1. Economic Order Quantity
Bus M361-2
Sabrina Wu
11/28/2005
My name is Sabrina Wu. I am a student in the Business M361-2 class. This tutorial is an explanation of Economic Order Quantity.

2. Economic Order Quantity
EOQ
Economic Order Quantity
Definition of EOQ
How to use the EOQ model in a business organization
How the EOQ model works
Real world example
In this short tutorial, I will introduce the concept of EOQ. EOQ means the Economic Order Quantity. It is a great tool used in business. In order to introduce EOQ I will present in the following order:
First, a clear definition of EOQ.
Second, I will show how to use the EOQ in a business organization.
Third, I will show how the EOQ actually works. Not only will I show you the formula used in calculating the EOQ, but I will explain in detail how the formula was derived and how to identify the correct values of each of the variables.
Next, I will provide a real world example of the EOQ model in use. I hope to show how useful and important the EOQ is in everyday business. In this example, I will give you a practice exercise that we can do together. This is to ensure that you have a clear understanding of how to use the EOQ tool.
Now that I have laid out basic order of this presentation, let us proceed to the first section, defining the EOQ.

3. The Definition of EOQ
EOQ, or Economic Order Quantity, is defined as the optimal quantity of orders that minimizes total variable costs required to order and hold inventory.
Every company worries about two things when deciding how to manage their inventory. How much should we order? And how often should we order? These represent variables that come with their own changing costs. The Economic Order Quantity, or EOQ, is that magic number that represents the optimal quantity of orders that minimizes total variable costs required to order and hold inventory. Let me restate that. The EOQ helps us to determine the appropriate amount and frequency when ordering and holding inventory. Let me show you how this helps a business.

4. How to use EOQ in your organization
How much inventory should we order each month?
For most businesses, there is a large amount of inventory that has a constant unit price and a known demand rate that happens every month. But holding too much or ordering too often will increase our holding and purchasing costs. So, the question arises, how much should we order each month? The solution is to use the EOQ model. We can use the EOQ model to determine the quantity of that inventory that should be purchased at each time we place an order to minimize the purchasing and holding costs of this item.
The EOQ tool can be used to model the amount of inventory that we should order each month.

5. The Principles Behind EOQ: The Total Cost Curve
How EOQ Works
The Principles Behind EOQ: The Total Cost Curve
& 
Let me first talk about what we are trying to achieve.
In box (a) we see the inventory carrying costs, or the costs associated with holding inventory. These costs increase as you hold more and more inventory. I will discuss these holding costs shortly.
In box (b) we see the order processing costs, also known as the procurement costs. The costs decrease as the order quantity increases. I will also discuss these procurement costs in a minute.
In box (c) these two graphs are combined to reflect the total variable costs associated with the order quantity. This new graph is called the Total Cost Curve. By looking at the minimum cost per unit on the graph, we can determine what is the proper order quantity, or Economic Order Quantity. Let me back up a bit and make sure that I have clearly explained the holding and procurement costs.

6. The Principles Behind EOQ: The Holding Costs
How EOQ Works
The Principles Behind EOQ: The Holding Costs
Keeping inventory on hand
Interest
Insurance
Taxes
Theft
Obsolescence
Storage Costs
The Holding Costs, as we saw before are variable. They increase the cost per unit as the order quantity grows. What sort of cost are we talking about? Let me list just a few of the main costs. Keeping inventory on hand, Interest, Insurance, Taxes, Theft, Obsolescence, and Storage Costs. Why do these costs increase as the quantity grows? Let me show you a few examples.

7. The Principles Behind EOQ: The Holding Costs
How EOQ Works
The Principles Behind EOQ: The Holding Costs
Interest
Obsolescence
Storage
Let’s look at Interest, Obsolescence, and Storage Costs. When we purchase more inventory, we need to take out loans to pay for them. Loans all carry interest. This interest is an cost that increases as we take out larger loans to afford more inventory. When we talk about obsolescence, we are talking about the natural, and inevitable process of product redesign. Take the Porsche for example. Even though it was a great car 40 years ago, it has been redesigned so many times that those old parts are now obsolete. Old parts sitting unused in a warehouse somewhere is an additional cost that is ameliorated into the overall cost per unit of having inventory on hand. And lastly, storage is pretty straightforward. The more inventory you have on hand, the more room you need to store it. This space needs to be paid for, so we see again how the costs increase with quantity.

