How to Calculate Reorder Point: The Formula Is Short, the Lead Time Is the Hard Part

The reorder point formula

The reorder point is the stock level at which you order a part, so that the bin doesn't run empty before the delivery is booked in.

Reorder point = consumption per day × replenishment lead time in days + safety stock

ROP = d × L + SS

Consumption per day. d is what leaves the store in a period, divided by the days in that period. This article divides a year's consumption by 365 calendar days.

Replenishment lead time. L runs from the day stock reaches the reorder point to the day the delivery is booked in and can be picked. The supplier's delivery time is one part of it. Count it in the same days as consumption, calendar days here.

Safety stock. SS is the quantity you hold in case the delivery is late or more parts go out than planned. The plain rule is consumption per day × days of cover. The section on the safety stock formula says what that rule leaves out.

The first half of the formula, d × L, is what you use up while you wait. A part with 1,200 pieces a year, 35 days of lead time and 30 pieces of safety stock has a reorder point of 1,200 × 35 ÷ 365 + 30 = 145.1, rounded up to 146 pieces.

The example: reorder points for six spare parts

This is an illustrative example with invented figures and an invented company. It uses the stock list from how to calculate inventory turnover, a pump maker's spare parts store over a year of 365 days.

That article supplies the items, yearly consumption and closing stock, the 35 days for the electric motor, and for the control board 20 weeks, a safety stock of 150 and an order quantity of 300. Every other lead time and safety stock was added for this article. The 35 days and the 20 weeks count as the full replenishment lead time here, ordering and goods receipt included.

Quantities are in pieces. Every sum uses the unrounded consumption per day. Intermediate figures are shown with one or two decimals, and the reorder point is rounded up to whole pieces.

Step 1: consumption per day

For the electric motor that is 1,200 pcs ÷ 365 days = 3.29 pcs per day.

Step 2: consumption during the lead time

1,200 pcs × 35 days ÷ 365 days = 115.1 pcs

Step 3: add safety stock

115.1 pcs + 30 pcs = 145.1 pcs, rounded up to 146 pcs

When available stock of motors falls to 146, the order is due. If the delivery is on time, what is left on the shelf that day is the safety stock.

The same sums for all six items:

What the list says at the year end

Hold each reorder point against closing stock. Four items are above it. The housing for the old series is 168 × 365 ÷ 40 = 1,533 days away from its reorder point of 12.

Two items are below. The store holds 120 motors, 26 under the reorder point. If no order is open, it is 26 × 365 ÷ 1,200 = 7.9 days overdue. The control board is 91 below its reorder point at 290. That is no alarm while the order for 300 is on its way. It was due 91 × 365 ÷ 600 = 55.4 days ago.

The comparison runs on book stock

A system compares the reorder point with book stock, and book stock can be wrong. In the turnover article a count finds 96 motors where the system shows 120. If those 24 have been missing for a while, the shelf holds 122 motors on the day the system reports 146. By the time the delivery arrives, 115.1 have gone out and 122 − 115.1 = 6.9 are left. With a correct book stock it would be 30.9. 24 of the 30 pieces of safety stock existed only in the system. How such gaps come about is in the article on stock discrepancies.

How to draw the reorder point on a stock chart

The standard picture is a sawtooth: stock climbs straight up when a delivery is booked in, then slopes down as parts are used, over and over. Sketching it once makes the formula easier to explain to purchasing and the warehouse. Take the electric motor and suppose it is ordered 200 at a time, a quantity the list doesn't give.

Put time in days along the bottom, 0 to 130, and stock in pieces up the side, 0 to 250. Then draw:

• a flat line at 30 pieces, labelled safety stock
• a flat line at 146 pieces, labelled reorder point
• the stock level, starting at 230 on day 0 (30 left plus a delivery of 200) and falling 3.29 pieces a day
• a mark where the falling line crosses 146, the day the order goes out
• a bracket along the time axis from that mark to the next delivery, labelled lead time, 35 days

These are the corners to join:

Each tooth is 200 ÷ 3.29 = 60.8 days wide. The drop from the reorder point line to the safety stock line takes one lead time, which is the d × L part of the formula drawn as a slope.

Now draw a late delivery to see what safety stock is for. If the second delivery arrives on day 66 instead of 61, the line keeps falling for five more days and bottoms out at 30 − 5 × 3.29 = 13.6 motors. The bin isn't empty, but most of the safety stock is gone. A chart of real booked stock from your ERP shows the same thing for every item: each tooth that dips below the safety stock line marks a delivery that was late or a stretch where more went out than planned.

Safety stock formula: what the plain rule covers

The plain rule sets safety stock in days.

Safety stock = consumption per day × days of cover

Run it backwards and you can check a quantity somebody entered years ago. The 150 control boards are 150 × 365 ÷ 600 = 91.25 days, about 13 weeks. The 80 mechanical seals are 80 × 365 ÷ 6,000 = 4.9 days. In days, the figure tells you how late a delivery may be at the usual consumption before the bin is empty.

