Quantifying Expediting in Terms of Confidence

The first and most obvious dimension of safety stock is service level – in other words, the safety-stock level is determined statistically to achieve a target fill rate. However, a correctly-determined, statistically-based safety-stock level is not simply a value, but a range of values. At the lower end of this range is a (lower) safety-stock level that provides a lower likelihood – less confidence (and more expediting) – of achieving the target service level during any period of time. At the higher end of the range is a (higher) safety-stock level providing a higher likelihood – more confidence (and less expediting) – of achieving the target service level. LS3 (the on-demand product offering from TopDown Lean Systems) is a comprehensive and correct statistical safety-stock model that quantifies confidence, and therefore also the incremental expediting required to achieve the target service level.

LS3 enables your financial analyst to assign a quantifiable, valid monetary amount to the incremental expediting required to improve your service levels. In fact, LS3 enables your supply-chain and demand-management teams to select the optimal confidence for each inventory item. After all, some of your items are easily and quickly expedited, allowing a lower confidence (and lower safety-stock level). On the other hand, certain items cannot be expedited, and these require a high level of confidence (and higher safety-stock level).

Confidence has a dramatic effect on safety stock: A 98% confidence may require 2-3 times more safety stock than does a 50% confidence. LS3 quantifies the relationship between safety stock and confidence, so your financial analyst may assign incremental inventory-carrying costs to safety stock. The following chart shows an example of the relationship of safety stock to confidence for a specific inventory item at a specific service-level target.


Confidence is affected by all relevant replenishment parameters, and substantially influenced by two in particular: lead time and replenishment interval (RI). To illustrate this, picture what is commonly called a “sawtooth” diagram – a graphic representation of on-hand inventory quantity over time, reflecting receipts, usage and reorders:

The vertical axis of the sawtooth diagram is quantity on hand, and the horizontal axis is time. The “saw” has two components. We could call the first component the “blade,” and the second component the “teeth”:

  • The blade’s vertical dimension represents safety-stock quantity, which is theoretically always on-hand.
  • Each tooth has two dimensions that are directly related to each other. The height of the tooth (above the blade), on the diagram’s vertical quantity axis, is reorder quantity (ROQ), which is typically determined by minimum order quantity (MOQ), economic order quantity, lot size, package size or usage during reorder-review interval. For example, an inventory item with an MOQ of 1,000 has a “taller” tooth than does an inventory item with an MOQ of 175.

The tooth’s width, on the diagram’s horizontal time axis, denotes the RI, and RI is simply ROQ ÷ average daily demand. This is why each tooth’s two dimensions completely describe an inventory item’s reorder policy as represented by quantity and time. So an inventory item with an MOQ of 1,000 has a wider (and taller) tooth than it would have with an MOQ of 175.

The triangular shape of the tooth represents inventory quantity on hand over the RI as a result of reorder parameters and average usage. Average reorder-parameter inventory on-hand, or cycle stock, is defined as MOQ ÷ 2. The height of the rectangular area on which the tooth rests represents average daily quantity on hand as a result of safety stock. Overall, then, total average daily quantity on hand = Safety Stock Quantity + (MOQ ÷ 2)

Of course, this is all “Inventory 101” so far. It is also very theoretical, which may not be practical for our real world inventory and supply chain circumstances, so how are safety stock, demand variation, RI, and confidence related? We’ll explore that in our next post.

NB: For more information on LS3, and a free trial analysis, please visit our web site!