8. The Principles Behind EOQ: The Procurement Costs
How EOQ Works
The Principles Behind EOQ: The Procurement Costs
Primarily the labor costs associated with processing the order:
Ordering and requisition
A portion of the freight if the amounts vary according to the size of the order
Receiving, inspecting, stocking
Invoice processing
The Procurement costs are also variable. They decrease as more and more quantity is ordered. Each event of ordering has a certain cost associated with it. A certain amount of paperwork needs to be filled out, people need to be contacted and told how much to order. When the inventory comes in, it has to be inspected, then stocked. Then the invoices need to be processed. The cost per unit decreases as the quantity ordered at each event of ordering. Note that the curve for the procurement costs is dramatically different from the holding cost curve. Now that we understand the principles working behind EOQ, let us take a closer look at the nuts and bolts.

9. How EOQ Works The Total Cost Formula
The first thing we want to look at is the total cost formula. While this formula does not tell us the EOQ, the derivative of this formula will. The equation for total cost is simply the constant purchase cost, PR, plus the order costs (CR over Q), plus the holding costs (PFQ over 2). Let me explain step by step where this equation comes from and what are the variables that comprise it.
Total Cost = Purchase Cost + Order Cost + Holding Cost

10. This represents the unchanging fixed costs
How EOQ Works
The Total Cost Formula
This represents the unchanging fixed costs
The unchanging fixed costs are simply the amount required per unit multiplied by the monthly usage. This is the simplest part of the equation. Most businesses are very aware of their fixed costs.
P = Purchase cost per unit
R = Forecasted monthly usage

11. This represents the variable order costs
How EOQ Works
The Total Cost Formula
This represents the variable order costs
The order cost is very tricky. Remember, the order cost is not all the costs associated with the purchasing and receiving departments. These costs are not associated with the quantity ordered but primarily with physical activities required to process the order.
P = Purchase cost per unit
R = Forecasted monthly usage
C = Cost per order event (not per unit)
Q = The number of units ordered

12. This represents the variable holding costs
How EOQ Works
The Total Cost Formula
This represents the variable holding costs
The holding cost is also variable. This too is often over-stated by businesses. The holding cost factor is the factor of the purchase cost that is used as the holding cost (this is usually set at 10-15%, though circumstances can require any setting from 0 to 1). Multiplying the purchase cost times the holding cost factor times the quantity then averaging by two gives us the holding costs.
P = Purchase cost per unit
R = Forecasted monthly usage
C = Cost per order event (not per unit)
Q = The number of units ordered
F = Holding cost factor

13. How EOQ Works The EOQ Formula Total Cost Formula
Taking the derivative of both sides of the equation and setting equal to zero to find the minimum value of the function, one obtains:
In order to find the relative minimum for the Total Cost Curve, we take the derivative of it then set it equal to zero.

14. The Economic Order Quantity
How EOQ Works
The EOQ Formula
The result of differentiation
Q prime is our Economic Order Quantity. As you see, the formula for computing the EOC is pretty simply, but the key is to make sure that you have the right inputs for those variables.
The Economic Order Quantity

15. How EOQ Works The EOQ Formula Review and Summary of the EOQ Formula
In summary, this formula will give us the optimal quantity of units that should be purchased each month in order to minimize the variable costs. This optimal quantity is the EOQ.
P = Purchase cost per unit
R = Forecasted monthly usage
C = Cost per order event (not per unit)
F = Holding cost factor

16. Here is the a graphic representation of the EOQ equation
How EOQ Works
The EOQ Formula
Review and Summary of the EOQ Formula
Here is the a graphic representation of the EOQ equation
Here is a graphical representation of what we just found. By taking the derivative of the total cost curve and finding the minimum value for it, we can easily see where the cost per unit value isi the lowest. At that value, we also find the corresponding Economic Order Quantity.

17. Real Life Example:
Let us take a country convenience store as an example. The name of the store is aptly named the Stop and Slurp. Even this small little convenience store can benefit from knowing how much and when they should restock their inventory. Due to the limited room in the store, holding costs must be factored in. Also, because there is not enough resources to hire more helpers, the time spent ordering and procuring new inventory must be also be considered. Let’s review the facts the we know about the store.

18. Real Life Example:
Here is a report from the Stop and Slurp containing the information that we need to determine the optimal quantity of their order each year. Note that these numbers are projected for the annual quantity, not the monthly quantity. To determine the monthly quantity, simply divide the EOQ by 12 months. But, how do we start to find the EOQ of Coca Cola for the Stop and Slurp?