That is the one case the rule covers. It doesn't know how often the supplier is late or by how many days, and it doesn't know how far consumption swings from one day to the next. Set the days by gut feeling and every item has a number while none has a reason. An ABC analysis ranks the same list by consumption value, with nine items added, and shows which items to work out properly first.

The formula with a service level

A second formula works from the spread of consumption.

Safety stock = z × σ × √lead time

σ is the standard deviation of consumption per day, and z is a factor that depends on the service level you want. For 95%, z is 1.65, and stock then lasts through 95 of 100 lead times. Suppose daily consumption of the mechanical seal varies with σ = 6 pcs. Safety stock is then 1.65 × 6 × √12 = 34.3 pcs, rounded up to 35. The list has 80. How to do an XYZ analysis shows how to get σ from twelve months of consumption and convert it to a daily figure.

This formula leaves things out as well. It assumes a fixed lead time, so late deliveries are not in it. It also assumes that daily consumption scatters around its mean like a bell curve. On most days nobody takes a housing for the old series, and the formula doesn't fit that item.

Five ways to get the reorder point wrong

1. Taking the lead time from the supplier's catalogue

The supplier of the mechanical seal quotes eight days. Suppose two days pass before the purchase order goes out, and goods receipt needs two more to book the delivery in. That makes 2 + 8 + 2 = 12 days, the figure on the list.

Eight days give 6,000 × 8 ÷ 365 + 80 = 211.5, rounded up to 212 pcs where 278 is right. Order at 212 and 212 − 197.3 = 14.7 pcs are left when the delivery arrives. Most of the 80 seals of safety stock are gone each time, even when the supplier is on time.

Measure lead time on your last ten orders, from the day stock reached the reorder point to the booking at goods receipt.

2. Averaging a seasonal item over the year

The gasket set has no season of its own. In the XYZ analysis of the same list its monthly figures stay between 680 and 830, which puts it in X. The seasonal part there is the pressure switch, and that one is not among these six items. So borrow the gasket set's figures and give it a season for this calculation. Suppose 4,500 of the 9,000 went out in the 100 days of a maintenance season. The yearly average would still be 24.66 a day, but in season it would be 45 a day, and 16.98 a day over the other 265 days.

The reorder point from the yearly average is 768 pcs. In season, 45 × 21 = 945 sets go out during the 21 days of lead time. You are 177 short, and the bin is empty 177 ÷ 45 = 3.9 days before the delivery.

On the season's consumption the reorder point is 945 + 250 = 1,195 pcs. Outside the season it is 16.98 × 21 + 250 = 606.6, rounded up to 607. A seasonal item needs two reorder points and a date on which somebody switches them.

3. Counting the safety margin twice

The control board has 150 pcs of safety stock. Suppose the system holds 24 weeks of lead time instead of 20, to be on the safe side. That gives 600 × 168 ÷ 365 + 150 = 426.2, rounded up to 427 pcs. It is 46 boards more than 381. At the unit cost of €120.00 from the turnover list, another €5,520 sits on the shelf, and nobody decided on it as safety stock.

Put the margin in one place in the formula, the safety stock. Leave the other inputs as measured.

4. Leaving the reorder point alone after a change of supplier

The impeller's reorder point is 139 pcs, calculated with 30 days. Suppose purchasing moves to a cheaper supplier who needs 56 days. The right figure is now 1,200 × 56 ÷ 365 + 40 = 224.1, rounded up to 225 pcs.

If 139 stays in the system, the bin is empty after 139 × 365 ÷ 1,200 = 42.3 days. The delivery comes after 56. The store has no impeller for 13.7 days.

The reorder point has three inputs. When one of them changes, calculate it again.

5. Leaving open orders out of the count

After the order goes out, stock of the control board keeps falling for 140 days, from 381 to 381 − 230.1 = 150.9 pcs. On every one of those days it is below the reorder point. A check that looks only at the shelf proposes a new order each day.

So the figure to compare is available stock.

Available stock = stock on hand + open orders − reserved quantities

With the 300 boards on order it is above 381, and no proposal appears.

Suppose the company halves the order quantity to 150. The shelf then never holds more than 150 + 150 = 300 boards, fewer than the reorder point. 150 boards last 91.25 days and a delivery takes 140, so at least one order is always on its way. With 231 boards on the shelf and one open order for 150, available stock is 381 and the next order is due. Which order quantity costs least for a given ordering and holding cost is worked out on the same list in how to calculate economic order quantity.

The next step

Take ten items that ran out or needed a rush order in the last twelve months. For each one, write down the reorder point in the system, yearly consumption, the measured lead time and the safety stock, and recalculate. Note next to it when the reorder point was last changed and by whom.

If you want to know where the days go between requirement, purchase order and goods receipt, that is the scope of our process analysis. Fixed scope, fixed duration, fixed price.