SmartShelfKart

Guide

The reorder point formula

A reorder point is the stock level at which you must place the next order to avoid running out before it arrives. The formula is short. Getting the inputs right is the entire job.

· · 5 min read

The formula

Reorder point = lead time demand + safety stock = (d × L) + Z × √( L × σd² + d² × σL² )

Two parts, and they answer two different questions. Lead time demand is what you will sell while you wait. Safety stock is what covers you when either the selling or the waiting goes worse than average.

The calculator is here if you want the number now; the rest of this page is why it is that number.

Lead time demand: the part everyone gets nearly right

Average daily demand times lead time in days. Sell 40 a day, supplier takes 7 days, you will sell 280 while you wait. If you order at 280 you arrive at zero exactly as the delivery lands — assuming nothing varies, which is the assumption safety stock exists to remove.

The word doing the damage in that paragraph is lead time. It is not what the supplier quotes. It is the elapsed time from you deciding to order to the stock being available to sell, and it includes:

  • The time before the order actually goes out — approval, batching it with other orders, waiting for Monday.
  • The supplier's real fulfilment time, not their promise.
  • Transit.
  • Receiving, checking and put-away at your end.

A "3-day" supplier is routinely a 6-day lead time once those are counted. Businesses that measure the whole span rather than the middle of it fix most of their stockout problem without changing anything else.

The safety stock term, and why it has two parts

safety stock = Z × √( L × σd² + d² × σL² )

Under the square root are two independent risks:

  • L × σd² — demand bouncing around its average, accumulated over L days. Variances add over time, which is why it is L and not L².
  • d² × σL² — the supplier being late while you keep selling at rate d. Each extra day of lateness costs you d units, so the demand rate is squared here.

They are combined as variances and then square-rooted because they are independent. Adding the two standard deviations directly would size you for both going maximally wrong at once, which is real but rare, and paying for it permanently is poor value.

Z converts your chosen service level into a multiplier: 1.65 for 95%, 2.33 for 99%.

A worked example

Inventory level over time against the reorder point Stock declines as units sell. Each time the level crosses the reorder point an order is placed; the delivery arrives after the lead time, just as stock reaches the safety-stock floor, and the level jumps back to its maximum. max ROP SS 0 lead time order placed delivery time →

Scroll the diagram sideways →

Stock falls as units sell. Crossing the reorder point (ROP) is what triggers the order; the delivery lands one lead time later, just as the safety stock floor is reached. Set the ROP too low and the sawtooth cuts through the floor before the delivery arrives.

A distributor sells a fast-moving line:

  • d = 40 units/day, σd = 12 units/day
  • L = 7 days, σL = 1.5 days
  • Target service level 95%, so Z = 1.65
Lead time demand = 40 × 7 = 280 Demand variance = 7 × 12² = 1,008 Supply variance = 40² × 1.5² = 3,600 σ = √(1,008 + 3,600) = 67.9 Safety stock = 1.65 × 67.9 = 112 Reorder point = 280 + 112 = 392 units

Now read the diagnosis rather than just the answer. 78% of the variance comes from the supplier, not from demand. This business does not have a forecasting problem; it has a supplier reliability problem. Halving σL to 0.75 days drops the buffer from 112 to about 66 units — a 41% cut in buffer stock from one conversation with the supplier, with no change to service level.

This variance split is the most useful thing the formula produces, and it is invisible if you use a simplified version. It tells you whether to invest in forecasting or in supply reliability.

The simple version, and when it is fine

Reorder point = (d × L) + (d × buffer days)

Lead time demand plus a few days of cover. It is crude, but it is enormously better than a flat global threshold and it takes seconds per product. Use it for your C-class items — the long tail where the full calculation is not worth the effort — and do the proper version for A-class items where the money is. ABC analysis tells you which is which.

Three ways a correct formula still fails

1. Using the quoted lead time

Covered above, and it is the big one. Measure your own, end to end, including the time before the order leaves and the time after it arrives.

2. One reorder point for everything

The formula is per-product because d, L, σd and σL are all per-product. A global "alert under 10" is wrong for essentially every line, and being wrong in both directions simultaneously means people learn to ignore the alert entirely — which is worse than having no alert at all.

3. Never recalculating

Demand drifts, suppliers change, seasons turn. A reorder point set eighteen months ago describes a business that no longer exists. Quarterly is a reasonable cadence; immediately is the right answer after a supplier change.

Applying it across a catalogue without losing a week

Nobody calculates 2,000 reorder points by hand, and any process that requires it will be abandoned. The practical route:

  1. Run ABC analysis and identify the A items — usually about 20% of lines.
  2. Calculate reorder points properly for those, at a 98–99% service level.
  3. For B items, use the simple version at 95%.
  4. For C items, apply a flat days-of-cover rule. Being slightly wrong on a slow mover costs very little.
  5. Load them in bulk — export the catalogue to a spreadsheet, calculate in a column, import back matching on SKU.

Then the number needs to actually do something. In SmartShelfKart the reorder point is the product's low-stock threshold, checked against live stock, so crossing it puts the item on the Low Stock list and into the reorder suggestions rather than waiting for someone to notice.

Questions

What is the reorder point formula?

Reorder point = (average daily demand × lead time) + safety stock, where safety stock is Z × √(L × σd² + d² × σL²). The first term covers what you will sell while waiting; the second covers demand and supplier variability.

What lead time should I use?

Your own measured lead time, from deciding to order through to stock being available to sell — including approval delays before the order goes out and receiving time after it arrives. Supplier quotes routinely understate this by several days.

Do I need the full formula, or is the simple one enough?

Use the full version for A-class items where the money is, and the simple version — lead time demand plus a few days of cover — for the long tail. The full version also tells you whether demand or supply variability is the real problem, which the simple one cannot.

How often should reorder points be recalculated?

Quarterly for most items, and immediately after any supplier change or a visible shift in a product's demand pattern.

Can the reorder point be lower than the safety stock?

No. The reorder point always includes safety stock plus lead time demand, so it is at least as large. If you compute otherwise, one of the inputs is wrong.

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