Why is a 99% service level so expensive?

Because the service factor grows faster than the level. Ninety to ninety-five costs about a quarter more safety stock; ninety-five to ninety-nine costs another sixty percent on top.

Does lead time variability matter more than demand variability?

Usually yes. Its term is multiplied by daily demand, so an unreliable supplier costs far more safety stock than an erratic customer at the same coefficient of variation.

Businessoperations

Reorder Point Calculator

The stock level at which to place the next order, covering demand through the lead time plus a buffer for variability in both demand and lead time. Lead time variability is usually the larger of the two and is the one most often left out.

Also called: reorder level calculator, when to reorder stock.

Reorder point

1,117

1,117 units: 780 to cover the lead time plus 337 of safety stock at a 95% service level. At 900 on hand you are already at or below the reorder point. The order should go in now. Safety stock of 337 covers variability in both demand and lead time. Of the two, the lead time term contributes 91% of the variance here, since it is multiplied by the daily demand itself. Moving to 99% would take the buffer to 476, which is where the inventory budget goes.

Demand during the lead time

780

Safety stock

337

Days of cover at the reorder point

17.2

Days until you hit it

Safety stock at 99%

476

Safety stock at 90%

262

Where you stand

At 900 on hand you are already at or below the reorder point. The order should go in now.

On the variability

Safety stock of 337 covers variability in both demand and lead time. Of the two, the lead time term contributes 91% of the variance here, since it is multiplied by the daily demand itself. Moving to 99% would take the buffer to 476, which is where the inventory budget goes.

How this is calculated

Safety stock by service level

Service level	Safety stock	Reorder point	Above the 90% buffer
90%	262	1,042	0%
95%	337	1,117	28%
98%	420	1,200	60%
99%	476	1,256	82%
99.9%	633	1,413	141%

Method and background

How this is calculated

The base is simple: average demand multiplied by the lead time is what will be consumed while the order is in transit. The safety stock is the part that needs care. It combines variability in demand with variability in the lead time, and the second term is multiplied by the daily demand itself, which makes an unreliable supplier expensive in a way an erratic customer is not. The service factor comes from the normal distribution, and its cost is sharply non-linear: going from ninety to ninety-five percent costs about a quarter more safety stock, and going from ninety-five to ninety-nine costs another sixty. The last few points of service level are where the inventory budget goes.

lead time demand plus a buffer covering variability in both the demand and the lead time, which is where the second term matters most

d: Daily demand
L: Lead time
z: Service factor

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a twelve day lead time with variable demand

Average daily demand: 65
Lead time: 12
Daily demand variability: 18
Lead time variability: 3
Service level: 95%
Stock on hand: 900

Reorder point1,117

1.6449 x sqrt(12 x 324 + 4225 x 9)

Open this example

a reliable supplier needs far less buffer

Average daily demand: 65
Lead time: 12
Daily demand variability: 18
Lead time variability: 0
Service level: 95%
Stock on hand: 900

Reorder point883

boundary: removing lead time variability cuts the safety stock by 70%

Open this example

Method and limits

What it assumes

Normally distributed demand, which understates the buffer for intermittent demand.

What it deliberately does not model

Intermittent or lumpy demand is not normal, and this formula understates the stock such patterns need.
A service level is a probability of not stocking out in a cycle, not a promise about any particular cycle.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why is a 99% service level so expensive?: Because the service factor grows faster than the level. Ninety to ninety-five costs about a quarter more safety stock; ninety-five to ninety-nine costs another sixty percent on top.
Does lead time variability matter more than demand variability?: Usually yes. Its term is multiplied by daily demand, so an unreliable supplier costs far more safety stock than an erratic customer at the same coefficient of variation.