To understand the economic order formula, you’ve first got to understand how inventory costs are calculated. To find your total cost, you’ve got to add the price of your inventory items to the cost of storing those items and the manufacturing costs for your orders.
The formula for total cost looks like this:
TC = (P x D) + [(H x Q) / 2] + [(S x D) / Q]
Here’s what all those letters stand for:
- TC = total cost. In other words, this is the total cost of making and storing your inventory for the given time period.
- P = price per unit. This represents the unit cost for the product in question.
- D = number of units needed. This is the number of products you expect to sell during the time period you’re analyzing.
- H = holding cost per item. This is the cost to store each individual unit over the course of the entire time period.
- Q = quantity ordered. This represents the number of units you buy per order. This is the number you’ll play with to figure out the most economical ordering method.
- S = fixed cost of each order. Put another way, “S” equals any manufacturing or tooling fees your manufacturer applies to each order.
So let’s say you run a construction company, and you’re trying to figure out the best way to balance inventory costs for your supply of cement (purchased in bags). You usually use around 15,000 50-pound bags of concrete per year, and each bag costs $4 to order—plus a $100 order fee from the manufacturer on every order. Once you receive your cement bags, it costs $3 per bag per year to store your concrete.
Assuming you kept inventory levels of 1,250 bags at a time, your total inventory cost calculation would look something like this:
Total cost = ($4 x 15,000) + [($3 x 1,250) / 2] + [($100 x 15,000) / 1,250]
When we do the math, that would mean the total inventory costs for your cement during the year would come out to $63,075.
Now, assuming that variables like cost per item, production fees, and storage costs remain constant throughout the year, that would mean the only variable that can change the total inventory cost for your cement would be the quantity you order.
So let’s say you decided to order 1,000 bags of concrete at a time instead of 1,250. That would change your total cost to:
Total cost = ($4 x 15,000) + [($3 x 1,000) / 2] + [($100 x 15,000) / 1,000]
When you do the math, you find that ordering fewer units at a time brings your total cost down to $63,000.
From there, you might assume that ordering even fewer cement bags at a time will lower your total costs even more, right? So you decide to order 300 bags at a time instead. That would change your EOQ calculation to:
Total cost = ($4 x 15,000) + [($3 x 300) / 2] + [($100 x 15,000) / 300]
Unfortunately, ordering such a low quantity of bags at a time means you have to place more orders throughout the year, which means you pay the $100 purchasing fee more often. So your total costs would come out to $65,400—$2,375 more than you’d pay if you ordered 1,250 bags at a time.
So how do you determine the optimal number of items to order at a time? That’s where the EOQ formula comes in.
The key with the EOQ formula is to make your annual holding cost (the second part of the total cost formula) and your production cost (the third part of the total cost formula) as close to equal as possible. You do that by using the formula:
EOQ = square root of [(2 x D x S) / H]
So for our construction business, this formula would look like this:
EOQ = square root of [(2 x 15,000 x $100) / $3]
Rounding, that would make the ideal number of cement bags per order 1,000. If we apply that to our total cost model, that gives us:
Total cost = ($4 x 15,000) + [($3 x 1,000) / 2] + [($100 x 15,000) / 1,000]
That would give us a total annual inventory cost of roughly $63,000—the lowest possible result. And if you’ll notice, maintaining this inventory level makes your storage costs and manufacturing costs roughly equal:
Storage costs: [($3 x 1,000) / 2] = $1,500
Manufacturing costs: [($100 x 15,000) / 1,000] = $1,500
Now, the example we used above is pretty simplistic—and unfortunately, calculating real-life inventory costs is rarely that easy.
The good news is you can adjust your EOQ model to accommodate some of the common wrinkles that may affect your ideal order quantity.
Many manufacturers, for example, offer quantity discounts to encourage their clients to make large orders. So if your cement manufacturer waives their production fee on orders of 1,010 bags or more, you can compare your EOQ calculation (with its total cost of $63,000) to the calculation below (which takes the higher required lot size and lower manufacturing fee into account):
Total cost = ($4 x 15,000) + [($3 x 1,010) / 2] + [($0 x 15,000) / 1,010]
From the formula above, we see that ordering the higher quantity would bring our inventory costs down to $61,515—a $1,485 savings.
If your business experiences consistent seasonality (where customer demand isn’t constant throughout the year), you can also adjust your EOQ formula to cover a shorter time period (like a quarter instead of a year). That way, you can get a more accurate idea of your inventory holding costs for your busy season and adjust your reorder rates to keep up with higher customer demand.