Inventory planning: reorder point, safety stock, and EOQ

Inventory planning is three questions asked in order. When do I place the next order? How much stock should sit as a buffer? How much should the order be? Each has a formula that runs on the same few inputs: how much you use, how long a delivery takes, and what an order costs you.

This page works through all three with the same part, so the numbers connect. The calculators on this page take the inputs and return the answers; the sections below explain what the answers mean and where they mislead.

The three questions, and what answers them

Question	Measure	Formula	Inputs it needs
When do I order?	Reorder point	average daily usage × lead time + safety stock	usage per day, lead time in days, buffer
How much buffer do I hold?	Safety stock	(peak daily usage − average daily usage) × lead time	peak and average usage, lead time
How much do I order?	Economic order quantity	√(2 × annual demand × order cost ÷ holding cost per unit per year)	annual demand, order cost, unit cost, holding rate

The three answers fit together. Safety stock feeds the reorder point. The reorder point decides the day you buy. The order quantity decides how often you buy again.

Reorder point: when to place the order

The reorder point is the stock level that triggers a purchase. It covers the demand you expect while the next delivery is in transit, plus the buffer you keep for surprises.

Reorder point = (average daily usage × lead time) + safety stock

A part used at 10 units a day with a 7-day lead time and 28 units of safety stock reaches its reorder point at 98 units. The first 70 units cover the week the order is in transit; the 28 cover the days when the supplier is late or the line runs faster than usual.

The order of events matters. You order when the count hits 98, not when it falls below. By the time the count is 60, the delivery is already behind schedule and the buffer is being spent.

What changes the number

Lead time is the input that moves most. A supplier that slips from 7 days to 14 doubles the demand side of the formula, and the reorder point has to follow. Usage that trends up does the same, slowly enough that nobody notices until a stockout explains it.

Supplier minimums push the other way. If the smallest order a supplier will ship covers 45 days of use, a reorder point built for a 30-day cycle leaves you ordering twice and paying twice. Set the reorder point from the cycle you can actually buy in.

Seasonality is the input people forget. A part used at 8 a day in summer and 14 a day in November needs a different reorder point in each season, or one reorder point set for November that leaves cash sitting in the rack from June.

Safety stock: the buffer you hold on purpose

Safety stock exists because the average is not the whole story. It absorbs a busy week, a late truck, or a batch that arrives short.

The simple method uses the gap between normal and peak usage over one lead time:

Safety stock = (peak daily usage − average daily usage) × lead time

For the same part, a peak of 14 a day against a 10-a-day average over a 7-day lead time gives 28 units. Hold less and a normal busy week turns into a stockout. Hold more and the extra units sit on the shelf for weeks.

The service-level method

The other common method treats usage as a distribution and picks a buffer that meets a target. It multiplies a service factor by the standard deviation of daily usage and the square root of the lead time:

Safety stock = z × σ(daily usage) × √lead time

A 95% target uses a factor of 1.65. A part with a daily usage deviation of 3 units and a 7-day lead time needs about 13 units. The gap between 28 and 13 is the gap between covering the worst week you have seen and covering a probability. Both are defensible; the first is easier to explain to a team, the second is easier to defend in a budget.

What the buffer costs

Every unit of safety stock is cash on a shelf plus space plus a small risk that it ages out. Set it per item, not once for the whole catalog. An item with a stable supplier and steady demand needs little; a part with one unreliable supplier and a line that stops without it needs more.

EOQ: how much to order at once

Every order costs money to place, independent of how many units it carries: the purchase order, the receiving time, the inspection, the paperwork. Every unit you hold costs money to keep: storage, insurance, capital, and the risk of damage or obsolescence. EOQ finds the order size where the two costs add up to the least.

EOQ = √(2 × annual demand × cost per order ÷ holding cost per unit per year)

The holding cost per unit is usually stated as a rate rather than a number. A unit that costs $12 with a 20% annual holding rate carries $2.40 a year.

What the answer means

EOQ returns an order size, and everything else follows from it. Orders per year is annual demand divided by the order size. Total cost is the ordering cost plus the holding cost of the average inventory, which is half the order size.

The formula is flat near the minimum, so it does not need precision. An order size 20% away from the EOQ costs a few percent more per year, not a few times more. That tolerance is why a round number, or a number that matches a pallet, is usually the right answer.

