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					Economic Order Quantity
Materials Management

By - Puneet Rane

Inventory

Precursor
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Inventory

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Role of Material Manager
Need For Inventory Control

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Economic Order Quantity
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The model was developed by F. W. Harris in 1915 R. H. Wilson is credited in-depth analysis of the model It gives optimal quantity to order that minimizes total variable costs required to order and hold inventory.

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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.

How to use EOQ in your organization
How much inventory should we order each month?

The EOQ tool can be used to model the amount of inventory that we should order each month.

The Balance
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Maximum Stock Level

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Economic Stock Level
Minimum Stock Level

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Focal Points
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Running of Plant

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Capital
Carrying Cost Ordering Cost

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How EOQ Works
The Principles Behind EOQ: The Total Cost Curve

&

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Cost Components
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Annual Usage/Demand Order Cost Carrying cost
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Interest Insurance Taxes Storage Costs & Maintenance Cost

How EOQ Works
The Principles Behind EOQ: The Holding Costs Keeping inventory on hand Interest Insurance Taxes Theft Obsolescence Storage Costs

How EOQ Works
The Principles Behind EOQ: The Holding Costs

Interest

Obsolescence

Storage

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

How EOQ Works
The Total Cost Formula

Total Cost = Purchase Cost + Order Cost + Holding Cost

How EOQ Works
The Total Cost Formula

This represents the unchanging fixed costs
P = Purchase cost per unit R = Forecasted monthly usage

How EOQ Works
The Total Cost Formula

This represents the variable order costs
P = Purchase cost per unit R = Forecasted monthly usage C = Cost per order event (not per unit) Q = The number of units ordered

How EOQ Works
The Total Cost Formula

This represents the variable 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

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:

How EOQ Works
The EOQ Formula The result of differentiation

The Economic Order Quantity

How EOQ Works
The EOQ Formula Review and Summary of the EOQ Formula

P = Purchase cost per unit R = Forecasted monthly usage C = Cost per order event (not per unit) F = Holding cost factor

How EOQ Works
The EOQ Formula Review and Summary of the EOQ Formula Here is the a graphic representation of the EOQ equation

Simple to calculate
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Total cost per period = inventory holding costs per period + order costs per period Cost = The Number of Orders Placed in the period x Order Costs

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Carrying Cost = Average Inventory Level x the Carrying Costs of 1 unit of Stock for one period

Simplifying Calculations
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Q = order quantity A = demand per time period (e.g. Annual Demand) S = Carrying / Holding Cost of 1 unit of Stock for one period P = Order Cost

Advantages
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The purpose of the EOQ model is to minimize the total costs of inventory. Shortages or Stock-outs do not occur, as delivery of the order is immediate.

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Assumptions of the Model
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Demand is known

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The lead time
The receipt of inventory is instantaneous Quantity discounts are not possible

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Economic Order Quantity

Production EOQ:
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Instead of instantaneous replenishment, we include the finite Production Rate R which leads to the following formula: (You can see, that production rate must be greater than demand rate, in order to fulfill the demand!) EOQ = sqrt ( 2 * A * P / (S*(1-A/R))

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Variations
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Quantity discount

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Spoilage or to Prevent obsolescence
Ratio of production to consumption Safety stock calculation

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Case

Stop n Slurp Convenience Store Annual Demand: 5200 Cases of Coca Cola Fixed Ordering Cost: 500 per order Cost Per Case: 100 Holding Cost: 20% of value of inventory per year Suppose EOQ assumptions hold (Constant demand, no lag/lead time, no shortages) How Much Coca Cola should Stop n Slurp Order?

Solution
EOQ Parameters:
Annual Usage = 5200 Order Cost = 500 Annual Carrying Cost = 20% of 100 = 20

Optimum Ordering Policy:
Q = sqrt(2 x 5200 x 500)/(20) = 509.9 ~ 510 Cases

Closing Comments
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EOQ is a tool, not a simple solution.

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EOQ is useful in determining optimal order quantity
Understand the equation and what you are trying to find Find accurate inputs for the equation

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Additional Resources on EOQ
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Materials Management an Integrated Approach – P. Gopalakrishnan Cost Accounting http://www.caam.rice.edu/~timredl/caam376/ http://www.findarticles.com/p/articles/mi_m0KAA/is_5_31/ ai_94771293 http://www.inventoryops.com/economic_order_quantity.htm http://www.pafis.shh.fi/~stecon02/afis/ws2/ http://en.wikipedia.org/wiki/Economic_order_quantity


				
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