1. Inventory Control Models 6 To accompany Quantitative Analysis for Management, Twelfth Edition, by Render, Stair, Hanna and Hale Power Point slides created by Jeff Heyl Copyright ©2015 Pearson Education, Inc.

2. After completing this chapter, students will be able to: LEARNING OBJECTIVES Copyright ©2015 Pearson Education, Inc.6 – 2 1.Use the economic order quantity (EOQ) to determine how much to order.

3. 6.1Introduction 6.2Importance of Inventory Control 6.3Inventory Decisions 6.4Economic Order Quantity: Determining How Much to Order CHAPTER OUTLINE Copyright ©2015 Pearson Education, Inc.6 – 3

4. Introduction Inventory is an expensive and important asset Any stored resource used to satisfy a current or future need –Raw materials –Work-in-process –Finished goods Balance high and low inventory levels to minimize costs Copyright ©2015 Pearson Education, Inc.6 – 4

5. Introduction Lower inventory levels –Can reduce costs –May result in stockouts and dissatisfied customers All organizations have some type of inventory planning and control system Determine what goods/services are produced or purchased Copyright ©2015 Pearson Education, Inc.6 – 5

6. Introduction Copyright ©2015 Pearson Education, Inc.6 – 6 FIGURE 6.1 – Inventory Planning and Control Planning on what to stock and how to get it Feedback metrics to revise plans and forecasts Forecasting parts/product demand Controlling inventory levels

7. Importance of Inventory Control Five uses of inventory 1.The decoupling function 2.Storing resources 3.Irregular supply and demand 4.Quantity discounts 5.Avoiding stockouts and shortages Decouple manufacturing processes –A buffer between stages –Reduces delays and improves efficiency Copyright ©2015 Pearson Education, Inc.6 – 7

8. Importance of Inventory Control Storing resources –Seasonal products stored to satisfy off-season demand –Materials stored as raw materials, work-in-process, or finished goods –Labor can be stored as a component of partially completed subassemblies Irregular supply and demand –Not constant over time –Inventory used to buffer the variability Copyright ©2015 Pearson Education, Inc.6 – 8

9. Importance of Inventory Control Quantity discounts –Lower prices may be available for larger orders –Higher storage and holding costs –More cash invested Avoiding stockouts and shortages –Stockouts may result in lost sales –Dissatisfied customers may choose to buy from another supplier –Loss of goodwill Copyright ©2015 Pearson Education, Inc.6 – 9

10. Inventory Decisions Two fundamental decisions 1.How much to order 2.When to order Major objective is to minimize total inventory costs 1.Cost of the items (purchase or material cost) 2.Cost of ordering 3.Cost of carrying, or holding, inventory 4.Cost of stockouts Copyright ©2015 Pearson Education, Inc.6 – 10

11. Inventory Cost Factors Copyright ©2015 Pearson Education, Inc.6 – 11 ORDERING COST FACTORSCARRYING COST FACTORS Developing and sending purchase ordersCost of capital Processing and inspecting incoming inventoryTaxes Bill payingInsurance Inventory inquiriesSpoilage Utilities, phone bills, and so on, for the purchasing department Theft Salaries and wages for the purchasing department employees Obsolescence Supplies such as forms and paper for the purchasing department Salaries and wages for warehouse employees Utilities and building costs for the warehouse Supplies such as forms and paper for the warehouse TABLE 6.1

12. Inventory Cost Factors Ordering costs are generally independent of order quantity –Many involve personnel time –The amount of work is the same no matter the size of the order Holding costs generally vary with the amount of inventory or order size –Labor, space, and other costs increase with order size –Cost of items purchased can vary with quantity discounts Copyright ©2015 Pearson Education, Inc.6 – 12

13. Economic Order Quantity Economic order quantity (EOQ) model –One of the oldest and most commonly known inventory control techniques –Easy to use –A number of important assumptions Objective is to minimize total cost of inventory Copyright ©2015 Pearson Education, Inc.6 – 13

