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

*Continuation from previous subsection (11.3.2)*

A variant of the order point technique described above is the min-max (reorder) system.

With the *min-max (reorder) system*, the “min” (minimum) is the order point, and the “max” (maximum) is the *order-up-to level* or *target inventory level*. The order quantity is variable and is the result of the max minus physical inventory minus scheduled receipts. An order is recommended when the sum of the physical inventory plus scheduled receipts is below the minimum. The *periodic review system* is a variant of the min-max system in which an order is placed every fixed number of time units. The order quantity is variable and essentially replaces the items consumed during the current time period. Cf. [ASCM22].

These techniques define maximal storage space requirements. This is particularly important for racks and shelves in supermarkets, for example.

Another variant of the order point technique is a system that is used frequently for management of distribution inventory.

The *double order point system* has two order points. The smallest equals the traditional order point, which covers the demand forecast during the replenishment lead time. The second, higher order point is the sum of the first order point plus the demand forecast during the replenishment lead time o*f the preceding structural level*, most usually the production lead time or the purchasing lead time. Cf. [ASCM22].

Figure 11.3.2.3 shows the principle for applying the double order point system. RLT1 is the replenishment lead time of the traditional order point technique (e.g. when ordering from the central warehouse), and RLT2 is the replenishment lead time of the preceding structural level (e.g. when ordering directly from the producer).

**Fig. 11.3.2.3** The double order point system.

As soon as inventory at the regional distribution center drops and reaches order point 2, the information is sent to the central warehouse as an order proposal, which the regional distribution center would have to release at about this time if it were ordering directly from the manufacturer or supplier instead of from the central warehouse.

The central warehouse has now got advance warning that an order is pending. It enables the central warehouse to forewarn the manufacturer of future replenishment orders. The advantage is that in theory, no safety stock needs to be held at the central warehouse.

## 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.