A Quick Method to Estimate the Impact of Lower Average Order Size

By John Alleman, Productivity Measurement & Improvement Advisor

During the off-season, the sales department announces that they would like to book smaller orders to fill plant capacity. They have asked you, the production manager, how this will impact product costs. Intuitively you know: when the plant processes smaller orders for a given product, that means more total time used on product changeovers, and plant machinery runs for less time with more changeover interruption.
   Plant output decreases during a given period of time; fixed product costs per unit of production increase, and direct labor costs increase for a given production volume. Overall production costs per unit of output increase. From a computing standpoint, estimating total plant production output could end up being an Excel worksheet as large as a football field. A real nightmare!

There is a quicker way to estimate this and give sales the information they need. For most manufacturing operations there is normally a good correlation between average order size and direct labor intensity. Average order size is measured in some number of units of output per order. This could be pounds, cases, gallons, etc. It has to be a unit which works well across all of the products and product sizes. Direct labor intensity is simply the number of production units per hour of direct labor.

Figure 1: Theoretical Correlation of Average Order Size vs. Labor Intensity

A typical correlation of average order size and direct labor intensity is shown in Figure 1. 
Intuitively the shape of this curve makes sense. When average order size is low (on the X axis), product runs are shorter, with more changeovers, less-efficient use of labor, and lower labor intensity (on the Y axis). When average order size is high, the opposite is true – up to a point. The plant can only be so efficient – i.e. if there were no product changeovers, there would be an absolute limit of labor intensity. This is why the curve levels off at higher average order values. With an understanding of this concept we can now gather data from our production control system (ERP, BPCS, etc.) for each month going back about 24 months. 
Figure 2 summarizes the data you’ll need to collect and analyze each month. Production units must be consistent across all product lines. Typically pounds work best, but other units such as cases, gallons, containers, etc. may be more appropriate.

Figure 2: Collected & Computed Data

After computing our Production Units per Order (the X data ) and the Production Units per Direct Labor Hour (the Y data), the next step is to plot these points and apply a best-fit curve to the data. The trendline function on Excel works very well for this. Go to “trendline options,” select a second order trendline and check the boxes to display the equation and the R2 value. The R2 value should normally be 0.75 or greater for a good correlation. If the correlation value is lower, try a different set of common units of production to gain a better R2 value. If it’s still low, evaluate your division of direct and indirect labor.

Let’s consider a practical example for illustration. Suppose our food manufacturing plant has the average order size and direct labor intensity plotted in Figure 3. In this case, it made sense to use pounds as the common production unit. With our 24 months  of data plotted, we add the trendline (blue curve) to fit our data and the formula that expresses the trendline (shown in the blue box). The R2 value is 76%, so we are confident this is a good fit.

Figure 3: Example Labor Intensity vs. Avg. Order Size

During the previous month we averaged about 6,000 lbs per order. We would like to know how product costs will increase if we lower average order size by half (to 3,000 lbs/order) while still producing the same amount of finished product. From our correlation, we can predict that direct labor intensity will decrease from 360 lbs per direct hour to 260. 
The next thing to consider is which product costs will change. If we are going to make the same amount of product in both scenarios, then raw material, packaging and indirect labor costs per pound of finished product should remain the same. Because we will need to run the plant longer to make the same amount of product, direct labor, energy, and utility costs per unit of finished product will increase. But by how much? If the unit cost of direct labor is about $0.05/Lb when we are at 6,000 Lbs/order, then direct labor cost per direct labor hour should be $0.05/Lb x 360 Lbs/Direct labor hour = $18/Direct hour (fully loaded direct labor rate). When we reduce the average order size to 3,000 Lbs/order, then at the same fully loaded labor rate, the direct labor cost per pound increases to $18/Direct hour.

Figure 4: New Direct Labor Unit Value Computation- Lbs/Direct Hour = $0.069/Lb.

The computation is illustrated in Figure 4.

If we repeat this calculation for the other unit costs that will vary with direct labor intensity (energy and utilities), the results should similar to those summarized in Figure 5.

Figure 5: Summary of Units Costs and Changes

Raw material, packaging, and indirect labor are assumed to remain constant. In reality, packaging costs may increase slightly due to increased loss from more product startups. Also note that we assumed that energy and utilities increased by the same ratio as direct labor. This will generally hold true for operations in which water, electricity, wastewater, and natural gas consumption are proportional to time of plant operation vs. productive units of output. For our example, the final result of the halving of order size was a $0.026/Lb cost increase, about 5%. In summary, this is a quick and fairly reliable “cocktail napkin method” of estimating product cost changes with average order size changes. As always, IPC is available to help you use this tool.