When placing an order for a single period, the order quantity should be increased as long as

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As discussed earlier an organization’s inventory policy must answer the two basic questions: when to order and how much to order. There are two basic categories or choices in inventory policy that accomplish this: fixed-order quantity systems and fixed-time period systems. They work in slightly different ways. Let’s look at these now.

Fixed-Order Quantity System

The first policy choice is through a system called a fixed-order quantity system. Therefore, two variables define this system and answer the two basic questions of when to order and how much. The first is an order quantity, Q, and the second is a reorder point, ROP. As the name suggests, the quantity ordered with this system is constant or fixed and is denoted by Q. An order is placed when the inventory position drops to some predetermined level. This predetermined level is called the reorder point and is usually noted as ROP. Together these variables specify when to place an order: when inventory reaches the ROP. They also specify how much to order: the quantity Q.

A graphical presentation of this model is shown in Figure 1-5. Notice that the system assumes a constant demand rate of d by which the inventory position (IP) is reduced. When the IP reaches the ROP, an order is placed for the quantity Q. When goods arrive, the inventory is replenished, and all at once the inventory position is increased by Q. However, inventory cannot arrive the moment an order is placed as there is a certain amount of lead time, L, during which we have to wait for the order.

Figure 1-5 Fixed-order quantity systemt

Here inventory is monitored on a continual basis, and the assumption is that we always know the current level of inventory. When inventory levels reach the ROP, an order of quantity Q is placed. For example, let’s assume that a grocer uses a fixed-order quantity system for its inventory of canned tomato soup. Its policy may be that it always orders 200 cans of soup, for which it gets a nice quantity discount, and the order is made when the number of cans of soup drops to 25. Therefore, the ROP = 25, and the Q = 200.

In the classic version of this system Q is computed as the economic order quantity (EOQ)—an economically optimal order quantity—which we will compute later. For this reason this system is sometimes called the economic order quantity (EOQ) model. Other terms used to describe it are the Q-model as the quantity Q is constant. Sometimes it is called a continuous review system, as the inventory levels are continuously monitored. The model has even been called a sawtooth model, as the graph of inventory looks like a sawtooth. All these terms refer to the same type of inventory system, describing different features of the system itself.

Fixed-Time Period System

The second inventory policy is determined by a system called a fixed-time period system shown in Figure 1-6. This system checks inventory levels in fixed time intervals labeled as T. The result is that the quantity ordered varies based upon the inventory position when the system is checked. The system sets a target inventory level it wants to maintain, say R. Inventory is checked every T intervals, say every week or every two weeks, and an order is placed to restore the inventory level back to R. Based on the inventory level at time period T, the amount of inventory that needs to be ordered will be some quantity Q that varies from period to period. This quantity Q is the difference between the target inventory R and how much inventory is in stock—the IP at time T:

Figure 1-6 Fixed-time period system

where:

• Q = order quantity
• R = target inventory level
• IP = inventory position

Two variables define this system and answer the two basic questions of when to order and how much: T and Q. They specify when to place an order: at time interval T. They also specify how much to order: quantity Q, computed as the difference between the target inventory, R, and the inventory position, IP. Sometimes this system is called the periodic review system to indicate that the inventory level is checked periodically, rather than continuously.

We can assume that an auto manufacturer uses a fixed-time period mode for its inventory of alternators. Also, let’s say its policy is to check inventory levels every two weeks, and that it has a target inventory level R = 5,000 alternators. If after two weeks the company checks its inventory level and finds its inventory position IP = 2,800 alternators, it would place an order for quantity Q = R – IP = 5,000 – 2,800 = 2,200 alternators. This is essentially how this policy system works.

The biggest difference between the fixed-order quantity system and the fixed-time period systems is in the timing and quantities of the orders placed. With the fixed-order quantity system inventory is checked on a continual basis and the system is prepared to place orders multiple times per year on a random basis. This has an advantage of providing greater system responsiveness, but it also requires administrative processes to be in place on a continual basis. In addition, as different inventory items reach their reorder points at different time periods, it might be difficult to obtain quantity discounts based on a bundled order.

