1. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Inventory Management Chapter 15

2. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Inventory Costs  Interest or Opportunity Cost  Storage and Handling Costs  Taxes, Insurance, and Shrinkage

3. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Inventory Costs  Customer Service  Ordering Cost  Setup Cost  Labor and Equipment Utilization  Transportation Costs  Payments to Suppliers

4. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Types of Inventory Cycle Inventory Average cycle inventory = Q + 0 2 Safety Stock Inventory Anticipation Inventory Pipeline Inventory Pipeline inventory = D L = dL

5. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Types of Inventory Cycle inventory=Q/2 =280/2 =140 drills Example 15.1 Pipeline inventory=D L =dL =(70 drills/week)(3 weeks) =210 drills

6. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. ABC Analysis A processes of diving the items into three classes, according to their annual dollar usage. Thumb rule: Class A: About 20% of items- Top 80% of $ usage Class B: About 30% of items - Next 15% of $ usage Class C: About 50% of items – Bottom 5% of $ usage

7. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. ABC Analysis 102030405060708090100 Percentage of items Percentage of dollar value 100 100 — 90 90 — 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 30 — 20 20 — 10 10 — 0 0 — Figure 15.2 Class C Class A Class B

8. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. ABC Analysis – Problem #5 ItemUnit costDemand$ Usage A10440.2580 3,220 D20580.75120 9,690 X10410.00150 1,500 U40440.50150 6,075 L20560.7050 3,035 S10480.2020 1,604 X20580.1520 1,603 L10420.05100 2,005 28,732

9. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. ABC Analysis – Problem #5 Item Unit costDemand$ Usage % of $ usageCum. %Class D20580.75120 9,69033.7% U40440.50150 6,07521.1%54.9% A10440.2580 3,22011.2%66.1% L20560.7050 3,03510.6%76.6% L10420.05100 2,0057.0%83.6% S10480.2020 1,6045.6%89.2% X20580.1520 1,6035.6%94.8% X10410.00150 1,5005.2%100.0% 28,732

10. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. How Much? When! When!

11. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity

12. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity 1.Demand rate is constant 2.No constraints on lot size 3.Only relevant costs are holding and ordering/setup 4.Decisions for items are independent from other items 5.No uncertainty in lead time or supply Assumptions

13. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity Figure 15.3 Inventory depletion (demand rate) Receive order 1 cycle On-hand inventory (units) Time Q AveragecycleinventoryQ—2

14. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity Annual cost (dollars) Lot Size (Q) Figure 15.4 Holding cost (HC) Ordering cost (OC) Total cost = HC + OC

15. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Example 15.2 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Economic Order Quantity

16. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Example 15.2 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Economic Order Quantity Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $2925 + $108 = $3033

17. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $2925 + $108 = $3033 CurrentcostCurrentQ Example 15.2 Economic Order Quantity

18. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $2925 + $108 = $3033 CurrentcostCurrentQ Example 15.2 Economic Order Quantity

19. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 468 S = $45 Q = 468 units CurrentcostCurrentQ Example 15.2 Economic Order Quantity C = $3510 + $90 = $3600

20. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = EOQ C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H Example 15.3

21. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H Example 15.3

22. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H Example 15.3 C = $562 + $562 = $1124

23. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Example 15.3 Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H C = $562 + $562 = $1124 Lowestcost Best Q (EOQ)

24. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Example 15.2 Economic Order Quantity Example 15.3 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H C = $562 + $562 = $1124 Lowestcost Best Q (EOQ)

25. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lowestcost Best Q (EOQ) Example 15.2 Economic Order Quantity Example 15.3 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H C = $562 + $562 = $1124 Time between orders TBO EOQ = = 75/936 = 0.080 year EOQ D TBO EOQ = (75/936)(12) = 0.96 months TBO EOQ = (75/936)(52) = 4.17 weeks TBO EOQ = (75/936)(365) = 29.25 days

26. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity Effects of change EOQ = 2DS H Change in demand rate (D) Change in setup cost (S) Change in holding cost (H) Error in estimating D, H, and S

27. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. How Much? When! When!

28. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. How much to order? Two systems Continuous review (Q) system (aka: Reorder point (ROP) system) Place order when IP = ROP Periodic review (P) system Place an order at regular intervals of time

29. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Continuous Review Soup Figure 15.7 Time On-hand inventory R TBO L TBO L TBO L Orderreceived Orderreceived Q OH OrderplacedIPOrderreceived Q OH Orderplaced IP Orderreceived OrderplacedIPQ OH

30. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time On-hand inventory R TBO L TBO L TBO L Orderreceived Q OH Orderplaced IP Orderreceived Q OH OrderplacedIPOrderreceived Q OH Orderplaced IP Orderreceived Continuous Review Soup Example 15.4 Chicken Soup R= Average demand during lead time = (25)(4) = 100 cases IP= OH + SR – BO = 10 + 200 – 0 = 210 cases

31. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Uncertain Demand Figure 15.8 Time On-hand inventory TBO 1 TBO 2 TBO 3 L1L1L1L1 L2L2L2L2 L3L3L3L3 R Orderreceived Q Orderplaced Orderplaced OrderreceivedIPIP Q Orderplaced Q Orderreceived Orderreceived OH

32. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Reorder Point / Safety Stock Figure 15.9 Average demand during lead time Cycle-service level = 85% Probability of stockout (1.0 – 0.85 = 0.15) zLzLzLzL R

33. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Reorder Point / Safety Stock Example 15.5 Average demand during lead time Cycle-service level = 85% Probability of stockout (1.0 – 0.85 = 0.15) zLzLzLzL R Safety Stock/R Safety stock= z  L = 2.33(22) = 51.3 = 51 boxes Reorder point= ADDLT + SS = 250 + 51 = 301 boxes

34. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions Figure 15.10  t = 15 + 75 Demand for week 1  t = 26 225 Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15

35. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions Example 15.6  t = 15 + 75 Demand for week 1  t = 26 225 Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15 t = 1 week d = 18 L = 2  L =  t L = 5 2 = 7.1 Safety stock= z  L = 1.28(7.1) = 9.1 or 9 units Reorder point= dL + Safety stock = 2(18) + 9 = 45 units Bird feeder Lead Time Distribution

36. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions Example 15.6  t = 15 + 75 Demand for week 1  t = 26 225 Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15 Reorder point= 2(18) + 9 = 45 units t = 1 week d = 18 L = 2 Bird feeder Lead Time Distribution C = ($15) + ($45) + 9($15) 75 2 936 75 C = $562.50 + $561.60 + $135 = $1259.10

37. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Periodic Review Systems Figure 15.12 PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH

38. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Periodic Review Systems Example 15.7 T = 400BO = 5 OH = 0SR = 0 IP = 0 + 0 – 5 = –5 sets Q = 400 – (–5) = 405 sets TV Set - P System IP = OH + SR – BO Q t = T - IP t

39. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Example 15.8 Periodic Review Systems Bird feeder— Calculating P and T T= Average demand during the protection interval + Safety stock = d (P + L) + z  P + L = (18 units/week)(16 weeks) + 1.28(12 units) = 123 units EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units  t = 18 units L = 2 weeks cycle/service level = 90% P = (52) = (52) = 4.2 or 4 weeks EOQ D 75 936  P+L =    P + L = 5 6 = 12 units

40. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Example 15.8 Periodic Review Systems Bird feeder— Calculating P and T EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units  t = 18 units L = 2 weeks cycle/service level = 90% P = 4 weeks T = 123 units C = ($15) + ($45) + 15($15) 4(18) 2 936 4(18) C = $540 + $585 + $225 = $1350

41. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Comparison of Q and P Systems P Systems Q Systems  Convenient to administer  Orders may be combined  IP only required at review  Individual review frequencies  Possible quantity discounts  Lower, less-expensive safety stocks