By Safock Procurement Research Team8 min read
A restaurant group uses 2,400 tins of olive oil a year and orders 80 at a time. The economic order quantity formula, the one in every operations textbook, says it should order about 180. Do that and the year's total cost drops by $414.
The supplier also offers a lower price at 200 tins and a lower one again at 500. Order 500 at a time and the year costs $6,611 less than today, and $6,197 less than the textbook answer. The formula leaves price breaks out, and for this item the price is by far the biggest cost.
Every order costs something to place: someone's time to raise and approve it, receive it, and match and pay the invoice. Order more at a time and you place fewer orders a year. But each order then sits on the shelf longer, tying up cash and space. That is the holding cost, usually expressed as a percentage of the item's price per year.
The economic order quantity is the order size where those two costs are smallest together. The idea is more than a century old: it is usually traced to an article by Ford W. Harris, published in Factory, The Magazine of Management in 1913 (Wikipedia).
EOQ = √( 2 × D × S ÷ H )
EOQ = √(2 × 2,400 × 45 ÷ 6.72) = 179 tins. The oil comes in cases of four, so that rounds to 180, about 13 orders a year.
At 180 tins, ordering costs $600 a year and holding costs $604.80, almost exactly equal. That is what the formula does: it finds the point where the two lines cross.
The supplier's price list:
| Order size | Price per tin |
|---|---|
| Any quantity | $28.00 |
| 200 or more | $26.50 |
| 500 or more | $25.20 |
These are all-units breaks: order 500 and every tin costs $25.20. Now the yearly purchase cost belongs in the comparison, because it changes with the order size:
Total cost a year = purchase cost + ordering cost + holding cost
| Order size | Price | Purchase | Ordering | Holding | Total a year |
|---|---|---|---|---|---|
| 80 (today) | $28.00 | $67,200 | $1,350 | $269 | $68,819 |
| 180 (classic EOQ) | $28.00 | $67,200 | $600 | $605 | $68,405 |
| 200 | $26.50 | $63,600 | $540 | $636 | $64,776 |
| 500 | $25.20 | $60,480 | $216 | $1,512 | $62,208 |
| 1,000 | $25.20 | $60,480 | $108 | $3,024 | $63,612 |
Moving from 180 to 500 tins raises holding cost by $907 a year and saves $6,720 on the oil itself. The ordering and holding costs, the whole subject of the classic formula, are under 3% of the total here. Ordering past the last break only adds holding cost: 1,000 tins costs $1,404 a year more than 500.
With price breaks, the cheapest order size is always one of a few candidates:
Round each candidate to whole cases, work out the total yearly cost for each, and pick the cheapest. That is what the calculator does.
Buying 500 tins at a time only works if the oil is used before it goes off. At 2,400 tins a year, a site uses about 6.6 tins a day:
| Usable shelf life | Most you can use in time | Best order | Total a year |
|---|---|---|---|
| 180 days | 1,183 tins | 500 at $25.20 | $62,208 |
| 60 days | 394 tins | 200 at $26.50 | $64,776 |
| 30 days | 197 tins | 180 at $28.00 | $68,405 |
At 30 days, the site can use 197 tins in time, three short of the 200-tin break, and the best it can do is the classic EOQ at full price. That gap is worth $3,629 a year. It's worth asking the supplier whether the break could start at 196, or whether deliveries could be split across sites that share the order.
Change the usage, costs, price breaks and shelf life. The defaults are the olive oil, with today's order of 80 tins.
Best order size · same maths as the full calculator · cases of 4
Ordering enough to reach a price break beats the classic EOQ.
Open with these numbersFree tool
EOQ Calculator with Price Breaks
Enter your usage, order and holding costs, any number of price breaks, the case pack, a minimum order and shelf life, and see the total cost curve across every order size, with the cheapest one marked.
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A larger order also means fewer orders to place, receive and pay, and fewer three-way matches to resolve. When storage is the limit, a central store that buys at the price break and transfers to sites can get the discount without every site holding the stock.
The order size that minimises the yearly cost of ordering and holding an item. Ordering more at once means fewer orders but more stock sitting on the shelf; EOQ is the balance point between the two.
EOQ = √(2 × annual usage × cost per order ÷ yearly holding cost per unit). For 2,400 tins a year, $45 per order and a holding cost of 24% of a $28 tin, EOQ is about 179 tins.
With quantity discounts, the unit price usually matters more than the ordering and holding costs. Work out the total yearly cost, including the purchase price, at the classic EOQ for each price tier and at each tier’s minimum quantity, and choose the cheapest. In the example in this guide, ordering 500 tins to reach the lowest price saves $6,197 a year over the classic EOQ.
The yearly cost of keeping a unit in stock, usually expressed as a percentage of its price: the cost of the cash tied up, storage space, insurance, and the risk of damage, theft or expiry. Work it out from your own costs; a borrowed rule of thumb can be far off for perishable stock. Our inventory carrying cost guide shows how.
When it would mean holding more than you can use before the stock expires, when storage space is limited, when a supplier’s minimum order is larger, or when a price break makes a larger order cheaper overall. The best order size is the cheapest one that meets those limits.