Reorder Point Calculator

The reorder point is the stock level that tells you to place the next order. Set it so the stock you have left covers everything you'll sell while you wait for the delivery (the lead time), plus a cushion of safety stock in case sales run faster or the delivery runs late.

The formula

daily demand (d) = demand a week ÷ 7, or demand a month × 12 ÷ 365
used during the lead time = d × lead time in days
reorder point = d × lead time + safety stock

worst case: safety stock = highest daily demand × longest lead time − d × average lead time
service level: safety stock = z × daily demand variation × √lead time
lead time varies too: safety stock = z × √(lead time × daily variation² + d² × lead-time variation²)
days of cover: safety stock = d × days

days of stock on hand = stock ÷ d
days until you reorder = (stock + already on order − reorder point) ÷ d
average stock = order size ÷ 2 + safety stock
EOQ = √(2 × yearly demand × cost per order ÷ holding cost per unit a year)

Worked example

A shop sells 40 units a day on average and its supplier takes 10 days to deliver. While it waits it sells 40 × 10 = 400 units.

On its busiest days it sells 60, and the slowest delivery took 14 days. The worst case is 60 × 14 = 840 units, so safety stock = 840 − 400 = 440 units and the reorder point = 400 + 440 = 840 units.

It has 1,500 in stock now: 1,500 ÷ 40 = 37.5 days of stock. It should reorder in (1,500 − 840) ÷ 40 = 16.5 days, so on day 16 from the stock count. Ordering 1,200 at a time, it places 40 × 365 ÷ 1,200 = 14,600 ÷ 1,200 = 12.17 orders a year, one every 1,200 ÷ 40 = 30 days. Average stock is 1,200 ÷ 2 + 440 = 1,040 units and the most it holds, just after a delivery, is 1,200 + 440 = 1,640.

The same shop with a service level

The worst-case method is easy but often gives a lot of safety stock, because it assumes the busiest days and the slowest delivery happen together. If daily sales vary with a standard deviation of 8 units and the shop wants a 95% chance of not running out in each lead time (z = 1.645): safety stock = 1.645 × 8 × √10 = 1.645 × 25.30 = 41.6 units, so the reorder point is 400 + 41.6 = 441.6, rounded up to 442.

If the 10-day delivery also varies by 2 days (standard deviation), demand during the lead time varies by √(10 × 8² + 40² × 2²) = √(640 + 6,400) = √7,040 = 83.9 units. Safety stock = 1.645 × 83.9 = 138.0 units and the reorder point is 538.0, rounded up to 539. A late delivery matters far more than a busy day here.

The service level here is the chance of not running out during one lead time (cycle service level). The fill rate is different: the share of units ordered by customers that you can supply from stock. It's higher, because when you do run short it's usually by only a few units. In the 95% example, you'd expect about 25.30 × 0.0209 = 0.53 units short per order cycle, a fill rate of 1 − 0.53 ÷ 1,200 = 99.96%.

Order size and the EOQ

The reorder point says when to order; the order size says how much. If ordering costs $50 each time and holding one unit costs $2 a year, the economic order quantity is √(2 × 14,600 × $50 ÷ $2) = √730,000 = 854 units. See the EOQ calculator for price breaks, pack sizes and production runs.

Tips

• Work out demand variation from at least 8–12 weeks of daily or weekly sales. A weekly figure is converted to daily by dividing by √7.
• If your reorder point is bigger than your order size, you'll often have one order on the way when you place the next. Count stock on order when you check, as this calculator does.
• Recheck the numbers before busy seasons, promotions or when a supplier changes delivery times.
• If you only check stock once a week, add the time between checks to the lead time.

Standard reorder point and normal-distribution safety stock formulas (see e.g. Silver, Pyke & Thomas, Inventory and Production Management in Supply Chains). Results are a guide for planning: real demand and lead times can swing more than a normal curve suggests.