1. Supplement E - Special Inventory Models

2. 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

3. 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 I max = (p – d) = Q ( ) QpQp p – d p

4. 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 C = (H) + (S) I max 2 DQDQ

5. 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 C = ( ) + (S) DQDQ Q p – d 2 p

6. 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

7. 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

8. 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) DQDQ Q p – d 2 p Example E.1

9. 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) 10,500 4873.4 4873.4 190 – 30 2 190

10. 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 = $430.91 + $430.91 Example E.1

11. 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) ELS D Example E.1

12. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 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 Example E.1

13. 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 = ELS p Example E.1

14. 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 = 25.6, or 26 days Example E.1

15. Special Inventory Models Economic Production Lot Size Figure E.2

16. 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

17. 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 EOQ 57.00 = 2(936)(45) 0.25(57.00)

18. 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

19. 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 unitsEOQ 60.00 = 75 units Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2

20. 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 unitsEOQ 60.00 = 75 units C = (H) + (S) + PD Q2Q2 DQDQ Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2

21. 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 unitsEOQ 60.00 = 75 units C 75 = [(0.25)($60.00)] + ($45) + $60.00(936) 75 2 936 75 Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 Example E.2 C 75 = $57,284

22. 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 unitsEOQ 60.00 = 75 units C 75 = $57,284 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) 300 2 936 300

23. 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 unitsEOQ 60.00 = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 C 300 = $57,382 Example E.2

24. 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 unitsEOQ 60.00 = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 C 300 = $57,382 C 500 = [(0.25)($57.00)] + ($45) + $57.00(936) 500 2 936 500 Example E.2

25. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 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 unitsEOQ 60.00 = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 C 300 = $57,382 C 500 = $56,999 Example E.2

26. 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 unitsEOQ 60.00 = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$60.00 300 – 499$58.80 500 or more$57.00 C 300 = $57,382 C 500 = $56,999 Example E.2

27. Special Inventory Models Figure E.4

28. 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 20 30 40 50 D Q1020304050 For Q ≤ D Payoff = pQ Example E.3

29. 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 = pQ Example E.3

30. 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

31. 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) Example E.3

32. 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

33. 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

34. Special Inventory Models Figure E.5

35. 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 Expected payoff 30 = Example E.3

36. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 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 Expected payoff 30 =0.2($0) + 0.3($150) + 0.3($300) + 0.1($300) + 0.1($300) Example E.3

37. 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 Expected payoff 30 =$195 Example E.3

38. 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$100 2050200200200200170 300150300300300195 40–50100250400400175 50–10050200350500140 D Q1020304050Expected Payoff Figure E.6

39. 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$100 2050200200200200170 300150300300300195 40–50100250400400175 50–10050200350500140 D Q1020304050Expected Payoff Figure E.6