# throughput accounting measurement units Earlier today I was reading about the key business measures used in the Theory of Constraints, and running some examples in my head while I tried to make sure I understood exactly what was being said. Here’s what I learned…

To recap, the only business measures considered by TOC are

Throughput (T)
Cash receipts for actual sales, minus the cost of the raw materials used towards those sales.
Operating Expense (OE)
The expenditure required to produce what we sold, including heat/light, payroll etc.
Investment (I)
The money invested up front, or tied up in the operation. This includes depreciation on machinery, buildings, and other assets and liabilities.

These can be combined to give other measures; for example return on investment:

`ROI = (T - OE)/I`

(For more detail see throughput accounting on Wikipedia, for example.)

What struck me were the units used to express these measures. The only one I’ve seen explicitly stated was Throughput, which is expressed as “cash receipts per unit of time” – let’s call it dollars-per-day. So in order for the ROI calculation to make arithmetical sense, operating expense (OE) must also be measured in dollars-per-day. So far so good.

Now I had been expecting Investment (I) to simply be a sum of money. But in that case ROI would turn out to have units of “per-day”, which is clearly nonsense. So Investment must also be measured in dollars-per-day, and now I see that makes sense too. And in turn, this all implies that ROI is just a number, a scalar value. (Better perhaps to express it as a ratio or a percentage – so that an ROI of 1.50 is easier to understand as a 3:2 return or a 150% return.) Other traditional measures are calculated as follows:

```Net profit (NP) = T-OE
Return on investment (ROI) = NP/I
Productivity (P) = T/OE
Investment turns (IT) = T/I```

If my logic above is correct, Net Profit is expressed in dollars-per-day and all the others turn out to be scalar, unit-less numbers – and that alone helps me understand them much more.

## 2 thoughts on “throughput accounting measurement units”

1. Murray Tait says:

I think the unit for ROI of “per day” possibly works, but should be put as “scalar per day”. Consider that a interest bearing bank account gives you a ROI of 5% per annum or 1.000133 per day (assuming compound interest).

2. kevin says:

Murray: I use the term “dollars per day” as shorthand for “dollars per unit of time” – I should have explained that. But still your point is well made. Perhaps the compounding of interest needs to be seen as another revenue stream, with its own ToC model. I have no idea what ToC has to say on this subject – can anyone else help?