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

*o determine**the safety factor*that corresponds to a desired*service level**Continuation from previous subsection (11.3.3b)*

If demand follows a *normal distribution*, or a bell-shaped curve, the service level corresponding to the safety factor s is the area shown in gray in Figure 11.3.3.5.

**Fig. 11.3.3.5** Normal integral distribution function (service function).

Therefore, the safety factor is also the inverse function of the integral distribution function. It is the numerical value used in the service function (based on the standard deviation of the forecast) to provide a given level of service.

Figure 11.3.3.6 reproduces examples for corresponding values of the service level and the safety factor. They can be read from tables, such as the following table from [Eilo62], p. 26.

**Fig. 11.3.3.6** Service level and safety factor when demand follows a normal distribution. (From [Eilo64], p. 26.)

Figure 11.3.3.7 shows the resulting formula for safety stock. With a normal distribution, it is possible to use 1.25 * MAD (mean absolute deviation) instead of the standard deviation.

**Fig. 11.3.3.7** Formula for safety stock.

*Continuation in next subsection (11.3.3d).*

Exercise: Get used to the influence of the safety stock on order point calculation by chosing different values for the service level.

## 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.