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Home » A new way to measure inventory leanness

October 27, 2015

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Because inventory management is so important for an organization's operational and financial success, inventory leanness is never far from a supply chain leader's mind. And good inventory management requires good measurement. As the adage goes, you cannot manage what you cannot measure.

Traditionally, inventory leanness has been measured using inventory turns, which in simple terms can be expressed as the ratio of sales to the average inventory level. The inventory turns measure was easy to compute, easy to explain, and easy to use, so it was widely adopted and many variants were developed. Yet the basic idea has never changed: simply compare inventory levels to sales. In this article, we present a new way to measure inventory leanness, which we refer to as the Empirical Leanness Indicator (ELI). The benefit of using ELI is that it gives managers a more accurate assessment of inventory leanness in cases where inventory turns could be misleading. The reason is that ELI considers both the economies of scale in inventory management and industry-specific relationships between sales and inventories. Inventory turns and its many variants ignore both of these important factors.

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What is ELI?

While inventory turns simply compare a company's inventories to its sales, ELI compares inventories to a benchmark inventory level, which depends on a company's size (sales) and industry. This benchmark inventory level is based on the concept of turnover curves developed by Ballou^{1} and shown in Figure 1. A turnover curve describes the relationship between sales and inventories in a specific industry. Since this relationship can change from industry to industry, only data from companies in the same industry are used in estimating the turnover curve. This way, the turnover curve establishes a benchmark for proper comparisons.

In Figure 1, blue dots represent companies, the x-axis represents sales (size), and the y-axis represents inventory levels. The turnover curve captures the benchmark inventory level that a company should hold given its size. For example, the benchmark inventory level for Firm A is indicated by the green dot. The difference between actual and benchmark inventory levels (denoted by the dashed line) forms the basis for ELI. Companies below the turnover curve are considered lean, as they carry relatively less inventory for their size. The opposite is true for those above the turnover curve. To continue our example, Figure 1 shows that Firm A is not lean because it holds more inventory than it should for its size.

Comparison of ELI and inventory turns

Extensive empirical analyses (such as Eroglu and Hofer 2011) indicate that turnover curves are typically concave.^{2} That is, as a company grows (its sales increase), its inventory level also increases, but at a slower pace. This means that companies become more efficient in managing their inventories as they sell more products. Thus, there are economies of scale in inventory management.

Figure 2 illustrates a situation where inventory turns can be misleading because that measurement ignores economies of scale. Suppose that Firm B doubles its sales and inventories and moves from the green dot to the blue dot. Since both its sales and its inventories doubled at the same time, its inventory turns will stay constant. Moreover, if Firm B's inventory turns were higher than the industry average in the beginning, they will remain so after its sales double. However, the existence of economies of scale suggests that as Firm's B's sales doubled, its inventories should have less than doubled.

In the beginning, Firm B was below the turnover curve, indicating that its inventory was lean. After its sales and inventories doubled, it moved above the curve, because it has not experienced the efficiency gains that would be expected as a result of increased sales. Nevertheless, inventory turns suggest that Firm B is still as efficient as before. ELI, by contrast, captures a more accurate view by showing that Firm B has become less lean, as it failed to capture the economies of scale in inventory management.

The turnover curve can change from industry to industry due to the many different factors that can shape the inventory-sales relationship, such as different production technologies, the perishable nature of some products, and the intensity of competition in a particular industry. The turnover curve can be flatter in some industries and more curved in others. Similarly, the turnover curve can change over time—as new technologies are adopted, for example. ELI takes into account industry and time differences because a turnover curve is estimated for a group of companies in the same industry and the same time period. Hence, ELI assesses how lean a company is compared to its peers (competitors) in the same industry and during the same time period. Inventory turns, in contrast, calculate the ratio of sales to inventories in isolation of all the factors that may influence the relationship between the two.