19. Real Life Example: First, Recall the EOQ Equation:
Let is first recall what is the EOQ Equation. And what are the variables? P is the Purchase Cost per Unit. R is the Forecasted monthly usage. C is the Cost per order, not to be confused with the cost per unit. And F is the Holding Cost factor, or the proportion of the purchase cost allotted to the holding costs.
P = Purchase cost per unit
R = Forecasted monthly usage
C = Cost per order event (not per unit)
F = Holding cost factor

20. Real Life Example: Next let’s identify the correct variables…
Next let’s identify the correct variables in our specific Stop and Slurp example. Here it what was provided to us by the Stop and Slurp management.

21. Real Life Example: Next let’s identify the correct variables…
Forecasted Amount
R is the forecasted amount. Notice that this is the annual demand, not the monthly demand. Using either will give you the same result. Just make sure that you are constant in your use of monthly or annual forecasts. Here we see that the Annual demand is projected to be 5200 cases of Coca Cola.

22. Real Life Example: Next let’s identify the correct variables…
Ordering Costs
C is the ordering cost. Here we see that the ordering cost for a each ordering event is 10 dollars. That could include the amount of time and labor that the owners for Stop and Slurp spend on creating the purchase order, calling the Coca Cola distributor, receiving the order and putting it in the refrigerator, and filing the invoice.

23. Real Life Example: Next let’s identify the correct variables…
Cost per Unit
P is the Cost per Unit. This cost is pretty low, because they are ordered in bulk amounts. Here we see that the cost per unit is 2 dollars per case.

24. Real Life Example: Next let’s identify the correct variables…
F is the holding cost factor. This means 20 percent of the cost per case is allotted for holding costs. These would be the costs to rent the storage space in the back, the cost of refrigerating the Coca Cola, and the inevitable costs of some inventory being broken or stolen and never being sold. These costs are all figured into the holding cost factor. Here the Stop and Slurp has set the holding Cost Factor at 20 percent of the inventory per year.
Holding Cost Factor

25. Real Life Example: R = Annual demand C = Fixed ordering cost
P = Cost per case
F = Holding Cost Factor
Let’s put it all together now. We know the Annual Demand, the fixed ordering cost, the cost per case, and the holding cost factor. Now let’s plug it into the formula.

26. Real Life Example: R = 5200 C = $10 per order P = $2
F = 20% of value of inventory per year
Here are the variable values that we will use in our equation.

27. Real Life Example: EOQ = R = 5200 C = $10 per order P = $2
F = 20% of value of inventory per year
Once we have set all the variables in the right places all that remains is entering it into our calculator and finding out what is our EOQ. 2
(10)
(5200)
EOQ =
(2 )(.20)

28. Real Life Example: EOQ = EOQ = 510 cases 2 (10) (5200) (2 )(.20)
Our EOQ is 510 cases each time we order. According to the EOQ model, this quantity will minimize our holding costs and our procurement costs. Good thing the Stop and Slurp used the EOQ.
EOQ = 510 cases

29. Wrapping It Up
EOQ, or Economic Order Quantity, is defined as the optimal quantity of orders that minimizes total variable costs required to order and hold inventory.
To wrap things up, let me restate the main points about EOQ. First, the EOQ is that magic number that minimizes our cost to order and hold inventory. Second, remember that we are simply finding the point on the total cost curve where cost per unit reaches a minimum. This cost is set up as in the EOQ equation.

30. Closing Comments EOQ is a tool, not a simple solution.
EOQ is useful in determining optimal order quantity
Understand the equation and what you are trying to find
Find accurate inputs for the equation
In closing, I have shown how the EOQ can be used as a successful tool in business planning. But remember that this is only a tool, not a simply solution to inventory problems. The EOQ can help us to determine the optimal order quantity if we understand the equation and know what we are trying to find, as opposed to blindly plugging numbers into a formula. Accurate inputs are the key to optimizing the use of the EOQ formula. If we have this basic understanding of EOQ, we relieve ourselves of the headache commonly found in business. We can now confidently answer the question of How much? And How often should we order inventory. Thank you for your time and your attention.

31. Additional Resources on EOQ
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I enjoyed presenting this topic to you and I have listed three resources that I have found helpful in understanding the EOQ tool. Thank you.