So now that we’ve talked about Efficiency, let’s now turn our attention to the second performance metric, Productivity and see how it's different. ©

__Productivity__Productivity is another one of those metrics that has multiple uses and multiple ways of being calculated depending on how it is being used. You can use it for Economic productivity, Labor productivity, Total factor productivity, Service sector productivity, and several other forms of measurement. But for our discussion we want to look at the productivity metric as it applies to a production system. We’re looking for a metric to measure the system and answer the question: “Did we improve?” For a production system application we can define productivity as the ratio between output and input, or simply

**Productivity = Output quantity/Input Quantity (p = O/I)**

Mathematically the answer is a ratio and is calculated by determining the number of units completed (output) divided by the number of units input (usually hours). As an example, suppose you had completed 750 units of work and used 1000 hours completing the work the equation would look like this:

**0.75 = 750 units/1000 hours**

In essence, for every hour worked you completed 75% (0.75) of one unit of work. In this instance, the productivity measure is also the efficiency measure of the system. Now, when the system is measured we can answer the question “Did we improve?” The best means to improving productivity is to increase the numbers of units produced while the measured time stays the same or decreases. Or you could decrease the amount of time required to make the same number, or more, units.

A closer look reveals that productivity can actually sub-divided into two separate processes. The first is the

*production process*and, the second is the*monetary process.*The production process is a measureable component of the system, but the monetary process is also measureable, if you do it correctly. In the Theory of Constraints (TOC) measurements library there is a formula for measuring productivity. The formula is simple and is expressed as follows:**Productivity = Throughput/Operating Expense or (P = T/OE)**

In order for this to work both the output and input need a common denominator, which in this case is dollars. The output can be measured in dollars by using the throughput calculation. The definition of throughput is defined as: “

*the rate at which inventory is converted to sales*.” The monetary calculation for throughput is the selling price of the product minus the total variable costs (TVC.) Total variable cost are defined as the cost of raw material, plus any sales commission (for each product sold), plus the shipping costs. In others words, you are looking for all the costs associated with a single product. However, the labor costs are not included in the TVC. The labor costs are part of the OE dollars. The difference between the Selling Price (SP) and the Total Variable Costs (TVC) is considered to be the Throughput (T.) As an example, suppose we had a product that sold for $1.00 and the TVC was $0.40 then the Throughput (T) would be $0.60.The Operating Expense (OE) can be expressed in dollars and is calculated as labor, overhead, gas, lights, benefits and all other expenses. The attractiveness of using this type of measure is that it includes

*of your expenses and not just the labor expense in the form of hours used. This measure provides a much cleaner picture of the productivity and not just a partial look. Also, by knowing the Throughput and Operating Expense numbers it becomes very easy to calculate the Net profit during any given period. Net Profit (NP) is simply determined by subtracting the Operating Expense from the total Throughput number. In other words:*__ALL__**NP = (T – OE).**

The important aspect of accurately determining the productivity metric is converting units to throughput dollars and operating expense to dollars. The dollars component is the common denominator between units and hours. Once you have that information the productivity measurement accuracy improves greatly. Let move on to a discussion about Utilization.

In my last posting in this series, I’ll discuss the performance metric Utilization and then summarize what all three of these metrics really mean.

Bruce Nelson

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