The fixed-period order system requires carrying more safety stock inventory. The reason is that with this system we do not check the IP on a regular basis, and a sudden surge of demand could lead to a stockout. This system, however, allows more organized purchasing as inventory levels are checked in set time intervals. Orders can be bundled and quantity discounts obtained more easily, which can provide an advantage. In a fixed-order quantity system different items may reach reorder points at different times generating many orders at random intervals. On the other hand, a fixed-period system could ensure that inventory levels are checked on a regular basis for all items—say every two weeks. Then the orders for all the items could be bundled.

Optimal order quantity is an important inventory calculation for direct-to-consumer (DTC) retailers. For one, optimal quantity help businesses place timely orders and avoid costly stockouts events. But it can also improve revenue in a big way.

By incorporating optimal quantity into your strategy for inventory management, you can set yourself up for operational success and a more satisfied customer base.

What is optimal order quantity?

Optimal order quantity is the most cost-effective amount of inventory that a business should have at any given time.  Put simply, this calculation represents your ideal order size to meet demand without tying up too much working capital in excess stock. This calculation is also known as economic order quantity (EOQ) and is crucial for businesses to keep inventory costs low.

With the help of the optimal order quantity formula, you can minimize inventory expenses related to ordering, receiving, and storing your products.

Why you should calculate optimal quantity

For product-powered brands, calculating optimal order quantity is one of the most efficient methods for managing inventory, reducing dead stock, and boosting revenue.

Find the best reorder point

A reorder point (ROP) indicates when your stock needs to be replenished. Meaning, it tells you when to repurchase products, so you don’t run out. And your ROP works hand in hand with optimal order quantity to ensure you always have the right amount of inventory at the right time. 

In fact, the optimal order quantity formula helps you find the best reorder point for your business. So, when your inventory falls below a certain level, you know to reorder. This way, you safely avoid a stockout and fulfill orders as planned.

Stop accumulating dead stock

Dead stock refers to unsold products that take up space at your warehouse (and are unlikely to move anytime soon). And this dead inventory can be pretty costly for your business — since you have to pay more storage fees the longer those SKUs sit still. 

In fact, dead stock is estimated to cost brands 30% more than what the inventory is actually worth. 

The good news is, optimal quantity helps you order the right amount of inventory to prevent dead stock from accumulating in the first place. With the EOQ formula, you can decrease order inconsistencies and ensure you don’t over-purchase when demand is low.

Prevent out-of-stock situations

Even before the pandemic introduced new supply chain management challenges, retailers lost out on nearly $1T in sales due to out-of-stock events. That number is staggering, but it also poses a huge opportunity to give your brand a leg up on the competition. 

How? By leveraging optimal order quantity to reduce inventory shortages and stockout events. EOQ offers inventory visibility, i.e., insight into your past, present, and future stock counts to help you calculate how much (and how often) to reorder. 

This way, you can ensure you always have enough inventory available to satisfy demand. And when you're competition's out of stock, you can swoop in and steal the sale.

Cut down on inventory costs

Inventory costs are known by a few different names; however, carrying costs and holding costs tend to be the most popular. These costs are what retailers pay to store their inventory at one or more warehouse locations. 

For most DTC sellers, inventory carrying costs account for 15-30% of their total inventory value. But by using order quantity metrics to gauge what you do and don’t need to buy, retailers can operate with a leaner inventory. 

The EOQ formula finds the optimal number of units to purchase, so you’re not over-ordering products with a low velocity (or reordering goods you already have in stock). And in the process, you can minimize operational overhead, freeing up working capital and growing your margins.

Streamline inventory management

Smart, streamlined inventory management is the foundation for a successful retail brand. When your inventory is well-organized and optimized for efficiency, you put your company in the best position to increase retention and drive revenue.

