Applying Learning Curve Theory in Construction Cost Estimating

Ramani Sundaram
We are all familiar with the expression ‘learning curve’ or ‘practice makes perfect’ and probably have used it many times without thinking about the science or math behind it.

The basis for the ‘learning curve theory’ has stemmed from the observation that experience makes repetitive tasks easier to perform. When a particular task or sequence of work is repeated without interruption, subsequent operations require reduced time and effort. The principle of learning curve, which has been used effectively in manufacturing, can also be used in construction as labor productivity and equipment operations affect the cost of many repetitive activities. Estimators can use this theory in cost estimating. Contractors can apply it in productivity studies and productivity improvement and for future bidding of similar activities. Owners may utilize this theory in evaluating bids or change orders and subsequently for negotiating prices.

The theory of Learning Curve (LC), sometimes also called ‘experience curve’ or ‘dynamic curve’ was first developed by T.P. Wright in 1936 [1], while studying time required to make airplane parts. He observed that, as the workers gained more experience, less time was required to manufacture these parts. This effect was not linear, but seemed to have a constant decrease. To be more precise, he observed that the labor required for producing doubled quantities, decreased by a constant factor in relation to the original quantity.

The rate of improvement is referred to as the learning rate and is expressed in terms of slope of a curve. If it is a 70% curve, it represents a 30% reduction in effort with every doubling of experience. Similarly, an 80% curve corresponds to a 20% reduction in effort. This percentage varies with the type of industry, from 60% to 95%. Normally an 80% curve is used in construction. The effort required by the fourth unit will be 20% less than the second unit will; the hundredth unit will require 20% less effort compared to the fiftieth unit.

Table 1 (Partial) [2] - Method 1 – Unit Value declining by 80%

UnitsUnit ValueCumulative Total ValueCumulative Average Value
Column AColumn BColumn CColumn D
1 1.00 1.00 1.00
2 0.80 1.80 0.90
3 0.70 2.50 0.83
4 0.64 3.14 0.78
5 0.60 3.74 0.75
6 0.56 4.30 0.72
8 0.51 5.35 0.67
10 0.48 6.32 0.63

Table 2 (Partial) [2] - Method 2 – Cumulative Average declining by 80%

UnitsUnit ValueCumulative Total ValueCumulative Average Value
Column AColumn BColumn CColumn D
1 1.00 1.00 1.00
2 0.60 1.60 0.80
3 0.51 2.11 0.70
4 0.45 2.56 0.64
5 0.42 2.98 0.60
6 0.39 3.37 0.56
8 0.36 4.10 0.51
10 0.33 3.70 0.37

In the actual application of learning curve, two methods may be used as indicated in the above two tables (Using Log-Log plots).

  • Method (1) states the unit value (labor per unit) declines by a constant percent with doubled quantities [2] (Refer Column B in Table 1)

  • Method (2) states the cumulative average labor (the average direct labor hours for all units produced up to any particular point) declines by a constant percent with doubled quantities. [2] (Refer Column D in Table 2)

Though Method 2 is suggested for statistical reasons, if one wants to be conservative, Method 1 may be used.

Applications in Estimating

There are many repetitive tasks like construction of high-rise buildings with typical floors, erection of Structural framing, precast concrete unit installation, repetitive welding or drilling and so forth. For such activities, experience curves can be used in estimating and for productivity study and improvement. In construction, there are also many specialized activities that may involve an initial LC duration - for example tunnel boring with a TBM (Tunnel Boring Machine), complicated structural or equipment erection, etc. Using the LC theory, it is possible to calculate the right cost \ time allowances for the learning curve period.

Change Orders

For some change orders, a contractor may be asked to proceed with the work and the cost will be negotiated later based on data that is developed during the execution of the change. This will be a practice especially if the item is new and repetitive. Using Table 1 or 2, the reduction of man-hours can be incorporated in estimating the unit prices for such items.

Table 3 shows an actual estimate where LC theory was used for a miscellaneous metal change order estimate in one of the projects.

Table 3 – Hours are Tabulated using Method 1

LotUnitsHoursLC Factor
1 001 to 100 160.00 1.00
2 101 to 200 128.00 0.80
3 201 to 300 112.00 0.70
4 301 to 400 102.40 0.64
Total 0.33 502.40

The contractor originally submitted a proposal for a total of 640 hours ((quantity = 400) x 1.60 hrs/ea), based on his initial performance for the first 100 units. Using LC theory the total hours required were projected as 502.40 (Table -3) in our change order review. It is interesting to note that this is only 78.5%% of the original proposal. It was possible to convince the contractor to accept the reduced hours based on the learning curve principle for the balance work.

Learning Curve Quantity

Estimators often ask the question what quantity should be considered for applying the LC theory. Experimental studies show that “the application of "Learning Curve Theory" on a construction site should be limited to the first 25% or so of the total production under consideration” [3].

The LC theory is applicable in construction just as in manufacturing. Besides cost estimating, it can also be used for projecting labor requirements, productivity study and schedule analysis. The users have to pay attention to some caveats but still it is a valuable application that can be increasingly used by owners as well as contractors.

References:

[1] Wright, T.P., Factors Affecting the Cost of Airplanes, Journal of Aeronautical Sciences, 3.4 (1936): 122-128

[2] B. R. Elder, Learning Curves – Theory and Practice, AACE Transactions, 1963

[3] AEW Services, Vancouver, BC2001,p 20 of 26, Originally 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’.

Recommended Reading:

Stewart R et al, Learning Curves and Progress Functions, Cost Estimator’s Reference Manual (CH 5, P-176), John Wiley & Sons, Apr 1995

Technical Note 2, Learning Curves, (PDF 0.3MB) and Predict Fututre Failures From Your Maintenance Records (PDF 0.2MB)