*Intended learning outcomes: Calculate examples for the ABC Classification and for the combined ABC-XYZ classification. Differentiate between Safety Stock Variation and Demand Variation. Determine batch size depending on stockout costs. Assess the effectiveness of the order point technique.*

## 11.7.1 The ABC Classification

This exercise refers to Section 11.2.2. Perform an ABC classification for the items shown in the table in Figure 11.7.1.1, separately for two ABC categories 1 and 2. Class A accounts for 75% of sales turnover, and items in the B class account for 90% of turnover. Why does it often make sense to perform separate classifications for two or more ABC categories? Is your classification of the items as A, B, or C the only possible solution?

**Fig. 11.7.1.1** Sales and ABC categories
of some items.

*Solution:*

The division of the items into two categories for a meaningful ABC classification is necessary so that like items can be compared; the categories will reflect different types of items, such as individual parts and final products.

The classifications in the solution above do not represent the only possible solution. Certain classifications can be problematic around the break points. For example, why should item 4711 receive the classification B, while items 8639 and 9050 are assigned to classification C?

## 11.7.2 Combined ABC-XYZ Classification

A combined ABC-XYZ classification allows decision making as to the appropriate method of materials management for individual items. Mark the areas (items) in the matrix in Figure 11.7.2.1 for which Kanban control would be appropriate. Explain the reasoning behind your answer.

**Fig. 11.7.2.1** Combined ABC-XYZ classification.

*Solution:*

The prerequisite for the Kanban technique is continuous demand along the entire value chain. X items are particularly suitable for production in a Kanban system. For the Y group, A items should not be controlled by Kanban, for their consumption value is high, and fluctuating demand leads to lower stock-inventory turnover and thus longer storage time. For the same reason, Kanban control is as a rule not appropriate for Z items, whereby an exception can be made for C items, as carrying costs for C items may be lower than the costs of a more expensive control technique.

## 11.7.3 Safety Stock Variation versus Demand Variation

True or false: The safety stock level increases with increasing demand.

*Solution:*

As the formula in Figure 11.3.3.7 shows, this statement is generally not correct. The safety stock depends on the *standard deviation* of the demand during the lead time. Increasing demand does not automatically increase either the standard deviation during the statistical period or the lead time.

## 11.7.4 Batch Size Depending on Stockout Costs (*)

The carrying costs for a certain article are 2 per unit and year. Stockout costs are 5 per unit. The average annual consumption amounts to 1000, and the standard deviation of demand during lead time is 10. No safety stock is intended. Normal distribution is assumed.

a. How large should the batch size be, considering the optimum stockout probability? Can the fill rate target of 99% be met? What are the carrying costs per year?

b. Assume a batch size of only 250. What are the values for safety stock and fill rate corresponding to the optimum probability of stockout per order cycle?

c. Now assume a safety stock of 20 units. Again, the batch size is 250. What are the values for service level and fill rate?

*Solution:*

a. Zero safety stock entails a service level of 50% (see Figure 11.3.3.6, for example) and — by Figure 11.3.3.3 — a probability of stockout per order cycle of 50%. Because stockout can be expressed as cost per unit, the formulas in Figures 11.3.4.2, 11.3.4.4, and 11.3.4.5 apply. Therefore,

**· **Batch size = 1000 * 50% * (5/2) = 1250.

**· **Stockout quantity coefficient P(s) = 0.399.

**· **→ Fill rate = 1 – ((10/1250) * 0.399) = 99.68% > 99%.

**· **Average inventory = 1250/2 = 625.

**· **→ Carrying costs per year = 625 * 2 = 1250.

b. Again, the formulas in Figures 11.3.4.2, 11.3.4.4, and 11.3.4.5 apply:

**· **Optimum probability of
stockout = (2/5) * (250/1000) = 10%.

**· **→ Optimum service level = 1 – 10 % = 90%.

**· **→ Safety stock = 1.282 * 10 {note: the standard deviation}
≈ 13.

**· **→ Stockout quantity coefficient P(s) = 0.048.

**· **→ Fill rate = 1 – ((10/250) * 0.048) = 99.81%.

c. Applying the formulas in Figures 11.3.4.4, 11.3.4.2, and 11.3.4.5:

**· **Standard deviation = 10; => safety factor = 20/10 = 2.

**· **→ Service level ≈ 98%.

**· **→ Stockout quantity coefficient P(s) = 0.008.

**· **→ Fill rate = 1 – ((10/250) * 0.008) = 99.97%.

## 11.7.5 Effectiveness of the Order Point Technique

Figure 11.3.1.1 shows the famous saw-tooth-shaped curve that is characteristic of the order point technique. You can view the curve here:

Explore the changing shape of the inventory curve for continuous and less continuous demand (moving your cursor over the gray icon executes your input choice). Try out different parameters to calculate lot size and service level. Try other consumption values. Observe the effect of the consumption values on the order of the production or procurement batch size. Again, touching the “calculate” icon executes your input choice. The initial demand values are automatically reentered by moving your cursor over the gray demand shape icon.

## Course sections and their intended learning outcomes

##### Course 11 – Inventory Management and Stochastic Materials Management

Intended learning outcomes: Describe usage statistics, analyses, and classifications. Explain in detail the order point technique. Disclose how to calculate safety stock. Differentiate various batch or lot sizing techniques.

##### 11.1 Stores and Inventory Management

Intended learning outcomes: Present characteristic features of stores management. Produce an overview on inventory transactions. Describe physical inventory and inventory valuation.

##### 11.2 Usage Statistics, ABC Classification, XYZ Classification, and Other Anlayses

Intended learning outcomes: Present statistics on inventory transactions, sales, and bid activities. Explain the ABC Classification and the Pareto Chart. Describe the XYZ Classification and Other Analyses and Statistics.

##### 11.3 Order Point Technique and Safety Stock Calculation

Intended learning outcomes: Explain the order point technique and variants thereof. Describe the safety stock calculation with continuous demand. Disclose the determination of the service level and the relation of service level to fill rate.

##### 11.4 Batch Sizing, or Lot Sizing

Intended learning outcomes: Produce an overview on production or procurement costs, batch-size-dependent unit costs, setup and ordering costs, and carrying cost. Explain optimum batch size, optimum length of order cycle, the classic economic order quantity formally and in practical application. Disclose extensions of the batch size formula.

##### 11.5 Summary

.

##### 11.6 Keywords

.

##### 11.7 Scenarios and Exercises

Intended learning outcomes: Calculate examples for the ABC Classification and for the combined ABC-XYZ classification. Differentiate between Safety Stock Variation and Demand Variation. Determine batch size depending on stockout costs. Assess the effectiveness of the order point technique.

##### 11.8 References

.