1. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter 6 Inventory Control Models

2. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Learning Objectives Students will be able to: Understand the importance of inventory control. Use the economic order quantity (EOQ) to determine how much to order. Compute the reorder point (ROP) in determining when to order more inventory. Perform sensitivity analysis on basic inventory quantities.

3. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Learning Objectives continued Students will be able to: Determine the economic order quantity without the instantaneous receipt assumption. Handle inventory problems that allow quantity discounts or have planned shortages. Understand the use of safety stock with known and unknown stockout costs. Perform ABC analysis.

4. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline 6.1 Introduction 6.2 Importance of Inventory Control 6.3 Inventory Decision 6.4 Economic Order Quantity(EOQ): Determining How Much to Order 6.5 Reorder Point: Determining When to Order

5. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline - continued 6.6 EOQ without the Instantaneous Receipt Assumption 6.7 Quantity Discount Models 6.8 Use of Safety Stock 6.9 ABC Analysis 6.10 Sensitivity Analysis

6. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Inventory as an Important Asset Inventory can be the most expensive and the most important asset for an organization Other Assets 60% Inventory 40% Inventory as a percentage of total assets

7. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Inventory Planning and Control - Fig. 6.1 Planning on what Inventory to Stock and How to Acquire It Forecasting Parts/Product Demand Controlling Inventory Levels Feedback Measurements to Revise Plans and Forecasts

8. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Inventory Process SuppliersCustomers Finished Goods Raw Materials Work in Process Fabrication and Assembly Inventory Storage Inventory Processing

9. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Importance of Inventory Control Five Functions of Inventory Decoupling Storing resources Adapting to irregular supply and demand Enabling the company to take advantage of quantity discounts Avoiding stockouts and shortages

10. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Inventory Decisions How much to order When to order wish to minimize total inventory cost

11. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Inventory Costs Cost of the items Cost of ordering Cost of carrying, or holding inventory Cost of safety stock Cost of stockouts

12. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-12 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Ordering Costs Developing and sending purchase orders Processing and inspecting incoming inventory Bill paying Inventory inquiries Utilities, phone bills, etc., - purchasing department. Salaries/wages - purchasing department employees Supplies (e.g., forms and paper) - purchasing department

13. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Carrying Costs Cost of capital Taxes Insurance Spoilage Theft Obsolescence Salaries/wages - warehouse employees Utilities/building costs - warehouse Supplies (e.g., forms, paper) - warehouse

14. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-14 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Inventory Usage Over Time - Fig. 6.2

15. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Costs as Functions of Order Quantity - Fig. 6.3 Annual Cost Order QuantityQ*Q* Total Cost Curve Carrying (holding) Cost Curve Ordering (set-up) Cost Curve Minimum Cost

16. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Costs as Functions of Order Quantity - Fig. 6.3 Order Cost Carry Cost Total Cost Optimal Quantity Minimum Cost

17. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-17 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Steps in Finding the Optimum Inventory Develop an expression for the ordering cost. Develop and expression for the carrying cost. Set the ordering cost equal to the carrying cost. Solve this equation for the optimum desired.

18. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 EOQ : Basic Assumptions Demand is known and constant Lead time is known and constant Receipt of inventory is instantaneous Quantity discounts are not possible The only variable costs are the cost of setting up or placing an order, and the cost of holding or storing inventory over time Stockouts can be completely avoided if orders are placed at the appropriate time

19. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Annual ordering cost: Annual holding or carrying cost: Total inventory cost: Developing the EOQ

20. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-20 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 EOQ h C 2DC * Q  Per Unit Carrying Cost: Percentage Carrying Cost: IP DC Q *    0

21. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Inputs and Outputs of the EOQ Model EOQ Models Input ValuesOutput Values Annual Demand (D) Ordering Cost (C o ) Carrying Cost (C h ) Lead Time (L) Demand Per Day (d) Economic Order Quantity (EOQ) Reorder Point (ROP)

22. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-22 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Reorder Point (ROP) Curve - Fig. 6.4 ROP = (Demand per day) x (Lead time for a new order, in days) = d x L Inventory Level (Units) Q*Q* ROP (Units) Slope = Units/Day = d Lead Time (Days) L

23. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Inventory Control and the Production Process Inventory Level Demand Portion of Cycle Demand Portion of Cycle Maximum Inventory Level Time Production Portion of Cycle

24. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-24 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Production Quantity EOQ Annual Carrying Cost: Annual Ordering Cost: Setup Cost: Ordering Costs:

25. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-25 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Production Quantity EOQ

26. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-26 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Quantity Discount Models - Fig. 6.6

27. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-27 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Quantity Discount Steps 1. Calculate Q for each discount 2. Adjust Q upward if quantity is too low for discount 3. Compute total cost for each discount 4. Select Q with the the lowest total cost

28. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-28 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Use of Safety Stock Fig. 6.7 Inventory on Hand Inventory on Hand Stockout Time Stockout is avoided Time Safety Stock

29. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-29 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Use of Safety Stock Known stockout costs: Given probability of demand, find total cost for each safety stock alternative Unknown stockout costs: Set service level; use normal distribution

30. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-30 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Service Level versus Carrying Costs

31. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-31 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Summary of ABC Analysis Table 6.6 Group A Items - Critical Group B Items - Important Group C Items - Not That Important Inventory Group Dollar Usage (%) Inventory Items (%) Are Complex Quantitative Control Techniques Used? ABCABC 70 20 10 20 70 Yes In some cases No

32. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-32 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 ABC Inventory Analysis 100 90 80 70 60 50 40 30 20 10 0 Percent of Inventory Items Percent of Annual Dollar Usage 1 2 3 4 5 6 7 8 9 10 A Items B Items C Items

33. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-33 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 ABC Inventory Policies Greater expenditure on supplier development for A items than for B items or C items Tighter physical control on A items than on B items or on C items Greater expenditure on forecasting A items than on B items or on C items