Optimal order quantity helps DTC merchants manage their inventory and make better business decisions across the board. By relying on EOQ, you can say goodbye to guesswork and gut feelings and instead order exactly what you need, exactly when you need it.

Boost earnings and revenue

When retailers have too little or too much inventory on hand, it often becomes a barrier to their profitability. Excess stock translates to greater storage costs, whereas insufficient stock limits your fulfillment capacity. So whatever way you look at it, your revenue will take a hit.

Thankfully, optimal order quantity makes it easy to keep inventory levels right where you want them. And when you have the products you need (nothing more, nothing less), you can fulfill orders accurately and on time. This then gives a huge boost to your overall earnings.

What you need to know before calculating optimal quantity

Before you can calculate optimal order quantity, there are a few inventory analytics you’ll want to familiarize yourself with. Namely, annual unit demand, order costs per purchase, and holding costs per unit.

Annual unit demand

As its name suggests, annual unit demand is the customer demand you receive for a specific product each year. To confirm annual demand for your own business, take a look at your historical inventory data like turnover ratio, reorder points, and purchase orders.

These data points will give you a good idea of how many units you’ve sold year-over-year. And it will make it easier to accurately calculate EOQ.

Order costs per purchase

Order costs per purchase are all the costs involved with creating and processing an order with a supplier. This might include preparing a purchase order or inspecting goods on arrival. 

And these expenses have a big influence on optimal order quantity. Not only do order costs feed into total inventory costs, but they also affect certain aspects of order fulfillment (like receiving a shipment or storing goods at a warehouse).

Holding costs per unit

Holding costs per unit typically happen 2 ways: 

1. As direct costs from storing inventory.
2. As opportunity costs from retaining said inventory. 

Before calculating EOQ, you'll need to know what you spend on inventory holding costs per unit annually.

To calculate holding costs, use the following formula:

inventory holding cost = (employee salaries + storage costs + opportunity costs + depreciation costs) / total value of annual inventory

Or, in other words, start by adding employee salaries, storage fees, opportunity costs, and depreciation costs. Then, divide this sum by the total value of your annual inventory. The answer (expressed as a percentage) will be your inventory holding cost.

Optimal order quantity formula

To calculate optimal order quantity for your DTC brand, use the following formula:

optimal order quantity = the square root of ([2DO] / H)

Note that in this equation:

• D = Annual unit demand
• O = Order costs per purchase
• H = Holding costs per unit

How to calculate optimal order quantity

Let’s look at the EOQ calculation a little closer by breaking it into 4 distinct steps:

1. Multiply annual unit demand by order costs per purchase.
2. Multiply the answer from Step 1 by 2. 
3. Divide the answer from Step 2 by holding costs per unit.
4. Find the square root of the answer from Step 3.

Optimal order quantity example

Let's consider how this formula might work in the real world. Imagine you're a DTC brand that sells 1,000 lavender candles each year. Your company pays $4 per unit to hold these candles in inventory, and the order cost comes in at $2 per purchase.

In this scenario, the optimal order quantity = the square root of (2 x 1,000 candles x $2 order cost) / ($4 holding cost). When rounded, you should get an answer of 31.6.

This means the optimal amount of lavender candles is ~32 units. By ordering this quantity, you'll adequately meet demand while simultaneously minimizing overhead costs. 

However, this EOQ calculation assumes your business' growth has plateaued. Or, if you're still growing, you must routinely rerun your calculation for accuracy, which can be time-consuming. 

Luckily, you can simplify this process by keeping a close eye on your inventory levels using an ops optimization tool like Cogsy. This tool allows you to monitor all your inventory data — real-time and historical — in a single source of truth. 

With access to this data, Cogsy automatically runs optimal quantity calculations for you (and does so continuously as your brand grows or product offerings change).

Plus, Cogsy then uses your unique replenish point to autofill a PO and remind you when to restock. This way, you can ensure operational excellence (meaning you're fully stocked up while keeping costs down) in less time and with much less effort.