How to apply ELI

ELI can be easily calculated in Excel. All you need is sales and inventory figures for businesses in a given industry at a particular point in time. This information is freely available for publicly traded companies from sources such as EDGAR or Yahoo Finance.

As an example, Figure 3 shows the sales and inventory figures (Columns B and C) of publicly traded companies operating in the audio and video equipment manufacturing industry (NAICS 334310) in the first quarter of 2003. First, we estimate the equation for the turnover curve *Inventory* = Î±*(Sales)*^{Î²}. (Please see the sidebar for a more detailed explanation of this functional form.) Although it may look intimidating at first, this equation can be linearized by simply taking the natural logarithm of both sides, which yields ln*Inventory* = lnÎ± + Î²(ln*Sales*). The natural logarithms of sales and inventory are shown in Columns D and E in Figure 3. To estimate Î± and Î², we can run a linear regression analysis in Excel with ln*Inventory* as the y variable and ln*Sales* as the x variable. In the "regression" dialog box, it is important to check the "standardized residuals" box.

The estimation results from Excel are shown in Figure 4. The estimates for lnÎ± and Î² are 2.32 and 0.89, respectively (cells H15 and H16). Moreover, the R square value (cell H3) is 0.89 (which by coincidence equals the estimate for Î²), which suggests that the model explains 89 percent of the variation in inventories. In other words, 89 percent of the differences in inventory levels among companies are attributable to the differences in sales volumes. This means that sales volume is the single most important driver of inventories. Such strong results are very typical in our analyses of dozens of industries over several decades. There is a very fundamental, very basic relationship between inventories and sales. In our experience, the explanatory power of this simple model, as measured by R square, rarely drops below 70 percent, and it is not uncommon to see R square values above 95 percent. This attests to the scientific validity of our model.

The coefficient Î² determines the shape of the turnover curve; that is, the extent of economies of scale. When Î² < 1, there are economies of scale in inventory management, which is true for most industries. When Î² > 1,there are diseconomies of scale, which is rarely observed. In Figure 4, the estimate of Î² is 0.89 (cell H16). Given the logarithmic transformation, this estimate means that for every 1 percent increase in sales, inventories increase by 0.89 percent on average. Hence, there are economies of scale in this particular industry.

The Excel output in Figure 4 also gives us the turnover curve. While Column M identifies firms 1 through 16, Column N (titled "Predicted Y") shows their benchmark inventory levels; that is, the point on the turnover curve corresponding to each company's inventory level. Column O lists the residuals, which represent the deviation from the estimated regression line (benchmark inventory level). A positive residual suggests that the company lies above the regression line, while a negative residual suggests the opposite. While there is no upper or lower limit on the residuals, the standardized residuals are scaled to range from -3 to +3. This standardization aids cross-industry comparisons. Hence, we use standardized residuals for ELI, which is calculated by multiplying the standardized residuals by -1. This way, a company that has a lot of inventories, and therefore lies above the regression line and has a positive standardized residual, will have a negative (low) leanness value. Similarly, a firm below the regression line will have a positive (high) leanness value.

To summarize, follow these steps for calculating the ELI:

- Obtain sales and inventory data for companies in a given industry and time period.
- Calculate the natural logarithm of sales and inventories.
- Use regression in Excel with ln
*Inventory*as the y variable and ln*Sales*as the x variable. Ask for standardized residuals. - Multiply standardized residuals by -1 to obtain ELI values.

A more detailed explanation of ELI can be found in Eroglu and Hofer (2011). For those who are interested in experimenting, we have calculated the turnover curves in various industries in 2013. You can benchmark your company's inventory leanness by going to our companion website for additional information, an instructional video, and a sample Excel file.

Beyond company-level comparisons

In this article, we have introduced ELI as a new way of measuring inventory leanness. ELI ranges on a continuum from -3 to +3. If a firm's ELI value is close to zero, it must be close to the turnover curve and therefore carries approximately the benchmark inventory for its size (sales). As a firm's ELI value increases it becomes leaner. Conversely, as its ELI decreases it becomes less lean. Note that ELI is not a categorical variable where a firm is either lean or not lean. Rather, ELI is about the *degree* of leanness.

