Supplement E - Special Inventory Models. Special Inventory Models Production quantity Demand during production interval Maximum inventory Production and.

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Presentation transcript:

Supplement E - Special Inventory Models

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

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

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

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

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

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

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) DQDQ Q p – d 2 p Example E.1

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, –

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 = $ $ Example E.1

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) ELS D Example E.1

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

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 = ELS p Example E.1

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 = 25.6, or 26 days Example E.1

Special Inventory Models Economic Production Lot Size Figure E.2

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

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

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

Special Inventory Models Quantity Discounts Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ = 77 units EOQ = 76 unitsEOQ = 75 units Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 Example E.2

Special Inventory Models Quantity Discounts EOQ = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ = 76 unitsEOQ = 75 units C = (H) + (S) + PD Q2Q2 DQDQ Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 Example E.2

Special Inventory Models Quantity Discounts EOQ = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ = 76 unitsEOQ = 75 units C 75 = [(0.25)($60.00)] + ($45) + $60.00(936) Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 Example E.2 C 75 = $57,284

Special Inventory Models Quantity Discounts EOQ = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ = 76 unitsEOQ = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 C 300 = [(0.25)($58.80)] + ($45) + $58.80(936)

Special Inventory Models Quantity Discounts EOQ = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ = 76 unitsEOQ = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 C 300 = $57,382 Example E.2

Special Inventory Models Quantity Discounts EOQ = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ = 76 unitsEOQ = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 C 300 = $57,382 C 500 = [(0.25)($57.00)] + ($45) + $57.00(936) Example E.2

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

Special Inventory Models Quantity Discounts EOQ = 77 units Annual demand = 936 units Ordering cost = $45 Holding cost = 25% of unit price EOQ = 76 unitsEOQ = 75 units C 75 = $57,284 Order QuantityPrice per Unit 0 – 299$ – 499$ or more$57.00 C 300 = $57,382 C 500 = $56,999 Example E.2

Special Inventory Models Figure E.4

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 = pQ Example E.3

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 = pQ Example E.3

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

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) Example E.3

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

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

Special Inventory Models Figure E.5

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 30 = Example E.3

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

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 Expected payoff 30 =$195 Example E.3

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 Expected Payoff Figure E.6

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 Expected Payoff Figure E.6