Cutting Logs Part 2: Counting Feet

Introduction 

In the last post, I looked at how much mileage I could get out of a single bottle of melatonin. For this next part, I'll be expanding on the concept of the evolving probability of partial replacement by looking at how construction companies build things out of wood.

The Problem

As a sometimes builder myself, I've often observed construction sites as I walk past to try to understand more about the approach to making new things - a kind of anecdotal meta-study. One thing I've noticed over the years is that there seems to be a lot of leeway for workers to use raw materials as needed, especially wood. I'm also aware that construction projects often drop off excess wood at liquidators to salvage costs on unused materials. In an age when engineering software allows us to predict usage so accurately, I'm curious how companies end up with extra.

There are three parts to this question, as I see it, that I would like to be able to answer:
1. How much material is purchased up front, and how often should new material be ordered?
2. Can different strategies for carving out raw materials save on eventual excess? If so, is the implementation of those strategies practical enough to justify putting them into practice?
3. Would project planning software add value, and if so, how much? 

Approach

Before I get started, I'm going to use one intuited assumption (that also links back to the first blog) to simplify - When working with wood products, only a finite number of lengths are used. 2 by 4 comes standard in 8 foot lengths, and for this analysis I'll assume that only whole number cut lengths (i.e. 1,2,3,4,5,6,7,8 feet) are allowed onsite.

The other big assumption here is that there is no correlation from one cut to the next. That means that whatever I need now has no bearing on the next cut I need. In truth, mostly 8 foot cuts are probably going to be needed most of the time, but I'm more concerned with the mechanics of replacing partially used 2 by 4's and worrying about the whole logs obfuscates that.

The general algorithm will look something like this:
1. Determine what length of wood is required
2. Check to see if there is a large enough piece in the inventory from which to cut it
3. If one exists, use that, otherwise order a new 8 foot piece and make cuts
4. Add to the inventory any excess from the previous steps

In Excel, I'm going to use VBA to first do an unconstrained build to start understanding some of the features of this problem. I'll assume that I know roughly how 'long' a house will be in total, i.e. that it will take a definite total length of wood to construct. For this, I'm assuming 5400 feet. 

Ignoring the supply side question for a moment, I'll look purely at the demand features. That is, I'll start by assuming wood shows up at the moment it is needed. To make cuts, I'll test both cutting new lengths out of the smallest or largest available to see if there is a better strategy.

Finally, I'll repeat the experiment for a constrained house where the exact number of each type of cut is known ahead of time. This will simulate the advantages of using software to analyze the structure ahead of time. 

Results

Question 1: Is there an optimal way to order the wood?

The initial question turns out to be the hardest to answer. The short version is 'not really'. The model I constructed does allow for predictable re-order points for a given starter inventory. However, in the unconstrained project, the smallest available cut strategy for new pieces leaves excesses of mostly the 6 foot lengths, while the largest available cut strategy leaves mainly 5 foot lengths. This seems to be more than a curiosity, and bares future investigation.

In real life, this anomaly is going to be massively overshadowed by how fast the crew is working. The recomendation is to measure how many cuts can be made and used by a crew in some time period and backtime that to minimize excess.

Question 2: Can we manage the amount of left-over at the end of the project with different strategies?

Yes, but not by a lot. Allowing cuts to be made from the largest available length adds about 10% to the ending excess footage (compared to the total length used to create the house), but both strategies leave close to 3% excess. 

Question 3: How much value does predictability add?

By setting the number of each type of allowable cut, the excess footage at the end of the project drops to 0. Drawing on the above findings, this means that tight planning and execution can cut up to 3% of costs by eliminating unused partial lengths. I'm not familiar with profit margin breakdown on a construction site, but anecdotally this seems pretty insignificant against the cost of project delays. 

 In the constrained version I needed about 675 total boards to make all my cuts. At $4 a pop (per Home Depot), the material cost of the project comes out to $2,700. Without constraint, the cost increase would be $81. This means that the prorated use of the planning software has to come in at less than $81 per project. If you're running 10 projects annually, for example, the software cost better be less than $810 per year. This ROI gets even tighter when you consider that some of the price of the excess can be recovered by selling to secondhand dealers. 

 Additional Findings

1. The main strategic finding is that worksite managers should enforce returning scrap to easily usable piles. 
2. Inventory doesn't stick around for long, and it is almost definitely not worth trying to pre-order smaller cuts if you have any idea how many of the largest cuts are needed
3. Both constrained and unconstrained houses ended up needing the same number of total lengths to complete. 

Conclusion

This analysis turned out completely different than expected, and from the one in Part 1. Instead of being able to precisely answer anything or determine any kind of underlying structure, what I ended up with was a tool whose insights are highly sensitive to the initial configuration. 

If there is a philosophical conclusion, it's that this analysis seems to remind us not to try to find a problem for every solution. Sometimes common sense is the cheapest software package there is.


Click to download the Excel file.

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