Inventory turns are universally known, and ELI is a relatively new measure. Naturally, there can be resistance to ELI. For example, it can be argued that the results obtained by measuring leanness using ELI and inventory turns do not always disagree. Indeed, there can be situations where there is a significant overlap between ELI and inventory turns. This is especially true when the coefficient Î² of the turnover curve is equal to or close to 1. However, one cannot predict the extent of overlap between the ELI and inventory turns before estimating the turnover curve. As Î² deviates from 1, the overlap between ELI and inventory turns decreases and the disagreement increases. But once you calculate the turnover curve, you have a measure that is more accurate than inventory turns. So, why not use ELI? If you do end up using inventory turns as a measure of leanness, use caution and remember that inventory turns can lead you to improper comparisons.

ELI's method can be extended in interesting ways. Turnover curves are useful in establishing benchmarks for various operations. For example, instead of comparing companies, you can compare how efficiently various stocking locations (warehouses, distribution centers, and so forth) manage inventories. Similarly, you can compare the inventory performance of your company's retail locations. In addition, instead of using dollar amounts for sales and inventories, you can use other measures, such as case pack, units, pallets, and more.

The beauty of ELI is that it captures the fundamental relationship between sales and inventories—knowledge that can be applied in many interesting ways to benchmark and improve inventory management. Please let us know if you have any questions or comments. We would be especially interested to know how you implement ELI in your supply chain operations.

**Notes:**

1. R.H. Ballou, "Estimating and auditing aggregate inventory levels at multiple stocking points," *Journal of Operations Management* 1, no. 3 (1981): 143-153.

2. C. Eroglu and C. Hofer, "Lean, leaner, too lean? The inventory-performance link revisited," *Journal of Operations Management* 29, no. 4 (2011): 356-369.

Estimating the equation for the turnover curve

We model the turnover curve with the equation *Inventory* = Î±*(Sales)*^{Î².} So, if a company's sales volume is *s,* the corresponding benchmark inventory level is obtained by raising *s* to the power of Î² and multiplying by Î±, expressed as Î±*s*^{Î²}. The elements Î± and Î² are industry-specific parameters whose values change from industry to industry. Hence, they have to be estimated separately for each industry.

The advantage of using this function is that it can take on different shapes depending on Î² (the shape parameter), as shown in Figure 5. For example, when Î² = 1 the equation becomes *Inventory* = Î± x *Sales* and the turnover curve becomes a straight line. This means that inventories and sales increase or decrease at the same rate. When sales double, the inventories also double. Thus, there are no economies or diseconomies of scale when Î² = 1.

When the shape parameter Î² is between 0 and 1, the turnover curve becomes concave. In this case, sales and inventory change at different rates. More specifically, inventories increase or decrease more slowly than sales. For example, when sales double, inventories less than double. In other words, a company needs less than double the amount of inventory to sustain double the sales. Hence, there are economies of scale.

The opposite is true when the shape parameter Î² is greater than 1. In this case, inventories change at a higher rate than sales. For instance, when sales double, inventories more than double, indicating diseconomies of scale. In other words, a company needs more than double the amount of inventory to sustain double the sales.

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Cuneyt Eroglu is Assistant Professor in the Supply Chain and Information Management Group at the D'Amore-McKim School of Business, Northeastern University.

Adenekan Dedeke is Lecturer in the Supply Chain and Information Management Group at the D'Amore-McKim School of Business, Northeastern University.

Christian Hofer is Associate Professor in the Supply Chain Management Department at the Sam M. Walton College of Business, University of Arkansas.

Adriana Rossiter-Hofer is Assistant Professor in the Supply Chain Management Department at the Sam M. Walton College of Business, University of Arkansas.

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