The Eoq Inventory Formula
The EOQ Inventory Formula
James M. Cargal
Mathematics Department
Troy University – Montgomery Campus
A basic problem for businesses and manufacturers is, when ordering supplies, to determine what quantity of a given item to order. A great deal of literature has dealt with this problem
(unfortunately many of the best books on the subject are out of print). Many formulas and algorithms have been created. Of these the simplest formula is the most used: The EOQ (economic order quantity) or Lot Size formula. The EOQ formula has been independently discovered many times in the last eighty years. We will see that the EOQ formula is simplistic and uses several unrealistic assumptions. This raises the question, which we will address: given that it is so unrealistic, why does the formula work so well? Indeed, despite the many more sophisticated formulas and algorithms available, even large corporations use the EOQ formula. In general, large corporations that use the EOQ formula do not want the public or competitors to know they use something so unsophisticated. Hence you might wonder how I can state that large corporations do use the EOQ formula. Let’s just say that I have good sources of information that I feel can be relied upon. The Variables of the EOQ Problem
Let us assume that we are interested in optimal inventory policies for widgets. The EOQ formula uses four variables. They are:
D:
Q:
C:
h:
The demand for widgets in quantity per unit time. Demand can be thought of as a rate. The order quantity. This is the variable we want to optimize. All the other variables are fixed quantities.
The order cost. This is the flat fee charged for making any order and is independent of Q.
Holding costs per widget per unit time. If we store x widgets for one unit of time, it costs us x@h.
The EOQ problem can be summarized as determining the order quantity Q, that balances the order cost C and the holding costs h to minimize total costs. The
James M. Cargal
Mathematics Department
Troy University – Montgomery Campus
A basic problem for businesses and manufacturers is, when ordering supplies, to determine what quantity of a given item to order. A great deal of literature has dealt with this problem
(unfortunately many of the best books on the subject are out of print). Many formulas and algorithms have been created. Of these the simplest formula is the most used: The EOQ (economic order quantity) or Lot Size formula. The EOQ formula has been independently discovered many times in the last eighty years. We will see that the EOQ formula is simplistic and uses several unrealistic assumptions. This raises the question, which we will address: given that it is so unrealistic, why does the formula work so well? Indeed, despite the many more sophisticated formulas and algorithms available, even large corporations use the EOQ formula. In general, large corporations that use the EOQ formula do not want the public or competitors to know they use something so unsophisticated. Hence you might wonder how I can state that large corporations do use the EOQ formula. Let’s just say that I have good sources of information that I feel can be relied upon. The Variables of the EOQ Problem
Let us assume that we are interested in optimal inventory policies for widgets. The EOQ formula uses four variables. They are:
D:
Q:
C:
h:
The demand for widgets in quantity per unit time. Demand can be thought of as a rate. The order quantity. This is the variable we want to optimize. All the other variables are fixed quantities.
The order cost. This is the flat fee charged for making any order and is independent of Q.
Holding costs per widget per unit time. If we store x widgets for one unit of time, it costs us x@h.
The EOQ problem can be summarized as determining the order quantity Q, that balances the order cost C and the holding costs h to minimize total costs. The