6 basic assumptions about optimal quantity

There’s no doubt optimum order quantity is a very useful tool. But the accuracy of your calculations hinges on a few assumptions about product demand, storage, and more.

As you read through these 6 assumptions, keep in mind that the ‘constants’ must all happen within the same time period. If not, your end calculations are going to be way off.

1. Product demand remains constant

For your EOQ calculations to be correct, product demand must remain constant over a designated time frame (like a fiscal quarter or a full calendar year). This way, you know that fluctuations in the demand curve aren’t affecting your order projections.

2. Holding costs remain constant

Another assumption about EOQ is that holding costs remain constant, as well. This means the fees to store your unsold inventory are unchanged over a specified period. Fixed costs are easier to plug into the EOQ formula and can be trusted to deliver accurate results.

3. Unit order prices remain constant

Unit order prices must remain constant to use optimal order quantity to its full advantage. Changes to unit prices will likely throw off EOQ calculations' accuracy and make it more difficult to understand when (and how much) to reorder.

4. Setup costs remain constant

Setup costs are all the costs related to ordering your inventory, like those for packaging and delivery. Although these costs can change over time, you’ll have to find a window where they’re consistent if you want a clear picture of your replenishment needs.

5. Orders arrive without delay

It’s safe to say nobody likes dealing with delays in the supply chain since these disruptions can negatively impact both productivity and profitability. Getting the most out of the EOQ formula will require your orders to arrive on time, every time.

6. No products sold at a discount

The final assumption about optimal order quantity is that none of your products were sold to you at a discounted rate. That is to say, you haven’t received a bulk discount or similar incentive for purchasing large volumes of inventory all at once.

Stay on top of your inventory levels with Cogsy

Want to reap the benefits of optimal order quantity? Cogsy can help you stay on top of your inventory levels. This way, you always have the most precise calculations possible.

Get timely inventory notifications

Every company that partners with Cogsy has access to automatic replenish alerts. Because these notifications are happening around the clock, you'll have visibility into your stock counts and product movement like never before. 

What's more, Cogsy's innovative replenish alerts empower your brand to purchase inventory more proactively, so you never miss out on a single revenue opportunity.

Eliminate guesswork and error

The reality of manual spreadsheets is that they’re prone to human error and inaccuracies. This winds up costing you a lot of money since your ordering process is totally thrown off. 

Fortunately, Cogsy operates in real-time, so you can eliminate all that guesswork and optimize your purchase order process. With just 1 click, Cogsy creates an optimized purchase order with the exact amount of inventory you need.

Monitor all inventory data in one place

Cogsy's operations platform is a single source of truth for all your inventory data. With Cogsy, you can store real-time and historical data in one place, so it's readily accessible at any time.

This clarity is the key to maintaining inventory control and allows you to capitalize on the growth opportunities that cross your path. After all, you need clarity to turn insights into actions that can take your company to the next level.

Ready to start optimizing your inventory today? Chat with the Cogsy team to see how you can take control of your brand's growth today.

Optimal quantity FAQs

Looking for a bit more on optimal order quantity? Check out the cheatsheet below.

What are the limitations of calculating optimal quantity?

Although optimal order quantity has its fair share of advantages, there are some limitations with it, as well. For instance, optimal quantity assumes your product demand, holding costs, and unit order prices remain unchanged by inventory shortages or purchase discounts.

What is the difference between optimal quantity and minimum order quantity?

Optimal order quantity is a calculation that determines the most cost-effective amount of inventory for your company to purchase. Essentially, this calculation represents your ideal order size to meet demand without overspending on excess stock.

Minimum order quantity (MOQ), on the other hand, is the amount of product a supplier requires that you buy at one time.

What is optimal safety stock quantity?

Safety stock describes the extra product you keep on hand to prevent an out-of-stock situation. The optimal safety stock quantity for your retail brand depends on your:

• Inventory velocity
• Current and future demand
• Supplier lead times