Concept: Recall that impediments and constraints (I/C) represent an opportunity cost to projects. Estimates of a project’s total I/C cost are comprised of periodic I/C costs. Such costs are observed when a task’s EV@AT is less than its PV@ESi.e., it’s an I/Ctask.
But, there’s a gap: paradoxically, the value of I/Ctasks observed within a period is not the periodic value. This gap must be filled in before hidden gems can be applied to schedule management.
Practice: The value planned and earned within a given period can be observed, but it does not represent the periodic value of either Rework or Impediments/Constraints. That sounds paradoxical: the value within the period is not the periodic value.
Here, we have another case in which common parlance is misleading. [1] The phrase “periodic value” can mean “within the period”, or it can mean “as of the period” (specifically, as of the period’s end).
Clearly, the total value associated with R or I/C tasks within a period is the sum of values that occur only within the period, i.e., the total value at the end of the period less the total value at the start of the period.
By contrast, the total value as of a period includes values carried over from previous periods, i.e., the total value from the start of the project to the end of the current period. It is possible for both R and I/C tasks to occur before the current period, and if that happens, the periodic value is not limited to a single period.
An example illustrates the point.
Figure 1
Figure 1 is a variation on the case cited in previous posts. In this variation, the value earned for Task 8 (3 units) has been removed. Consequently, the ES time occurs within Period 3, rather than at its end. [2] In such a case, the periodic value of Period 4 is not limited to the value planned and earned within that period. There is Rework value for task 5 in Period 3 and I/C value for tasks 2 and 4 also in Period 3. The value planned and earned as of Period 4 includes these values.
The clarification solves one puzzle but creates another. Calculating the value of Rtasks and I/Ctasks within a period is a simple matter of adding up the relevant values observed in the period. But, how is the value of Rework and Impediments/Constraints calculated as of a period’s end?
A bruteforce method would be to, first, track all individual tasks across the project timeline, calculating the ES at the end of each period and, then, to assess the resulting performance taskbytask against ES and AT. Adding to the complexity, the assessment would have to account for the fact that only a portion of Rtasks is designated for Rework. [3]
Fortunately, Walt Lipke has proposed a simpler method. The SAI includes both taskbytask analysis and an estimation of the Rework. Based on the SAI, the periodic value is approximated using geometry. For details on how this applies to Rtasks, click here and here.
Geometric approximation can also be applied to I/Ctasks. [4] Unsurprisingly, the calculation starts with SAI’s counterpart, the ICI. The ICI expresses impediments and constraints over all periods up to and including the current one. Thus, it takes account of value in other periods.
The difference between the ICI in two successive periods expresses the amount of work impeded or constrained as of the intervening period. Similarly, the Percent Complete (%C) taken at the same two successive periods expresses the amount of work completed as of the intervening period.
Let ICI_{1 }and ICI_{2 }indicate the fraction of work that is impeded or constrained as of the start and end of the target period. In addition, let C_{1 }and C_{2 }represent the fraction of work that is completed as of the same period. How much work is impeded or constrained as of the intervening period?
As already mentioned, the amount can be determined using geometry. First, depict ICI1, ICI2, C1, and C2 as successive points on a chart (see Figure 2).
Figure 2
The area of the rectangle (Width times Length) is given by the following formula:
…where Width is defined as the fraction complete and Length as the amount of ICI_{1}.
The area of the triangle (half of the Base times the Height) is given by the following equation:
…where the Base is defined as the fraction complete and Height as the difference between ICI_{2} and ICI_{1}.
The sum of the two areas gives the area under the curve.That sum, in turn, reduces to the following equation:
…and that is the formula for the area of a trapezoid, ((1/2 * (a+b)) * h. Hence, this is a special case of the trapezoidal approximation technique.
As the Area_{Sum} is the periodic I/C value (ICp), the total I/C value as of the end of a given period (ICcum) is easily calculated:
…where the cumulative amount is the sum of the periodic amounts from the first period to the Actual Time. [5],[6]
From the cumulative amount and the current ICI, an estimate of the total project I/C cost (IC$Tot) can then be calculated as follows:
…where the estimate acknowledges the observed I/C cost up to the current time (ICcum) and then forecasts the budget impact over the remainder of the project.
The forecast uses the current value of ICI (ICI_{AT}) as a benchmark for adherence to the schedule. [7] It then applies that level of performance to the remaining budget (BAC – EV).
In effect, the forecast says that, assuming the same level of performance on the remaining work (as represented by the remaining budget), here is the amount of budget that will be required for the impediments and constraints that are to come. Add that to the I/C cost already incurred, and the result is the I/C cost for the whole project. [8]
As mentioned in an earlier post, calculating IC$Tot is another new feature of the theory. It’s now time to address how the new features—the “hidden gems”—can be used to improve schedule performance.
Notes:
[1] In a previous post (13 Jan 16), I explained another problem created by common parlance: the criticism of ES theory that led to Longest Path. To my chagrin, I must also admit that my own criticism of SPI (the standard EVM metric for schedule performance) is flawed in the same way (see Van De Velde (2010)). Finally, in a future post, I will explain how different senses of “late” cause similar confusion. Clearly, ambiguities in common parlance can seem to undermine theories, but, just as clearly, delineation of the different senses dispels the confusion and preserves the theory.
[2] The ES is 2.85; the AT is 4; the Rtasks are 5 and 7; the I/Ctasks are 2 and 4.
[3] Recall that Rtasks are, strictly speaking, candidates for Rework. Just a fraction of their value is likely to incur rework. That fraction is determined by a mathematical model. It’s not clear whether the model would apply to individual tasks, as it does to the sum of their value. In any case, the brute force method of setting the periodic value is superseded by the approach that is introduced next.
[4] For I/Ctasks, the brute force method is feasible. The value that is impeded or constrained does not follow the same downward curve that characterizes rework and is not modeled mathematically. So, calculation of periodic I/C value is more straightforward than periodic Rework. Still, it demands measurement of each task’s EV@AT and PV@ES and accumulation of negative differences between them by period to and including the ES time. Either the results have to be stored or they have to be recalculated each time the analysis is performed. The estimation technique Walt developed for Rework is a simpler approach. That's why it's used here.
[5] The calculation assumes that the ICp from previous periods is available for calculation of the total. Tools such as MS Project attribute earned value to the time at which it is incurred, rather than to the original planned time. A Gantt chart in such cases looks different from the simple chart used in the text. It shows a time offset between the the EV and the baseline PV. MS Project automatically adjusts the current plan to align with value actually earned (unless the task is designated as manually scheduled). So, an I/Ctask that is impeded/constrained but earns value would appear as follows in a Gantt chart:
[6] Measuring the current EV against the Baseline PV ensures that the ICp and %Complete accurately represent the periodic value.
[7] This is a controversial assumption. Some think the inevitable variation in performance level over time undermines such benchmarks—see Alleman (especially the last three paragraphs). Others think that, over time, the level smooths out—initial irregularities are overcome by amoreorless typical level for the project. If so, the benchmark has credibility. Interestingly, traditional EVM seems sensitive to the issue. It offers different formulas for EAC that depend on the expected type of future behaviour.
[8] Similar to Rtot, this is reminiscent of the EVM formula for the Estimate at Completion (EAC), EAC=AC + ((BACEV)/CPI), where AC is the Actual Cost and CPI is the Cost Performance Index (Lipke, 2011a, p 9).
References:
Van De Velde, R. (2010). Managing the Unexpected with Earned Schedule. PM World Today, XII(X))
