAC – EV) ÷ CPI when prior variances are considered to be typical of future variances

11. Communications Channels

o Channels = [n(n – 1)] ÷ 2

where “n” = the number of people

12. Rule of Seven

In a control chart, the “rule of seven” is a heuristic stating that if seven or more observations occur in one direction either upward or downward, or a run of seven observations occurs either above or below the mean, even though they may be within the control lines, they should be investigated to determine if they have an assignable cause. The reason for this rule is that, if the process is operating normally, the observations will follow a random pattern; it is extremely unlikely that seven observations in a row

would occur in the same direction above or below the mean.

The probability of any given point going up or down or being above or below the mean is 50-50 (i.e.,

50%). The probability of seven observations being consecutively in one direction or above or below the mean would be calculated as 0.507, which equals 0.0078 (i.e., much less than 1%).