# 11.3.4 Determining the Service Level on the Basis of Stockout Costs

### Intended learning outcomes: Describe the order point technique where the length of order cycle provided by the batch size is a multiple of the lead time. Explain the probability of stockout in dependency on stockout costs per unit.

Figure 11.3.4.1 shows a typical order cycle using the order point technique shown in Figure 11.3.1.1, in which the length of order cycle, that is, the length of time the batch size will provide stockout coverage, is a multiple of the lead time. The batch size itself is a multiple of the expected demand during the lead time.

Fig. 11.3.4.1       Order point technique with an order cycle where the length of order cycle provided by the batch size is a multiple of the lead time.

If the length of order cycle divided by lead time equals 10, for example, and demand is not too discontinuous, then 90% of the batch size can be covered without stockout. Stockout will only occur for demand during the lead time, or for 10% of the batch size. If no safety stock were carried (safety factor is 0, that is, a service level of only 50%), the fill rate would be approximately 90% and higher. This shows that service level can usually be a percentage that is significantly smaller than the desired fill rate (which in most cases must be set at close to 100%; see the discussion in Section 5.3.1).

As mentioned above, determining the desired fill rate and service level has to be the quantitative application of the qualitative answer to the question of what stockouts will cost. Thus, fill rate and service level express an estimation of opportunity cost.

Stockout costs are the economic consequences of stockouts.

Stockout costs can include extra costs for express/emergency production or procurement or customer delivery, but also penalty costs, loss of sales, loss of contribution margin, loss of customer goodwill, and all kinds of associated costs. See the discussion in Section 1.3.1.

The following shows the derivation of two methods of determining the desired service level:

1. The first method is based on the assumption that opportunity costs can be assigned directly to each unit not filled.
2. The second method is based on the assumption that the total opportunity costs can be assigned to the fill rate during a particular time period (a year, for instance).

1. Determine service level on the basis of stockout costs for each unit of an item not filled.

Where stockout costs can be expressed as costs per unit (of measure) not delivered, [Cole00], [SiPy98], and [Ters93] offer the following direct calculation of the optimum probability of stockout (see Figure 11.3.4.2). Because a stockout can only happen at the end of an order cycle, the number of stockouts cannot be greater than the number of order cycles. Often the period chosen for the calculation is one year.

Fig. 11.3.4.2       Probability of stockout in dependency on stockout costs per unit.

As a consequence, the optimum service level results directly from the relation in Figure 11.3.3.3. Section 11.4 discusses determination of batch size, which often precedes safety stock calculation.

For example, if there are five order cycles per year (the average annual consumption is five times the batch size) and stockout costs per unit are four times greater than carrying cost, the resulting optimum probability of stockout is 0.05 and the optimum service level is 95%.[note 1104]

Continuation in next subsection (11.3.4b).

## Course section 11.3: Subsections and their intended learning outcomes

• ##### 11.3 ROP (Re)-Order Point Technique, and Safety Stock Calculation

Intended learning outcomes: Explain the (re-)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.

• ##### 11.3.1 The ROP (Re)-Order Point Technique

Intended learning outcomes: Present in detail characteristic data for the (re-)order point technique.

• ##### 11.3.1b Order Point Calculation

Intended learning outcomes: Explain the (re-)order point calculation. Identify the criterion for the release of a production or procurement order.

• ##### 11.3.2 Variants of the Order Point Technique

Intended learning outcomes: Identify the criterion for the release of a production or procurement order, if the customer allows a minimum delivery lead time. Explain the criterion for an early issuance of a production or procurement order.

• ##### 11.3.2b The Min-Max Reorder System and the Double Order Point System

Intended learning outcomes: Produce an overview on the min-max (reorder) system. Describe the double order point system.

• ##### 11.3.3 Safety Stock Calculation with Continuous Demand

Intended learning outcomes: Describe different techniques for determining safety stock. Identify different patterns of the deviation of demand from forecast.

• ##### 11.3.3b Service Level, Safety Factor, and Service Function

Intended learning outcomes: Explain safety stock in relation to service level. Identify the safety factor and the service function.

• ##### 11.3.3c Safety Stock Calculation with Continuous Demand Following a Normal Distribution

Intended learning outcomes: Disclose the normal integral distribution function (service function) to determine the safety factor that corresponds to a desired service level. Present the formula for safety stock.

• ##### 11.3.3d Safety Stock Calculation with Continuous Demand Following a Poisson Distribution

Intended learning outcomes: Disclose the Poisson distribution integral function to determine the safety factor that corresponds to a desired service level.

• ##### 11.3.4 Determining the Service Level on the Basis of Stockout Costs

Intended learning outcomes: Describe the order point technique where the length of order cycle provided by the batch size is a multiple of the lead time. Explain the probability of stockout in dependency on stockout costs per unit.

• ##### 11.3.4b Determining the Relation of Service Level to Stockout Quantity per Order Cycle

Intended learning outcomes: Present the service function (of the stockout quantity coefficient) P(s) in dependency upon the safety factor s. Produce an overview on and examples of the relation between fill rate and service level.

• ##### 11.3.4c Determining the Relation of Service Level to Fill Rate

Intended learning outcomes: Produce an overview on and examples of the relation between fill rate and service level.