Intermittent Demand Forecasting. John E. Boylan

Intermittent Demand Forecasting

and that performance is regularly monitored against target. Indeed, even if an SLA is not in place, it is vital that there is a common understanding of how service is measured, and that the measure is appropriate for the business. A number of measures have been proposed and we now proceed to review how these measures are calculated and how they should be used.

From a customer perspective, it would be ideal if all of their orders could be met in full, immediately from stock. Consider the example of a single customer order shown in Table 3.1.

There are three levels at which service may be evaluated:

1 Orders: In this example, the order is not completely filled because the order lines for SKUs B and E are not fully satisfied, and the order line for SKU C is not satisfied at all. To calculate the proportion of orders completely filled (the order fill rate [FR]) would require data on all relevant orders. If the order in Table 3.1 were included, it would be counted as unfulfilled.

2 Order lines: Two out of the five order lines are completely filled, for SKUs A and D, giving an order‐line fill rate of 40%.

3 Units: Table 3.1 shows that 18 out of 25 units are filled from stock, giving a unit fill rate of 72%. Alternatively, this could be calculated according to value. A value of £5100 is filled from stock, out of a total value requested of £6000, giving a value fill rate of 85%.

This example is restricted to a single order, but each of the measures can also be calculated at the aggregate level, over a whole collection of orders. We can find the total number of orders completely filled, the total number of order lines (over all orders) completely filled, and the total number of units filled (over all order lines and all orders). These totals can then be divided by the total orders, order lines, and units demanded, respectively.

Table 3.1 Order comprising five order lines.

SKU	Ordered	Filled	Ordered (£)	Filled (£)
A	5	5	500	500
B	10	8	1000	800
C	4	0	500	0
D	1	1	3000	3000
E	5	4	1000	800
Total	25	18	6000	5100

To perform well on the order and order‐line fill rate measures requires good service on a wide spectrum of SKUs, including slow‐moving and intermittent items. The unit fill rate is an important measure as it can be applied straightforwardly at both the aggregate and SKU levels. For an individual order line, the value fill rate is the same as the unit fill rate, but these measures may differ when calculated for a whole order, as illustrated in Table 3.1. Full satisfaction of the most expensive order line, for SKU D, has resulted in the value fill rate, of 85%, being somewhat higher than the unit fill rate of 72%.

Although complete order fulfilment is ideal from a client perspective, the percentage of orders completely filled should not be the only service level measure. Retailers usually submit numerous order lines in an order on a wholesaler. Even if the wholesaler improves the availability of stock, this will not necessarily be reflected by the complete order fill rate. For example, if the order lines for SKUs A, B, C, and D were filled completely but only four out of five units were filled for SKU E, then the order would still be counted as unfilled. The order‐line fill rate and the unit fill rate would be raised to 80% and 96%, respectively, thereby reflecting the improved stock availability.

The measures discussed here may be embedded in a broader framework of order fulfilment metrics. Johnson and Davis (1998) described how Hewlett‐Packard augmented inventory holding and fill rate metrics with a measure of customer delivery reliability. This helped to identify the impact of stockouts on delivery delays, including some cases where there was no impact because non‐available stock became available in time for the dispatch of the last truck.

3.3.3 Relationships Between Service Level Measures

Occasions may arise when an organisation needs to change from one service level measure to another, and new service level targets are required. If service levels have not been monitored according to the new measure, then a relationship between the old and new measures can help to set new targets. Boylan and Johnston (1994) showed how relationships may be obtained between order‐line and order fill rates, and between unit and order‐line fill rates. The relationship between the unit fill rate, FR Subscript Unit , and the order‐line fill rate, FR Subscript Line , is given by Eq. (3.1).

(3.1) FR Subscript Unit Baseline equals 1 minus left-parenthesis 1 minus FR Subscript Line Baseline right-parenthesis StartFraction u Subscript u Baseline Over l Subscript u Baseline EndFraction StartFraction l Subscript d Baseline Over u Subscript d Baseline EndFraction

where u Subscript u Baseline slash l Subscript u is the average number of units unfilled per unfilled order line and l Subscript d Baseline slash u Subscript d is the reciprocal of the average number of units demanded per order line. In Table 3.1, seven units are unfilled over three order lines, giving an average of u Subscript u Baseline slash l Subscript u Baseline equals 7 slash 3 equals 2.33 , to two decimal places. Also in Table 3.1, 25 units are demanded over five order lines, giving an average of u Subscript d Baseline slash l Subscript d Baseline equals 25 slash 5 equals 5 and a reciprocal of l Subscript d Baseline slash u Subscript d Baseline equals 0.2 . In this example, the product of the two ratios in Eq. (3.1) is 2.33 times 0.2 equals 0.466 . Applying Eq.

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