What Is Economic Order Quantity?
When it comes to replenishment, it can be tricky to balance costs. On the one hand, you want to take advantage of economies of scale (a.k.a. the savings available when you order a higher quantity of items at once). But on the other hand, ordering tons of items at once ramps up the storage costs for your inventory.
That’s where the economic order quantity (EOQ) model comes into play.
Applying EOQ calculations to your inventory management can be a huge cost saver. But it also involves doing a fair bit of math—making it a relatively difficult model to implement if you’re tracking your inventory manually.
Here’s the complete breakdown of the EOQ model, how it works, and how to implement it in your business.
What you need to know about economic order quantity
1. What is economic order quantity?
Economic order quantity (EOQ) is a replenishment model designed to help you minimize your inventory costs, and overall, improve your inventory and supply chain management.
Every time you place a purchase order, you have to pay the item manufacturer for your goods. In some cases, you may also have to pay a flat fee per order as well. But increasing your ordering cost by ordering more products at a time may allow you to enjoy a quantity discount (lower cost-per-item). Then, once you’ve received your products, you have to pay to store those products. And ordering more units at a time would make your storage cost higher.
The trick is knowing your optimal order quantity to help you balance your production costs and your inventory carrying costs.
The EOQ formula helps you determine your total inventory costs (including both production and storage costs). You can use this formula to determine the optimal quantity of products you should order at a time and how often to order (assuming customer demand stays constant).
2. What is the economic order quantity formula used for?
The economic order quantity model is most commonly used to determine the costs of inventory in a given time period. By manipulating the various parts of the formula, business owners can figure out the number of items they should order (and how often they should submit purchase orders) to minimize their storage and production costs.
Using the EOQ model as part of your inventory management strategy also allows you to manage your inventory levels. Once you’ve calculated the best replenishment method, you can feel confident that you’re not overpaying for storage costs. And with lower storage costs for your existing products, you can also lower your opportunity costs*.
One thing to keep in mind, though: the EOQ formula assumes that your customer demand will stay consistent throughout the time period in question. So if your business sees a lot of fluctuation in customer demand during various points in the year or quarter, EOQ can’t be used as a reliable replenishment model (at least not on its own).
*Opportunity cost = the money you’ve lost by ignoring a profitable opportunity because of something like lack of storage space in your warehouse
3. What is the economic order quantity formula?
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—as well as 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.
How to calculate EOQ
When it comes to calculating EOQ, the key is to make your annual holding cost, or carrying 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]
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 the inventory holding cost for your busy season and adjust your reorder rates to keep up with higher customer demand.
4. Downsides of the economic order quantity model
While the EOQ model is a good guideline for balancing the costs of your inventory on hand and the costs of producing your inventory, it isn’t foolproof.
Assumption of fixed costs
The biggest failing of the EOQ model is it assumes production costs and storage costs for your product are constant.
As any business owner knows, consumer demand can change at the drop of a hat. But if you continue ordering according to your EOQ plan, this assumption of constant demand may leave you with unsold products on your shelf during off-peak season. That will, in turn, drive up your inventory costs since you’re paying extra to store items that aren’t selling.
Manufacturing costs can likewise fluctuate based on time of year, turnaround rate, and more. The formula also doesn’t take extra costs into account—like setup costs on inventory orders for brand new products. If the cost per item is different every time you order, then the EOQ formula’s assumption of consistent production costs can be a massive thorn in your side.
Assumption of immediate fulfillment
The EOQ model also assumes that any orders you make are automatically added to your inventory. In other words, it assumes that as soon as you place an inventory order, those items are immediately available for your business to use or sell.
The problem? You usually have to wait a while to receive your products after ordering.
Fortunately, this problem is easily solved if you calculate a safe reorder point that takes your supply chain and manufacturer’s lead time into consideration.
Assumption of cash flow
The other thing that the EOQ formula doesn’t take into account is that not all businesses can afford to order economically.
Take the construction company example we used above. Sure, the most economical replenishment strategy would be ordering 750 cement bags at a time. But even with the manufacturer’s waived production fee, that’s still a $3,000 expense on every order.
That could be a huge problem if you’re still waiting for clients to pay their bills and you don’t have $3,000 on hand. In that case, you may have to bite the bullet and order fewer cement bags—even if it means higher inventory costs in the long run.
Economic order quantity is a replenishment model that helps you balance the costs of inventory—specifically, your production and storage costs. When used correctly, calculating EOQ helps you find the ideal number of items to order at a time to keep these costs as low as possible.
Ordering using the EOQ formula isn’t foolproof, though. The formula assumes that consumer demand, manufacturing costs, and storage costs stay consistent throughout the time period in question. It also assumes that ordered inventory is immediately available, and it doesn’t factor in limited cash flow.
If your business doesn’t see a lot of fluctuation, the EOQ formula can be easily implemented in a manual inventory tracking system. Otherwise, you may need to upgrade to an inventory management software to ensure you’re ordering the right number of products at the right time.
If your business has complex ordering needs, the EOQ model could still be an efficient way to cut costs—but we’d recommend using inventory management software to calculate your EOQ automatically. Get started by checking out our top-recommended inventory management platforms.
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