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1 Economic Order Quantity (EOQ) with Quantity Discounts Prepared by: Robbie Harmon Brigham Young University November 28, 2005

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2 Outline 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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3 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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4 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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5 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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6 How large should your orders be? If your orders are too large, youll have excess inventory and high holding costs If your orders are too small, you will have to place more orders to meet demand, leading to high ordering costs Order SizeHolding CostsOrdering Costs Too LARGEHighLow Too SMALLLowHigh EOQ helps you find the balance!!!

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7 EOQ is the quantity where Holding cost = Ordering cost

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8 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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9 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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10 Solve for Q algebraically (Q/2)H = (D/Q)S Q 2 = 2DS/H Q = square root of (2DS/H) = EOQ

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11 When should we place an order for Q units? SS = safety stock Reorder point = ROP = d L + SS

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12 Introducing Quantity Discounts What are quantity discounts? Example: Order Size Price per unit$20$18$16

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13 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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14 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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15 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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16 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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17 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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18 EOQ = 316

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19 Practice continued… Now suppose the following quantity discounts are available. Order Size Price per unit$20$18$16 What amount should be purchased?

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20 Summary Understanding EOQ and quantity discounts can result in substantial savings! Review

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21 Review What is EOQ? What 2 steps should be taken when considering quantity discounts?

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22 Reading List Bogner, Michael. Quantity Discounts / Economic Order Quantity. 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 ) 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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23 Reading List Schreibfeder, Jon. Effective Replenishment Parameters. Microsoft. Microsoft Business Solutions. aecb-4869-a920-2b5afccd7589/eimwp4_replenish.pdfhttp://download.microsoft.com/download/d/6/9/d69de816- aecb-4869-a920-2b5afccd7589/eimwp4_replenish.pdf Toomey, John W. Inventory Management: Principles, Concepts, and Techniques. Norwell, MA: Kluwer Academic Publishers, 2000 (pp )

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