Economic Order Quantity (EOQ)
EOQ is the ideal optimal quantity an organization should purchase/acquire to minimize the costs associated to inventory such as holding costs, shortage costs, as well as order costs.
Where:
- D = Annual demand (units)
- S = Ordering cost per order
- H = Holding cost per unit per year
What is EOQ? Understanding Economic Order Quantity
Economic Order Quantity (EOQ) is a fundamental inventory management model that determines the optimal order quantity with the goal of minimizing the total inventory costs. The EOQ formula helps organizations find the balance between ordering costs (the cost to place and receive an order) and holding costs (the cost to store inventory).
The economic order quantity formula was developed by Ford W. Harris in the 1910's and has since become a cornerstone of inventory management theory. It's based on several key assumptions:
- Demand is known, constant, and continuous
- Lead time is known and constant
- Receipt of inventory is instantaneous and complete
- Quantity discounts are not available (in the basic model)
- Ordering and holding costs are variable
- Stockouts can be completely avoided
Source: Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135-136, 152.
How to Use This EOQ Calculator
Our EOQ calculator supports multiple calculation methods to address different inventory scenarios. Follow these steps the optimum order quantity:
- Select Calculation Method: Choose from Basic EOQ, Quantity Discount, Production Order, or Backordering models
- Enter Demand Data: Input your annual demand in units
- Enter Cost Parameters: Provide ordering cost, holding cost, and other relevant cost information
- Calculate: Click the calculate button to see your optimal order quantity and associated costs
The calculator will provide calculated results including the optimal order quantity, order cycle time, number of orders per year, and minimized total inventory costs.
Calculation Method
Select the EOQ variation you want to calculate:
Basic EOQ Model
The standard EOQ model minimizes total inventory costs without considering discounts or backorders.
EOQ with Quantity Discounts
Calculate EOQ when parts/materials/stock suppliers offer price discounts for larger order quantities.
Production Order Quantity
Calculate optimal order quantity when items are produced internally rather than ordered.
EOQ with Planned Backorders
Calculate optimal order quantity when backorders are allowed and planned.
Calculation Results
Optimal Order Quantity (EOQ)
Orders per Year
Order Cycle (Days)
Total Annual Cost
EOQ Formula with Example
Let's examine the economic order quantity formula with a practical example:
Example: A company has the following inventory parameters:
- Annual demand (D): 10,000 units
- Ordering cost (S): $50 per order
- Holding cost (H): $2.50 per unit per year
Using the EOQ formula:
Therefore, the optimal order quantity is approximately 633 units. This would result in about 15.81 orders per year (10,000 / 632.46) and an order cycle of approximately 23.12 days (365 / 15.81).
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Frequently Asked Questions about EOQ
The basic EOQ formula is: EOQ = √(2DS/H), where:
- D = Annual demand in units
- S = Ordering cost per order
- H = Holding cost per unit per year
This formula calculates the optimal order quantity that minimizes total inventory costs.
The EOQ model has several limitations:
- Assumes constant, known demand
- Assumes constant ordering and holding costs
- Assumes instantaneous replenishment
- Doesn't account for quantity discounts in the basic model
- Assumes no stockouts are allowed
- May not account for real-world constraints like storage limitations
Despite these limitations, EOQ remains a valuable starting point for inventory analysis.
Use the EOQ with quantity discounts model when:
- Suppliers offer price reductions for larger orders
- The savings from lower unit prices may outweigh increased holding costs
- You need to evaluate multiple price breaks to find the truly optimal order quantity
This model calculates the EOQ for each price break and determines which quantity results in the lowest total cost (including purchase cost).
The production order quantity (POQ) model differs from basic EOQ in several ways:
- Items are produced internally rather than ordered from suppliers
- Replenishment occurs gradually over time rather than instantaneously
- Uses production rate instead of order quantity
- Considers the relationship between production rate and demand rate
- Setup costs replace ordering costs
The POQ model is more appropriate for manufacturing environments where production occurs in batches.
In practical terms, the EOQ meaning (also called the optimal order quantity or economic lot size) shows the order quantity that:
- Minimizes the sum of ordering and holding costs
- Helps maintain optimal inventory levels
- Balances the cost of ordering too frequently versus holding too much inventory
- Provides a benchmark for evaluating order quantities
While the exact EOQ may not always be practical to implement (due to actual package sizes, weight restrictions, etc.), it shows a target for inventory optimization efforts.
Key EOQ Terminology and Definitions
| Term | Definition | Symbol |
|---|---|---|
| Economic Order Quantity | The optimal order quantity that minimizes total inventory costs | EOQ or Q* |
| Annual Demand | The total number of units required per year | D |
| Ordering Cost | The fixed cost associated with placing and receiving an order | S |
| Holding Cost | The cost to store one unit of inventory for one year | H |
| Unit Cost | The purchase price per unit of inventory | C |
| Total Inventory Cost | The sum of ordering, holding, and purchase costs | TIC |
| Reorder Point | The inventory level at which a new order should be placed | ROP |
| Lead Time | The time between placing an order and receiving it | L |
Bibliography and Further Reading
- Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135-136, 152.
- Wilson, R. H. (1934). A scientific routine for stock control. Harvard Business Review, 13(1), 116-128.
- Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory Management and Production Planning and Scheduling. John Wiley & Sons.
- Nahmias, S. (2005). Production and Operations Analysis. McGraw-Hill/Irwin.
- Heizer, J., Render, B., & Munson, C. (2020). Operations Management: Sustainability and Supply Chain Management. Pearson.
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