Economic Order Quantity and Economic Production Quantity
Models for Inventory Management

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Professor Hossein Arsham   

Inventory control is concerned with minimizing the total cost of inventory. In the U.K. the term often used is stock control. The three main factors in inventory control decision making process are:

  • The cost of holding the stock (e.g., based on the interest rate).
  • The cost of placing an order (e.g., for row material stocks) or the set-up cost of production.
  • The cost of shortage, i.e., what is lost if the stock is insufficient to meet all demand.
The third element is the most difficult to measure and is often handled by establishing a "service level" policy, e. g, certain percentage of demand will be met from stock without delay.

The ABC Classification The ABC classification system is to grouping items according to annual sales volume, in an attempt to identify the small number of items that will account for most of the sales volume and that are the most important ones to control for effective inventory management.

Reorder Point: The inventory level R in which an order is placed where R = D.L, D = demand rate (demand rate period (day, week, etc), and L = lead time.

Safety Stock: Remaining inventory between the times that an order is placed and when new stock is received. If there are not enough inventories then a shortage may occur.

Safety stock is a hedge against running out of inventory. It is an extra inventory to take care on unexpected events. It is often called buffer stock. The absence of inventory is called a shortage.

Quantity Discount Model Calculation Steps:

  • Compute EOQ for each quantity discount price.
  • Is computed EOQ in the discount range?
  • If not, use lowest cost quantity in the discount range.
  • Compute Total Cost for EOQ or lowest cost quantity in discount range.
  • Select quantity with the lowest Total Cost, including the cost of the items purchased.

The following This JavaScript compute the optimal values for the decision variables based on currently available information about the above factors.

Enter the needed information, and then click the Calculate button.

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.


  1. The Classical Model
  2. Shortages Permitted Model
  3. Production and Consumption Model
  4. Production and Consumption with Shortages Model
  5. EOQ with Shortages and Lead Time
  6. The ABC Classification
  7. Inventory Control with Uncertain Demand


The Classical Model

Demand rate: x
Ordering cost: C1
Holding cost: C2
Optimal Ordering Is: Q*
Optimal Cycle Is: T*
Number of Orders Is: n*
Total Cost Is: TC


Shortages Permitted Model

Demand rate: x
Ordering cost: C1
Holding cost: C2
Shortage cost: C3
Backorder cost: C4
Optimal Ordering Is: Q*
Optimal Shortage Is: S*
Total Cost Is: TC
Shortage Period Is: T2
Period per Cycle Is: T


Production and Consumption Model

Production rate: K
Demand rate: x
Holding cost: C2
Set-up cost: C1
Optimal Run Size Is: Q*
Production Cycle Is: T 1*
Optimal Cycle Is: T*
Cost per Cycle Is: TC

Production and Consumption with Shortages Model

Production rate: K
Demand rate: x
Setup cost: C1
Holding cost: C2
Backorder cost: C4
Optimal Production Is: q*
Optimal Inventory Is: Q*
Optimal Shortage Is: P*
Total Cost Is: TC
Period per Cycle Is: T


EOQ with Shortages and Lead Time

I: Base Economic Order Quantity
Total Demand
Ordering Cost
Holding Cost/unit/year
Unit Price
Average Periodic Ordering Intervals
Total Number of Orders
Total Cost
II: EOQ with Shortages and Lead Time
Estimated Lead Time in Days
Shortage Cost/unit/year
Level for Reorder Point
Maximum Inventory Level
Total Cost
Longest Delay Time in Days

For Technical Details, Back to:
Decision Making in Economics and Finance

Kindly email your comments to:
Professor Hossein Arsham


Decision Tools in Economics & Finance

Probabilistic Modeling


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Professor Hossein Arsham   

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