Order cost, measured not guessed

The order cost is the part of the formula people invent. It is not the price of the goods; it is the internal cost of raising the purchase order, receiving the delivery, inspecting it, and putting it away. Time the next receiving run with a stopwatch and multiply by a loaded hourly rate. If a receipt takes twenty minutes including inspection and the loaded rate is $30 an hour, the order cost is $10, not the $50 that gets typed into the calculator because it looks plausible. The number matters: doubling the order cost raises EOQ by about 40%.

When to ignore it

EOQ assumes steady demand, a fixed order cost, and a fixed unit cost. Break any of those and the answer needs adjusting:

• Perishables. Holding cost is not a rate; it is the whole unit after the date passes. Order on shelf life instead.
• Quantity discounts. A cheaper unit cost at a higher quantity changes the comparison. Compute total cost at each price break and compare.
• Minimum order quantities. If the supplier will not ship below a floor, the floor is the order size.
• Lumpy demand. One order a month for a seasonal item is a planning decision, not an economic one.

Worked example: one part, all three numbers

A machined bracket used on one assembly line.

Input	Value
Average daily usage	10 units
Working days per year	250
Annual demand	2,500 units
Lead time	7 working days
Peak daily usage seen	14 units
Cost per order	$45
Unit cost	$12
Holding rate	20% a year, so $2.40 per unit per year

Safety stock. (14 − 10) × 7 = 28 units.

Reorder point. (10 × 7) + 28 = 98 units.

EOQ. √(2 × 2,500 × 45 ÷ 2.40) = √93,750 = 306 units, which is 31 working days of use at 10 a day.

The order cycle now falls out of the two numbers. At 10 units a day, 306 units last about 31 working days, so the part is bought roughly every six weeks, and the reorder point is hit seven days before the stock is expected to run out.

The annual cost of that plan is $369 in ordering (8.2 orders at $45) and $367 in holding (153 units average at $2.40), or about $736. Ordering monthly instead, at 208 units an order, costs $540 to order and $250 to hold, or $790. Ordering weekly at 48 units costs $2,340 to order and $58 to hold, or $2,398. The flatness of the curve is visible: the monthly plan is 7% worse than the EOQ plan, and the weekly plan is three times worse.

Where the numbers break

All three formulas run on history. They describe the demand you had, not the demand you will have, and they fail in the same few places.

Usage recorded at the wrong level. Daily usage averaged across a year hides a product that sold in two bursts. If usage is lumpy, plan per season or per promotion rather than per year.

Lead times that drifted. A reorder point computed from last year's lead time is wrong the first time a supplier moves a warehouse. Measure lead time from purchase order to stock on the shelf, not to the dock, and review it per supplier.

Costs that are guesses. EOQ is only as good as the unit cost behind the holding rate. A cost field left at zero turns the formula into a division by zero in spirit: the answer becomes enormous. Enter a cost per item before trusting the order quantity.

Rules the formula cannot see. Contract minimums, pallet quantities, shelf life, and storage limits all override the arithmetic. Write the rule next to the number so the next person knows why the order size differs from the calculator.

One average for the whole catalog. Planning every item with the same reorder rule produces a warehouse where slow movers are overstocked and fast movers are always short. Group items by how much they cost you per year, then give the expensive ones their own numbers and a rule of thumb for the rest. The ABC analysis calculator builds those groups from your own item list.

Keeping the inputs current

The three formulas need three inputs kept honest: usage, lead time, and cost.

Daizy records every stock change as a movement with an item, a location, a user, and a time. The movement totals report turns those records into usage over any date range, which is the number all three formulas start from. The same report lists stock exceptions: items at zero, negative, or below the reorder level you set.

Stock counts correct the usage figure. A part whose book quantity drifts away from the shelf makes every downstream number wrong, which is why a cycle count on high-value items is part of planning rather than an audit chore.

Lead time is the one input Daizy cannot measure for you. Record it per supplier when you review purchasing, and put the review on a calendar. Costs come from the item record; a single cost per item is enough for EOQ and for inventory valuation.

A monthly routine

Fifteen minutes a month keeps the three numbers useful:

1. Open the movement totals for the last 90 days and check that usage for your top items still looks like the pattern you planned for.
2. Compare actual arrival dates with quoted lead times for the suppliers you used. Update the lead times that moved.
3. Recompute the reorder point for items whose usage or lead time changed by more than 20%.
4. Review the stock exceptions list and decide which items need a count before the next order.
5. Recheck EOQ once a quarter, or whenever an order cost or unit cost changes enough to matter.

Planning gets better with attention, not with a more complicated model. The three formulas above are old, simple, and good enough for a stockroom of a few hundred items or a warehouse of a few thousand. What separates a plan that works from a plan that does not is whether the inputs are current.