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

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

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

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

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

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

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

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

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 = – 30 2(10,500)($200)$0.21 Example E.1

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 = – 30 2(10,500)($200)$0.21 Example E.1 ELS = barrels

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 = barrels C = ( ) (H) + (S) DQ Q p – d 2 p Example E.1

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 = barrels C = ( ) ($0.21) + ($200) 10, – Example E.1 C = $ $ = $861.82

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 = barrels C = $ TBO ELS = (350 days/year) ELSD Example E.1

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 = barrels C = $ TBO ELS = (350 days/year) = 162.4, or 162 days ,500 Example E.1

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 = barrels C = $ TBO ELS = 162.4, or 162 days Production time = ELSp Example E.1

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 = barrels C = $ TBO ELS = 162.4, or 162 days Production time = Example E.1 = 25.6, or 26 days

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) Purchase quantity (Q) First price break Second price break (a) Total cost curves with purchased materials added (b) EOQs and price break quantities Figure E.3

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

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

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

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 = $45 Holding cost = 25% of unit price EOQ = 77 units EOQ = 76 units Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 Example E.2

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 = $45 Holding cost = 25% of unit price EOQ = 77 units EOQ = 76 units EOQ = 75 units Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 Example E.2

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

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

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 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. 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$100$ D Q Example E.3 For Q = D Payoff = pQ For Q ≤ D Payoff = pQ

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 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$100$ 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. 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$100$ D Q For Q > D Payoff = ($10)(30) – ($5)(40 – 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. 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$100$ 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. 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$100$ – – 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. 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$100$ – – D Q Expected Payoff Example E.3 Expected payoff 30 =0.2($0) + 0.3($150) + 0.3($300) + 0.1($300) + 0.1($300) = $195

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 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$100$ – – D Q Expected Payoff Example E.3