Transcript (EOQ) with Quantity Discounts

Economic Order Quantity (EOQ)
with Quantity Discounts
Prepared by:
Robbie Harmon
Brigham Young University
November 28, 2005
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Outline
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What is EOQ?
When do I use it?
Definition of EOQ components
How does it work?
Introducing Quantity Discounts
Are there any limitations?
Real World Example
Practice
Summary
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What is EOQ?
• EOQ = mathematical device for arriving at
the purchase quantity of an item that will
minimize the cost equation below
total cost = holding costs + ordering costs
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So…What does that mean?
Basically, EOQ helps you identify the most
economical way to replenish your inventory
by showing you the best order quantity.
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When do I use it?
• Suppose you are responsible for ordering
inventory. You have the following information.
• It costs $5 to hold one widget in inventory for a year
• It costs $100 to place an order for widgets, regardless of size
• Customers demand 2,500 widgets every year
(Sales are distributed evenly throughout the year)
How large should your orders be to minimize total cost?
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How large should your orders be?
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If your orders are too large, you’ll have excess inventory and high holding
costs
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If your orders are too small, you will have to place more orders to meet
demand, leading to high ordering costs
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Order Size
Holding Costs
Ordering Costs
Too LARGE
High
Low
Too SMALL
Low
High
EOQ helps you find the balance!!!
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EOQ
Cost
Holding Cost
Ordering Cost
Total Cost
Order Quantity
EOQ is the quantity where Holding cost = Ordering cost
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Definition of EOQ Components
H = annual holding cost for one unit of inventory
S = cost of placing an order, regardless of size
P = price per unit
d = demand per period
D = annual demand
L = lead time
Q = Order quantity (this is what we are solving for)
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How does it work?
• Total annual holding cost = (Q/2)H
• Total annual ordering cost = (D/Q)S
• EOQ:
– Set (Q/2)H = (D/Q)S and solve for Q
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Solve for Q algebraically
• (Q/2)H = (D/Q)S
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• Q = 2DS/H
• Q = square root of (2DS/H) = EOQ
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When should we place an order for
Q units?
• SS = safety stock
• Reorder point = ROP = d L + SS
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Introducing Quantity Discounts
What are quantity discounts?
Example:
Order Size
1 - 100
101 - 200
201 - 300
Price per unit
$20
$18
$16
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EOQ with Quantity Discounts
• Minimize the following equation:
– Total cost = holding costs + ordering costs + item costs
(Total cost = (Q/2)H + (D/Q)S + DP)
• This is done in 2 steps
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2 Steps
1.
Calculate EOQ. If this amount can be purchased at the
lowest price, you have found the quantity that minimizes
the equation. If not, proceed to step 2.
2.
Compare total cost at the EOQ quantity with total costs
at each price break above the EOQ.
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Limitations of this basic model
1. H and S are often estimated imprecisely
2. Ordering costs and demand rates vary
throughout the year
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Real World example
• 1974 Report to Congress by the
Comptroller General of the U.S.
– “Proper Use of the Economic Order Quantity
Principle Can Lead to More Savings”
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Practice
• Suppose you are responsible for ordering inventory. You
have the following information.
• It costs $5 to hold one widget in inventory for a year
• It costs $100 to place an order for widgets, regardless of size
• Customers demand 2,500 widgets every year
(Sales are distributed evenly throughout the year)
• What is EOQ?
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EOQ
$3,000
$2,500
Cost
$2,000
Holding Cost
$1,500
Ordering Cost
Total Cost
$1,000
$500
$0
100
150
200
250
300
350
400
450
500
Order Quantity
EOQ = 316
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Practice continued…
• Now suppose the following quantity discounts are
available.
Order Size
1 - 200
201 - 350
351 - 500
Price per unit
$20
$18
$16
• What amount should be purchased?
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Summary
• Understanding EOQ and quantity discounts
can result in substantial savings!
• Review
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Review
• What is EOQ?
• What 2 steps should be taken when
considering quantity discounts?
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Reading List
Bogner, Michael. “Quantity Discounts / Economic Order Quantity.”
http://www.dau.mil/pubs/pm/pmpdf02/Sept_Oct/BOGSE-0C2.pdf
Bozarth, Cecil C., & Handfield, Robert B. Introduction to Operations and Supply
Chain Management. Upper Saddle River, NJ: Pearson Prentice Hall, 2005
Bragg, Steven M. Inventory Best Practices. Hoboken, NJ: John Wiley & Sons,
Inc., 2004
Ozcan, Yasar A. Quantitative Methods in Health Care Management. San
Francisco, CA: Jossey-Bass, 2005 (pp. 259 -267)
Report to the Congress by the Comptroller General of the United States. “Proper
Use of the Economic Order Quantity Principle Can Lead to More Savings”:
United States General Accounting Office, 1974 (pp. 1-10)
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Reading List
Schreibfeder, Jon. “Effective Replenishment Parameters.” Microsoft. Microsoft
Business Solutions. http://download.microsoft.com/download/d/6/9/d69de816aecb-4869-a920-2b5afccd7589/eimwp4_replenish.pdf
Toomey, John W. Inventory Management: Principles, Concepts, and Techniques.
Norwell, MA: Kluwer Academic Publishers, 2000 (pp. 61-72)
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