# Fill rate

Fill rate - probability that any given randomly selected demand will be immediately satiate from available inventory. It is described by following formula (L. Ling 2007, p. 187)$FR= 1.0-\frac{E(US)}{Q}$

Where:

Q- quantity of order or lot size

E(US)- expected units short per replenishment cycle

Next to fill rate there is also one measure of item performance- backorder. It describes the number of unfilled demand at an exact period of time. Whenever it is unable to fill the demand, backorder is established. It lasts until reorder or reparation of failed item. These two measures are related but also different in important ways. Fill rate is concerned only with what happens at a time demand takes place. Backorder measures number of demands which have not been fulfilled in any part of time. It is important to appreciate differences between these two. If the stock level on an item is increased, fill rate will increase but backorder will decrease. It is possible to have a system with both low fill rise and background but reverse situation would never exist (C.C. Sherbrooke 2004, p. 25-27).

Inventory managers are into fill rate because it is easy to measure. They only need to take into consideration what happens at the time every demand takes place- was it filled or not. Furthermore, numerical value is important- 95% fill rate is acceptable in their application, lower values cause complaints of customers (C.C. Sherbrooke 2004, p. 28).

## Item Fill Rate and Order Fill Rate

According to A. M. Beitler, P. A. Gupta and S.A. Ehap :

• Item fill rate is used to measure if buyer has a single item of each PO. It is a rare situation because usually buyer order multiple items to reduce transaction processing cost.
• In scenario above a more appropriate is order fill rate. It can be estimated by calculating the product of the item fill rates for all line items in particular order ( e.g. if the order has four lines items for four different items with an item fill rate of 80% for each, the order fill rate will be - 0.8*0.8*0.8*0.8= 40.96%)( 2006, p. 36).

## References

Author: Dominika Kuraś