Censorship reflects a society's lack of confidence in itself.
— Potter Stewart
Introduction
Figure 1: JLC Graph of Deck Building Costs Per
Square Foot As a Function of Total Square
Footage (Source).
I have spent much time during my career collecting data on how production costs vary with production rate. For example, I have good data to support that unit optical component costs have dropped by 7% for every doubling of quarterly use rate (discussion). The functional relationships between product cost and volume varies depending on the type of product.
The simplest functional relationship I see is with lead-acid batteries. For most quarterly purchase quantities, the cost of a standard lead-acid battery is strongly dependent on the commodity price of lead. Plastic enclosures show a similar cost dependency on the cost of petroleum.
Yesterday, I saw an interesting article in the Journal of Light Construction (JLC) that does an excellent job of showing how the per-square foot cost of a deck construction drops as the total area of the deck increases (Figure 1). I found this interesting because I am going to have a structure built on my lake property in northern Minnesota. I thought this data would provide a good illustration of how I use Mathcad generate product cost models.
Analysis
Raw Data
Figure 2 shows the raw data for deck cost per square foot as a function of total deck area.
Figure 2: Plot of Raw Data.
Figure 2 shows that the cost per square foot reduces dramatically as the area of the deck increases. The functional relationship looks nearly linear on a log-log plot, but there could be a bit of curve flattening for large deck areas.
Curve Fitting
Figure 3 shows my curve fitting exercise for two different functions: (1) a standard power law relationship, and (2) a power law relationship with offset (aka constant). The power law with offset looks like a better fit and is what I would use.
Figure 3: My Trial of Two Different Curves.
Total Cost
Figure 4 shows how the total cost of desk increases with area. You can see that the increase is linear with large deck sizes but starts to flatten out for small decks. This is analogous to other products where buying small quantities is expensive because vendors must charge for a fixed amount of overhead per transaction and there are few units over which to amortize that cost.
Figure 4: Plot of Total Deck Cost Versus Square Footage.
Conclusion
I spend a fair amount of time trying to develop models for product cost. I found it interesting that construction industry has the same interests and goes through the same sorts of analysis that I do.