1. Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Inventory Management Operations Management - 5 th Edition Chapter 12 Roberta Russell & Bernard W. Taylor, III

2. Copyright 2006 John Wiley & Sons, Inc.12-2 Lecture Outline   Elements of Inventory Management Types of inventory Inventory costs ABC classification   Inventory Control Systems   Economic Order Quantity Models   Reorder Point

3. Copyright 2006 John Wiley & Sons, Inc.12-3 What Is Inventory?   Stock of items kept to meet future demand   Importance of inventory management   Purpose of inventory management how many units to order when to order

4. Copyright 2006 John Wiley & Sons, Inc.12-4 Types of Inventory   Raw materials   Purchased parts and supplies   Work-in-process (partially completed) products (WIP)   Items being transported   Tools and equipment

5. Copyright 2006 John Wiley & Sons, Inc.12-5 Ch 12 - 4 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Types of Inventory (Purpose)  Cycle stock  Safety stock  Anticipation inventory  Pipeline inventory

6. Copyright 2006 John Wiley & Sons, Inc.12-6 Two Forms of Demand (Two Types of Items)  Dependent  Demand for items used to produce final products   Tires stored at a Goodyear plant are an example of a dependent demand item  Independent  Demand for items used by external customers   Cars, appliances, computers, and houses are examples of independent demand inventory

7. Copyright 2006 John Wiley & Sons, Inc.12-7 Inventory Costs  Carrying cost  cost of holding an item in inventory  Ordering cost  cost of replenishing inventory  Shortage cost  temporary or permanent loss of sales when demand cannot be met

8. Copyright 2006 John Wiley & Sons, Inc.12-8 Inventory Placement  Special items (make-to-order) (make-to-order)  Standard items (make-to-stock) (make-to-stock)

9. Copyright 2006 John Wiley & Sons, Inc.12-9 Ch 12 - 8 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e ABC Classification  The purpose  The process  The classifications

10. Copyright 2006 John Wiley & Sons, Inc.12-10 ABC Classification  Class A 5 – 20 % of units 5 – 20 % of units 70 – 80 % of value 70 – 80 % of value  Class B 30 % of units 30 % of units 15 % of value 15 % of value  Class C 50 – 60 % of units 50 – 60 % of units 5 – 10 % of value 5 – 10 % of value

11. Copyright 2006 John Wiley & Sons, Inc.12-11 ABC Classification: Example 1$ 6090 235040 330130 48060 530100 620180 710170 832050 951060 1020120 PARTUNIT COSTANNUAL USAGE

12. Copyright 2006 John Wiley & Sons, Inc.12-12 ABC Classification: Example (cont.) Example 10.1 1$ 6090 235040 330130 48060 530100 620180 710170 832050 951060 1020120 PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE 9$30,60035.96.06.0 816,00018.75.011.0 214,00016.44.015.0 15,4006.39.024.0 44,8005.66.030.0 33,9004.610.040.0 63,6004.218.058.0 53,0003.513.071.0 102,4002.812.083.0 71,7002.017.0100.0 $85,400 AB C % OF TOTAL CLASSITEMSVALUEQUANTITY A9, 8, 271.015.0 B1, 4, 316.525.0 C6, 5, 10, 712.560.0

13. Copyright 2006 John Wiley & Sons, Inc.12-13 Inventory Control Systems  Continuous system (fixed- order-quantity)  constant amount ordered when inventory declines to predetermined level  Periodic system (fixed-time- period)  order placed for variable amount after fixed passage of time

14. Copyright 2006 John Wiley & Sons, Inc.12-14 Economic Order Quantity (EOQ) Models   EOQ optimal order quantity that will minimize total inventory costs   Basic EOQ model

15. Copyright 2006 John Wiley & Sons, Inc.12-15 Assumptions of Basic EOQ Model  Demand is known with certainty and is constant over time  No shortages are allowed  Lead time for the receipt of orders is constant  Order quantity is received all at once

16. Copyright 2006 John Wiley & Sons, Inc.12-16 EOQ: Cost Trade-off Order Freq.Lot sizeAvg. Inv Order Freq.Lot sizeAvg. Inv Daily 105 Weekly 50 25 Monthly 200 100 Ordering Cost Carrying cost Ordering Cost Carrying cost

17. Copyright 2006 John Wiley & Sons, Inc.12-17 EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Total Cost Carrying Cost = CcQCcQ22CcQCcQ222 Slope = 0 Minimum total cost Optimal order Q opt Q opt Ordering Cost = CoDCoDQQCoDCoDQQQ

18. Copyright 2006 John Wiley & Sons, Inc.12-18 EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

19. Copyright 2006 John Wiley & Sons, Inc.12-19 EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 (150)(10,000)2,000(0.75)(2,000)2 TC min = $750 + $750 = $1,500 Orders per year =D/Q opt =10,000/2,000 =5 orders/year Order cycle time =311 days/(D/Q opt ) =311/5 =62.2 store days

20. Copyright 2006 John Wiley & Sons, Inc.12-20 Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0

21. Copyright 2006 John Wiley & Sons, Inc.12-21 Reorder Point Level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

22. Copyright 2006 John Wiley & Sons, Inc.12-22 Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 yards/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 yards

23. Copyright 2006 John Wiley & Sons, Inc.12-23 Safety Stocks  Safety stock  buffer added to on hand inventory during lead time  Stockout  an inventory shortage  Service level  probability that the inventory available during lead time will meet demand

24. Copyright 2006 John Wiley & Sons, Inc.12-24 Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

25. Copyright 2006 John Wiley & Sons, Inc.12-25 Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

26. Copyright 2006 John Wiley & Sons, Inc.12-26 Reorder Point With Variable Demand R = dL + z  d L where d=average daily demand L=lead time  d =the standard deviation of daily demand z=number of standard deviations corresponding to the service level probability z  d L=safety stock

27. Copyright 2006 John Wiley & Sons, Inc.12-27 Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L

28. Copyright 2006 John Wiley & Sons, Inc.12-28 Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d= 30 yards per day L= 10 days  d = 5 yards per day For a 95% service level, z = 1.65 R= dL + z  d L = 30(10) + (1.65)(5)( 10) = 326.1 yards Safety stock= z  d L = (1.65)(5)( 10) = 26.1 yards