14. Economic Order Quantity Assumptions: –Demand is known and constant –Lead time is known and constant –Receipt of inventory is instantaneous –Purchase cost per unit is constant –The only variable costs are ordering cost and holding or carrying cost These are constant throughout the year –Orders are placed so that stockouts or shortages are avoided completely Copyright ©2015 Pearson Education, Inc.6 – 14

15. Inventory Usage Over Time Copyright ©2015 Pearson Education, Inc.6 – 15 Time Inventory Level Minimum Inventory 0 Order Quantity = Q = Maximum Inventory Level FIGURE 6.2

16. Inventory Costs in the EOQ Situation Annual ordering cost is number of orders per year times cost of placing each order Annual carrying cost is the average inventory times carrying cost per unit per year Copyright ©2015 Pearson Education, Inc.6 – 16 INVENTORY LEVEL DAYBEGINNINGENDINGAVERAGE April 1 (order received)1089 April 2867 April 3645 April 4423 April 5201 Maximum level April 1 = 10 units Total of daily averages = 9 + 7 + 5 + 3 + 1 = 25 Number of days = 5 Average inventory level = 25/5 = 5 units TABLE 6.2

17. Inventory Costs in the EOQ Situation Copyright ©2015 Pearson Education, Inc.6 – 17 Annual ordering   cost Number of orders placed per year Ordering cost per order  × Ordering cost per order Annual demand Number of units in each order Q= number of pieces to order EOQ= Q* = optimal number of pieces to order D= annual demand in units for the inventory item C o = ordering cost of each order C h = holding or carrying cost per unit per year

18. Inventory Costs in the EOQ Situation Copyright ©2015 Pearson Education, Inc.6 – 18 Annual holding   cost Average inventory Carrying cost per unit per year Q= number of pieces to order EOQ= Q* = optimal number of pieces to order D= annual demand in units for the inventory item C o = ordering cost of each order C h = holding or carrying cost per unit per year

19. Inventory Costs in the EOQ Situation Copyright ©2015 Pearson Education, Inc.6 – 19 Minimum Total Cost Optimal Order Quantity Curve for Total Cost of Carrying and Ordering Carrying Cost Curve Ordering Cost Curve Cost Order Quantity FIGURE 6.3 – Total Cost as a Function of Order Quantity

20. Finding the EOQ When the EOQ assumptions are met, total cost is minimized when Annual ordering cost = Annual holding cost Copyright ©2015 Pearson Education, Inc.6 – 20 Solving for Q Thus

21. Finding the EOQ Equation summary Copyright ©2015 Pearson Education, Inc.6 – 21

22. Sumco Pump Company Sells pump housings to other companies Reduce inventory costs by finding optimal order quantity Annual demand = 1,000 units Ordering cost = $10 per order Average carrying cost per unit per year = $0.50 Copyright ©2015 Pearson Education, Inc.6 – 22

23. Sumco Pump Company Total cost Copyright ©2015 Pearson Education, Inc.6 – 23 Number of orders per year = (D/Q) = 5 Average inventory (Q/2) = 100

24. Sumco Pump Company Copyright ©2015 Pearson Education, Inc.6 – 24 $100 Q = 200 Curve for Total Cost of Carrying and Ordering Carrying Cost Curve Ordering Cost Curve Cost Order Quantity $50

25. Sensitivity Analysis with the EOQ Model The EOQ model assumes all values are know and fixed over time Values are estimated or may change Sensitivity analysis determines the effects of these changes Because the EOQ is a square root, changes in the inputs result in relatively small changes in the order quantity Copyright ©2015 Pearson Education, Inc.6 – 25

26. Sensitivity Analysis with the EOQ Model Sumco Pump example Copyright ©2015 Pearson Education, Inc.6 – 26 Increase C o to $40 In general, the EOQ changes by the square root of the change to any of the inputs