# ABC, XYZ classification

Russian: ABC, XYZ классификация

ABC classification

In multiple product problem for different products could be implemented different inventory management models[1], [2]. The reason is to increase the efficiency of inventory management subject to the certain service level. Different inventory policies require different workload. In the multiple product system it’s efficient to assign policies with higher workload to the products with the higher value. To do that, one should classify products to categories with similar characteristic. ABC analysis is one of techniques to provide such classification.

For ABC classifications different indicators could be used, such as consumption rate, sales volume, inventory costs etc. The most important products belongs to A group, and the others – to B and C. There are various rules to allocate products among the groups, one of them is Pareto's Principle (or the 80-20 Rule).

According to the principle products, which brings 80% revenue, correspond to category A. The next 50% of products belong to category B. The last products are in the C category. In a general case there are 3 groups in the classification, but sometimes companies implement 5 or more categories. An example of ABC classification in terms of sales volume is represented in the tableau 1:

Tableau 1. ABC classification

XYZ classification

XYZ classification corresponds to analysis of uncertainty in demand. Measure of uncertainty is a coefficient of variation (a ratio of RMS deviation to a mean value of series). For XYZ classification all products should be ranked by increasing mode subject to the coefficient of variation. Consider XYZ classification for monthly demand. General algorithm of XYZ analysis is the following:

1. Find mean of monthly demand for each product i:

$\mu _{i} =\frac{\sum _{j=1}^{n}D_{ij} }{n}$

where Dij is demand for a product i in a month j,j = 1,2,...,n.

2. Find standard deviation σi of demand for each product i:

$\sigma _{i} =\left(\frac{\sum _{j=1}^{n}(D_{ij} -\mu _{i} )^{2} }{n} \right)^{0,5}$

3. Calculate coefficient of variation CVi for each product i by the following formula:

$CV_{i} =\left(\frac{\sigma _{i} }{\mu _{i} } \right)\times 100$

4. Arrange all products by the coefficient of variation CVi on increasing mode (to form a ranked list).

5. Classify all the products to X, Y and Z groups according to the following rule, tableau 2:

Tableau 2. XYZ classification

Obviously, some categories could be empty under such a rule of classification. The classification rule in the Tableau 2 is based on the absolute values of coefficient of variation. The alternative rule is based on relative values. For instance, in the category X there are the first 20% products from the ranked list, in the category Y there are the next 30% of products in the ranked list, in the category Z there are the last 50%.

The results of XYZ classification could be different for calculations of coefficient of variation for different periods (days, months, years). For instance, consider sales of 10 types of automobile parts through 12 months, tableau 3.

Tableau 3. Sales

Construct a ranked list and provide XYZ classification, tableau 4:

Tableau 4. XYZ classification

## References

1. Bowersox D.J., Closs D.J. Logistical Management: The Integrated Supply Chain Process, McGraw-Hill, New York, 1996 .
2. Ramamurthy P. Operations Research - New Age International, 2007..