This paper was first published in the Canadian Journal of Civil Engineering, Vol. 21, 1994 pp 939-953, under the title "A Pragmatic Approach to Using Resource Loading, Production and Learning Curves on Construction Projects". It has been modified only to the extent necessary to make it presentable in web page format. Published here October, 2001.

## What can be Learned of Practical Value?

#### Manpower Consumption

In Figure 6, the data in Figure 1 has been replotted to a horizontal time scale of 100% and a vertical scale such that the overall average manpower loading is at 100%. Superimposed is a smoothed envelope curve representing the same data. This curve is in the shape of an asymmetrical dome and, since it is directly related to the shape of the manpower loading curves discussed earlier, also appears to be quite typical. The typical fit is never perfect of course, but it is suggested that the fit is sufficiently close to draw some conclusions relating to planning and management of similar type jobs.

##### Figure 6: Histogram, envelope, and empirical resource loading input of the Figure 1 civil contract example of site manpower

However, the mathematics of such a curve is complex and not particularly useful for preliminary planning purposes. A simple profile made up of straight lines would be more useful as a first approximation. Such a relationship has been suggested by Allen.

Allen puts forward the following simple empirical relationship as a first approximation to planned manpower loading (Allen 1979).

1. The maximum on-the-job manpower is 160% of the average manpower requirement.
2. The maximum on-the-job manpower first occurs after 40% of the total manpower requirement has been expended.
3. The period of maximum on-the-job manpower accounts for 40% of the total manpower requirement.
4. The maximum on-the-job manpower first occurs when 50% of the project time has elapsed.
5. The period of maximum on-the-job manpower occurs for 25% of the project time.
Note that manpower may be measured in man-hours or dollars.

The resulting figure is a trapezoid and for convenience will be referred to as a "Standard Resource Input" (SRI) profile. This profile is also shown in Figure 6. Summarizing, it will be noted that 40% of the total manpower requirements occurs in the first 50% of the time, a further 40% of the total manpower requirements occurs in the next 25% of the time, and the last 20% of the manpower requirements occurs in the last 25% of the time.

The period of peak loading at 160% of the overall average is a valuable indicator. Once the total man-days and duration of the work have been estimated, the level of site support services required for the work force during the period of peak production can be determined.

For comparison, this SRI profile is shown in Figure 7 superimposed over the NECA manpower envelope corresponding to the NECA S-curve shown in Figure 2. It will be seen that the profile is very similar, but that the peak electrical manpower loading occurs some 10-12% later than in the SRI profile. This is due to the longer Stage 1 for the reasons described earlier.

##### Figure 7: Standard resource input vs. typical manpower loading of electrical systems installation in new building construction - NECA

The SRI trapezoidal profile can be integrated to produce the cumulative total as shown by the S-curve marked as curve (a) in Figure 8.[3] Thus, this S-curve is made up of two quadratics and a middle linear portion. This curve will be referred to as the SRI S-curve.

#### Production S-curves in Practice

As described earlier, the typical S-curve effectively consists of three stages namely, Build-up, Steady-state and Run-down. Stage 1 is in fact the most critical since it is during this stage that the unique conditions of the site are experienced, and the stage is set for a steady, productive, and profitable run at the main body of the work. Stage 2 is important because peak productivity and efficiency must be attained and maintained without interruption for profit to be actually generated. Stage 3 is important for ensuring that the work is brought to an effective and satisfactory conclusion without time and money being wasted.

For example, if the manpower is cut too early the work gets extended. If it is cut too late unnecessary cost is incurred in paying for unproductive man-hours.

Since Stage 1 is the most critical to the subsequent successful conclusion of the work, so it is worth examining this stage more closely. As will have been gathered from the earlier descriptions, the shape of the S-curve in this stage is made up of two components.

1. The build-up of resources
2. Added production through productivity improvement

Build-up of resources has been discussed with examples in earlier sections.

Added production through productivity improvement implies that the rate of output achieved will exceed that which might be inferred simply from examining the resource loading. On a well-run project this is a key management expectation, which will be reflected in the shape and timing of the progress S-curve for the job. Indeed, this leads to a second simple empirical relationship.

### Empirical Relation #2

#### A First Approximation to a Project Progress Curve[4]

A first approximation to project progress or output is suggested by the following empirical relationship.

• 25% of total progress is achieved in the first third of the total time,
• Another 50% in the next third, and
• The remaining 25% in the last third.

This, a curve representing an accelerating rate of progress will be exhibited in the first 25% of the time, while a similar but opposite curve will occur in the last third.

Like the SRI S-curve, this curve is also made up of two quadratics and a linear section in the middle. For convenience it will be referred to as a "Standard Production Output" (SPO) S-curve. Note that if this profile is being used for planning or forecasting, the 100% Total Time base will correspond to the realistically planned duration. If, however, the profile is being used for post completion analysis, the Actual Total Time may be substituted. The units of progress may be expressed in units appropriate to the work, such as excavation volumes, numbers of piles, or value of work produced as shown in Figure 4.

The SPO S-curves is shown plotted as curve (b) in Figure 8. The differences between the two curves is essentially developed during Stage 1 of the S-curves, i.e. the first third of the Total Time. The shapes of the two curves are largely driven by the addition of resources. However, if the difference is attributed to improvement through learning, it can be shown that this difference is equivalent to a Learning Curve of 86% based on the LL-CA Model calculation discussed below. This is within the range of productivity-improvement-through-learning observed through independent measurements on construction sites.

3. Formulae for the determination of points on the S-curves are given in Appendix 1
4. This empirical progress curve has been used on the job by the author for many years and has been offered to students in cost management and cost control project management workshops.