# 11.3.1 The ROP (Re)-Order Point Technique

### Intended learning outcomes: Present in detail characteristic data for the (re-)order point technique. Explain the (re-)order point calculation. Identify the criterion for the release of a production or procurement order.

The order point technique, or reorder point technique, or order point system, is used for items with stochastic demand that is relatively continuous along the time axis. The characteristic inventory curve is the saw-toothed curve as shown in Figure 11.3.1.1.

Fig. 11.3.1.1       Characteristic data for the (re-)order point technique.

• After stock entry (point 1), the stock falls gradually until it is below a quantity called the order point. At this time, a production or procurement order is generated.
• The inventory level sinks continually during the replenishment lead time, that is, the total period of time from the moment of reordering until point 2, where the replenishment order quantity is available for use (determining this batch size is the subject of Section 11.4). After the stock entry, the cycle begins anew at point 1. The decline between the points 1 and 2 represents the demand during the lead time. This demand is a stochastic value.
• If the actual demand is larger than the expected (forecast) demand, the inventory level curve corresponds to the dashed line that leads to point 3. If no safety stock was maintained, there will be a stockout.
• If the actual lead time is longer than the (expected) lead time, then the inventory stock curve corresponds to the dashed line that leads to point 4. If no safety stock was maintained, there will be a stockout.

The order interval or order cycle is the time period between the placements of orders.

Cycle stock is the component of inventory that depletes gradually as customer orders are received and is replenished cyclically when supplier orders are received (cf. [APIC16]).

Safety stock is the component of inventory that serves as a buffer to cover fluctuations in lead time and in the demand during the lead time. Statistically, we need to draw on safety stock in half of all procurement cycles. For definitions, see Section 11.3.3.

This system is more difficult to manage in the case of discontinuous but regular demand (the case, for example, with seasonal components). The saw-toothed curve then has a shape that reproduces the seasonality of the demand (see Section 10.3.4).

The area under the saw-toothed curve, multiplied by a cost rate, yields the carrying cost for this item per time unit. These are equal to the storage costs for the mean stock per time unit.

We can derive average inventory for the order point technique in Figure 11.3.1.1 by using the following formula (Figure 11.3.1.2):

Fig. 11.3.1.2       Average inventory.

The order point, or reorder point (ROP), is calculated from safety stock and expected (forecast) demand during the procurement period according to the formula in Figure 11.3.1.3.

Fig. 11.3.1.3       Order point calculation.

Exercise: Get used to the order-point calculation by chosing different values for the parameters as well as the monthly gross requirements.

Calculation of the order point is executed after calculation of the demand forecast and always at the end of a statistical period. Order point calculation should be executed more frequently in cases of discontinuous demand, longer statistical periods, and shorter lead times, because the forecast may change significantly over the course of time.

In addition to physical inventory, also scheduled receipts cover the demand during the lead time. These include firmly or released ordered quantities (see the definition in Section 12.1.1), since these will all arrive during the lead time. If the formula contained in Figure 11.3.1.4 holds, a new production or procurement order should be released.

Fig. 11.3.1.4       Criterion for the release of a production or procurement order.

For management purposes, a periodically produced list contains each the items for which the criterion in Figure 11.3.1.4 is satisfied, together with an order proposal that contains all the required information, such as the predicted receipt to stock, the batch size, and information regarding earlier productions or procurements. Such an order proposal also serves to specify purchase blanket orders more precisely. Since the procurement decision must be made without delay, the proposal also contains bids from suppliers.

## 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. 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. 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. Explain safety stock in relation to service level. Disclose the normal integral distribution function (service function) and the Poisson distribution integral function. Present the formula for safety stock.

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

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. 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.