Calculating Composite Production Values – Forensic Use

By:  Charles B. Antone   

As a follow up to previous brief indicating the underlining governing equation for calculating composite production values for multi-item assemblies, I will show how to use the equation forensically, specifically to solve for an unknown individual production value.

To review, the Governing Equation is shown to be:

Where:

CP = the composite production value
n = individual item production values
∑ = is the mathematical symbol for summation, which is the operation of adding a sequence of numbers

In the previous brief, I cited an example of an interior wall assembly with multiple trade actions, as shown in Table 1 below.  Let’s use this example to show how one could find any given production value in the composite assembly if one knows the composite production value and all the other individual composite production values, less one.


Table 1:

Item		Description	Production	Unit	Labor Cost
1	Layout		?	LF	?
2	Top Track	10' each	275	LF	$572.51
3	Bottom Track	10' each	500	LF	$314.88
4	Studs	10' each, 16" O.C.	100	LF	$1,574.40
5	Insulation	16" x N Rolls	260	LF	$605.54
6	Drywall 0-8'	(8'x4') 32 SF Sheets	240	LF	$656.00
7	Drywall 8' +	(8'x4') 32 SF Sheets	80	LF	$1,968.00
8	Tapping 0-8'	(8'x4') 32 SF Sheets	300	LF	$524.80
9	Tapping 8' +	(8'x4') 32 SF Sheets	37.5	LF	$4,198.40

Now let’s solve for the unknown Layout value by using the CP equation.

Using the values from Table 1, and plugging them into the CP equation and a to represent the Layout value, we have:

Solving for a:

Taking the reciprocal of both sides:

Subtracting 0.0661492 from both sides:

Finally, again taking the reciprocal of both sides, we have:

 a=599.975 ≈ 600 Linear Feet per Man Day

We know from the previous blog entry, when we were solving for the composition production value using the data from Table 1, that the Layout production value was 600 LF, which can serve as a check for the above example.  It’s noted that one can find any one of the individual production values, not just the first, as in the example above.

Conclusion:

The above example shows that using the composition production equation, one can find items that may have been missed, or miss-reported, and many more.  For example, this could prove to be useful for Estimators/Project Managers who are tracking the production values realized on a project (verses the estimated values in the bid as a measure of ongoing profitability) but have missed tracking one of the individual items in the assembly.  Or a situation where, given the amount of man days allocated to the building of a particular assembly and the reported production values by the on-site manager, one would want to check a reported value that does not seem correct.