# 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.

Continuation from previous subsection (11.3.3)

The service level, or cycle service level, or level of service, is the percentage of order cycles that the firm will go through without stockout, meaning that inventory is sufficient to cover demand.

The probability of stockout is the probability that a stockout will occur during each order cycle before a replenishment order arrives.

According to these definitions, the following relationship holds (see Figure 11.3.3.3).

Fig. 11.3.3.3       Service level expressed as the complement of probability of stockout.

With the order point technique, fluctuating demand can be satisfied from stock even without safety stock in about half of all cases. For this reason, the service level using this technique can be assumed to be at least 50%.

Safety stock — and with it carrying cost — grows quantitatively in dependency upon service level, as Figure 11.3.3.4 shows. Once the desired service level is set, safety stock can be estimated accurately through statistical derivation.

Fig. 11.3.3.4       Safety stock — and thus carrying cost — in relation to service level.

The safety factor is the numerical value, a particular multiplier, for the standard deviation of demand.

The service function is the integral distribution function, for which the integral under the distribution curve for demand up to a particular safety factor s corresponds to the service level.

Continuation in next subsection (11.3.3c).

## 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.