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

2. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Production quantity Demand during production interval On-hand inventory Q Time p – d Figure E.1 Production and demand Demand only TBO

3. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Production quantity Demand during production interval Maximum inventory Production and demand Demand only TBO On-hand inventory Q Time I max p – d Figure E.1

4. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Production and demand Demand only TBO Production quantity Demand during production interval Maximum inventory On-hand inventory Q Time I max p – d Figure E.1 I max = (p – d) = Q ( ) QpQp p – d p

5. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Production and demand Demand only TBO Production quantity Demand during production interval Maximum inventory On-hand inventory Q Time I max p – d Figure E.1 C = (H) + (S) I max 2 DQDQ

6. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Production and demand Demand only TBO Production quantity Demand during production interval Maximum inventory On-hand inventory Q Time I max p – d Figure E.1 C = ( ) + (S) DQDQ Q p – d 2 p

7. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Production and demand Demand only TBO Production quantity Demand during production interval Maximum inventory On-hand inventory Q Time I max p – d Figure E.1 ELS = p p – d 2DS H

8. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = p p – d 2DS H Example E.1

9. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 190 190 – 30 2(10,500)($200)$0.21 Example E.1

10. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 190 190 – 30 2(10,500)($200)$0.21 Example E.1 ELS = 4873.4 barrels

11. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 4873.4 barrels C = ( ) (H) + (S) DQ Q p – d 2 p Example E.1

12. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 4873.4 barrels C = ( ) ($0.21) + ($200) 10,5004873.4 4873.4 190 – 30 2 190 2 190 Example E.1 C = $430.91 + $430.91 = $861.82

13. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 4873.4 barrels C = $861.82 TBO ELS = (350 days/year) ELSD Example E.1

14. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 4873.4 barrels C = $861.82 TBO ELS = (350 days/year) = 162.4, or 162 days 4873.410,500 Example E.1

15. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 4873.4 barrels C = $861.82 TBO ELS = 162.4, or 162 days Production time = ELSp Example E.1

16. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Economic Production Lot Size ELS = 4873.4 barrels C = $861.82 TBO ELS = 162.4, or 162 days Production time = 4873.4190 Example E.1 = 25.6, or 26 days

17. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. C for P = $4.00 C for P = $3.50 C for P = $3.00 PD for P = $4.00 PD for P = $3.50 PD for P = $3.00 Special Inventory Models Quantity Discounts EOQ 4.00 EOQ 3.50 EOQ 3.00 First price break Second price break Total cost (dollars) Purchase quantity (Q) 0100200300 Purchase quantity (Q) 0100200300 First price break Second price break (a) Total cost curves with purchased materials added (b) EOQs and price break quantities Figure E.3

18. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Quantity Discounts EOQ 57.00 = 2DS H Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2

19. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Quantity Discounts EOQ 57.00 = 2(936)(45)0.25(57.00) Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2 = 77 units

20. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Quantity Discounts EOQ 57.00 = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ 58.80 = 76 units Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2

21. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Quantity Discounts Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ 57.00 = 77 units EOQ 58.80 = 76 units Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2

22. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Quantity Discounts Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ 57.00 = 77 units EOQ 58.80 = 76 units EOQ 60.00 = 75 units Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2

23. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Quantity Discounts EOQ 57.00 = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ 58.80 = 76 units EOQ 60.00 = 75 units C = (H) + (S) + PD Q2DQ Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2

24. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models Quantity Discounts EOQ 57.00 = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ 58.80 = 76 units EOQ 60.00 = 75 units C 75 = [(0.25)($60.00)] + ($45) + $60.00(936) = $57,284 752 93675 Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 C 300 = [(0.25)($58.80)] + ($45) + $58.80(936) = $57,382 936300 3002 C 500 = [(0.25)($57.00)] + ($45) + $57.00(936) = $56,999 5002 936500

25. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 Example E.3

26. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 10 $100$100$100$100$100 20200200200200 30300300300 40400400 50 500 D Q1020304050 Example E.3 For Q = D Payoff = pQ For Q ≤ D Payoff = pQ

27. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 10 $100$100$100$100$100 20200200200200 30300300300 40400400 50 500 D Q1020304050 For Q > D Payoff = pD – I(Q – D) Example E.3

28. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 10 $100$100$100$100$100 20200200200200 30300300300 40400400 50 500 D Q1020304050 For Q > D Payoff = ($10)(30) – ($5)(40 – 30) – ($5)(40 – 30) Example E.3

29. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 10 $100$100$100$100$100 20200200200200 30300300300 40250400400 50 500 D Q1020304050 For Q > D Payoff = $250 Example E.3

30. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 10$100$100$100$100$100 2050200200200200 300150300300300 40–50100250400400 50–10050200350500 D Q1020304050 For Q > D Payoff = pD – I(Q – D) Example E.3

31. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 10$100$100$100$100$100 2050200200200200 300150300300300195 40–50100250400400 50–10050200350500 D Q1020304050Expected Payoff Example E.3 Expected payoff 30 =0.2($0) + 0.3($150) + 0.3($300) + 0.1($300) + 0.1($300) = $195

32. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Special Inventory Models One-Period Decisions Demand1020304050 Demand Probability0.20.30.30.10.1 Profit per ornament during season = $10 Loss per ornament after season = $5 10$100$100$100$100$100100 2050200200200200170 300150300300300195 40–50100250400400185 50–10050200350500160 D Q1020304050Expected Payoff Example E.3