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Special Inventory Models

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

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

3 Special Inventory Models
On-hand inventory Time Figure E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

4 Special Inventory Models
Production quantity Q On-hand inventory Time Figure E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

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

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

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

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

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

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

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

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

14 Special Inventory Models
Economic Production Lot Size To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

16 Special Inventory Models
Economic Production Lot Size 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 ELS = p p – d 2DS H Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

17 Special Inventory Models
Economic Production Lot Size 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 2(10,500)($200) $0.21 190 190 – 30 ELS = Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

18 Special Inventory Models
Economic Production Lot Size 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 2(10,500)($200) $0.21 190 190 – 30 ELS = Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

19 Special Inventory Models
Economic Production Lot Size 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 2(10,500)($200) $0.21 190 190 – 30 ELS = Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

20 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

21 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = ( )(H) (S) Q p – d p D Q Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

22 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = ( ) ($0.21) ($200) – 30 10,500 4873.4 Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

23 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = $ $430.91 Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

24 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = $861.82 Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

25 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = $861.82 ELS D TBOELS = (350 days/year) Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

26 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = $861.82 4873.4 10,500 TBOELS = (350 days/year) Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

27 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = $861.82 TBOELS = , or 162 days Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

28 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels ELS p C = $861.82 Production time = TBOELS = , or 162 days Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

29 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels 4873.4 190 C = $861.82 Production time = TBOELS = , or 162 days Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

30 Special Inventory Models
Economic Production Lot Size 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 ELS = barrels C = $861.82 Production time = 25.6, or 26 days TBOELS = , or 162 days Example E.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

31 Special Inventory Models
Economic Production Lot Size Figure E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

33 Special Inventory Models
Quantity Discounts Figure E.3 Total cost (dollars) Purchase quantity (Q) (a) Total cost curves with purchased materials added To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

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

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

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

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

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

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

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

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

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

44 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price 2DS H EOQ57.00 = Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

45 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price 2(936)(45) 0.25(57.00) EOQ57.00 = Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

46 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price 2(936)(45) 0.25(57.00) EOQ57.00 = Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

47 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

48 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

49 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

50 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

51 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

52 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

53 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

54 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

55 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

56 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units C = (H) (S) + PD Q 2 D Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

57 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units 75 2 936 75 C75 = [(0.25)($60.00)] ($45) + $60.00(936) Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

58 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units C75 = $57,284 Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

59 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units C75 = $57,284 300 2 936 300 C300 = [(0.25)($58.80)] ($45) + $58.80(936) Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

60 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units C75 = $57,284 C300 = $57,382 Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

61 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units C75 = $57,284 C300 = $57,382 500 2 936 500 C500 = [(0.25)($57.00)] ($45) + $57.00(936) Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

62 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units C75 = $57,284 C300 = $57,382 C300 = $56,999 Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

63 Special Inventory Models
Quantity Discounts Order Quantity Price per Unit 0 – 299 $60.00 300 – 499 $58.80 500 or more $57.00 Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units C75 = $57,284 C300 = $57,382 C300 = $56,999 Example E.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

64 Special Inventory Models
Figure E.4 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

65 Special Inventory Models
One-Period Decisions To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

67 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 10 20 30 40 50 D Q For Q = D Payoff = pQ Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

68 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 10 20 30 40 50 D Q For Q = D Payoff = ($10)(10) Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

69 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 10 $100 20 30 40 50 D Q For Q = D Payoff = $100 Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

70 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 10 $100 $100 $100 $100 $100 20 30 40 50 D Q For Q ≤ D Payoff = pQ Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

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

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

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

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

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

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

78 Special Inventory Models
Figure E.5 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

79 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = 10 $100 $100 $100 $100 $100 40 – 50 – D Q Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

80 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = 0.2($0) 10 $100 $100 $100 $100 $100 40 – 50 – D Q Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

81 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = 0.2($0) + 0.3($150) 10 $100 $100 $100 $100 $100 40 – 50 – D Q Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

82 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = 0.2($0) + 0.3($150) + 0.3($300) 10 $100 $100 $100 $100 $100 40 – 50 – D Q Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

83 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = 0.2($0) + 0.3($150) + 0.3($300) + 0.1($300) 10 $100 $100 $100 $100 $100 40 – 50 – D Q Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

84 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = 0.2($0) + 0.3($150) + 0.3($300) + 0.1($300) + 0.1($300) 10 $100 $100 $100 $100 $100 40 – 50 – D Q Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

85 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = $195 10 $100 $100 $100 $100 $100 40 – 50 – D Q Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

86 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 Expected payoff30 = $195 D Q Expected Payoff 10 $100 $100 $100 $100 $100 40 – 50 – Example E.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

87 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 D Q Expected Payoff 10 $100 $100 $100 $100 $100 $100 40 – 50 – Figure E.6 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

88 Special Inventory Models
One-Period Decisions Demand Demand Probability Profit per ornament during season = $10 Loss per ornament after season = $5 D Q Expected Payoff 10 $100 $100 $100 $100 $100 $100 40 – 50 – Figure E.6 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.


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