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Economic Order Quantity (EOQ) with Quantity Discounts

Economic Order Quantity (EOQ) with Quantity Discounts. Prepared by: Robbie Harmon Brigham Young University November 28, 2005. Outline. What is EOQ? When do I use it? Definition of EOQ components How does it work? Introducing Quantity Discounts Are there any limitations?

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Economic Order Quantity (EOQ) with Quantity Discounts

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

  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

  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

  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.

  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?

  6. How large should your orders be? • If your orders are too large, you’ll 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 • EOQ helps you find the balance!!!

  7. EOQ is the quantity where Holding cost = Ordering cost

  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)

  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

  10. Solve for Q algebraically • (Q/2)H = (D/Q)S • Q2 = 2DS/H • Q = square root of (2DS/H) = EOQ

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

  12. Introducing Quantity Discounts What are quantity discounts? Example:

  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

  14. 2 Steps • 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. • Compare total cost at the EOQ quantity with total costs at each price break above the EOQ.

  15. Limitations of this basic model • H and S are often estimated imprecisely • Ordering costs and demand rates vary throughout the year

  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”

  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?

  18. EOQ = 316

  19. Practice continued… • Now suppose the following quantity discounts are available. • What amount should be purchased?

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

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

  22. 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)

  23. Reading List Schreibfeder, Jon. “Effective Replenishment Parameters.” Microsoft. Microsoft Business Solutions. http://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. 61-72)

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