1. Copyright 2006 John Wiley & Sons, Inc. Inventory Management

2. Copyright 2006 John Wiley & Sons, Inc. Lecture Outline   Elements of Inventory Management   Inventory Control Systems   Economic Order Quantity Models   Quantity Discounts   Reorder Point   Order Quantity for a Periodic Inventory System

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

4. Copyright 2006 John Wiley & Sons, Inc. 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 Two Forms of Demand  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

6. Copyright 2006 John Wiley & Sons, Inc.12-6 Inventory and Quality Management   Customers usually perceive quality service as availability of goods they want when they want them   Inventory must be sufficient to provide high-quality customer service in TQM

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 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

9. Copyright 2006 John Wiley & Sons, Inc. ABC Classification  Class A 5 – 15 % of units 5 – 15 % 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

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

11. Copyright 2006 John Wiley & Sons, Inc. 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

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

13. Copyright 2006 John Wiley & Sons, Inc. 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

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

15. Copyright 2006 John Wiley & Sons, Inc. 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

16. Copyright 2006 John Wiley & Sons, Inc. EOQ Cost Model TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

17. Copyright 2006 John Wiley & Sons, Inc. 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. 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

19. Copyright 2006 John Wiley & Sons, Inc. Production Quantity Model   An inventory system in which an order is received gradually, as inventory is simultaneously being depleted   AKA non-instantaneous receipt model assumption that Q is received all at once is relaxed   p - daily rate at which an order is received over time, a.k.a. production rate   d - daily rate at which inventory is demanded

20. Copyright 2006 John Wiley & Sons, Inc. Production Quantity Model (cont.) Q(1-d/p) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average

21. Copyright 2006 John Wiley & Sons, Inc. Production Quantity Model (cont.) p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - Qp dp Average inventory level = 1 - Q2 dp TC = + 1 - dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

22. Copyright 2006 John Wiley & Sons, Inc. Production Quantity Model: Example C c = $0.75 per yardC o = $150D = 10,000 yards d = 10,000/311 = 32.2 yards per dayp = 150 yards per day Q opt = = = 2,256.8 yards 2C o D C c 1 - dp 2(150)(10,000) 0.75 1 - 32.2150 TC = + 1 - = $1,329 dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = 15.05 days per order Qp2,256.8150

23. Copyright 2006 John Wiley & Sons, Inc. Production Quantity Model: Example (cont.) Number of production runs = = = 4.43 runs/year DQDQ 10,000 2,256.8 Maximum inventory level =Q 1 - = 2,256.8 1 - =1,772 yards dpdp 32.2 150

24. Copyright 2006 John Wiley & Sons, Inc. Quantity Discounts Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

25. Copyright 2006 John Wiley & Sons, Inc.12-25 Quantity Discount Model (cont.) Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 ) ORDER SIZE PRICE 0 - 99 $10 100 – 199 8 ( d 1 ) 200+ 6 ( d 2 )

26. Copyright 2006 John Wiley & Sons, Inc. Quantity Discount: Example QUANTITYPRICE 1 - 49$1,400 50 - 891,100 90+900 C o =$2,500 C c =$190 per computer D =200 Q opt = = = 72.5 PCs 2CoD2CoDCcCc2CoD2CoDCcCc2(2500)(200)190 TC = + + PD = $233,784 C o D Q opt C c Q opt 2 For Q = 72.5 TC = + + PD = $194,105 CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 For Q = 90

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

28. Copyright 2006 John Wiley & Sons, Inc. 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

29. Copyright 2006 John Wiley & Sons, Inc. 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

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

31. Copyright 2006 John Wiley & Sons, Inc.12-31 Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

32. Copyright 2006 John Wiley & Sons, Inc. 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

33. Copyright 2006 John Wiley & Sons, Inc.12-33 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

34. Copyright 2006 John Wiley & Sons, Inc. 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

35. Copyright 2006 John Wiley & Sons, Inc.12-35 Order Quantity for a Periodic Inventory System Q = d(t b + L) + z  d t b + L - I where d= average demand rate t b = the fixed time between orders L= lead time  d = standard deviation of demand z  d t b + L= safety stock z  d t b + L= safety stock I= inventory level

36. Copyright 2006 John Wiley & Sons, Inc.12-36 Fixed-Period Model with Variable Demand d= 6 bottles per day  d = 1.2 bottles t b = 60 days L= 5 days I= 8 bottles z= 1.65 (for a 95% service level) Q= d(t b + L) + z  d t b + L - I = (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8 = 397.96 bottles