SPECIAL INVENTORY MODELS

Transcription

1 Sulement D Part 3 Designing And Managing Suly hains SPEIAL INVENTORY MODELS PROBLEMS 1. ANSWER NOT YET SUPPLIED.. Dorothy s Pastries The following ayoff matrix was constructed, where 0.40Q if Q D Payoff 0.40D 0.30Q D if Q D D Q $0 $0 $0 150 ($10) $60 $60 00 ($5) $45 $80 Now we can comute the exected ayoff for each baking quantity Q. Order Quantity Exected Payoff (0) (0) + 0.5(0) = $ ( 10) (60) + 0.5(60) = $ ( 5) (45) + 0.5(80) = $36.5 Therefore, 150 astries should be baked each day. 3. National Printing omany The ayoff matrix is constructed, using = 6Q if Q D Payoff = = 6D 1.00 ( Q D) if Q D The following table comes from the One-Period Inventory Decision Solver in OM Exlorer. Demand Probability Payoff Table Demand Quantity oyright 010 Pearson Education, Inc. Publishing as Prentice all.

2 Secial Inventory Models SUPPLEMENT D 309 Weighted Payoffs The best order quantity is 5,000 units. Order Exected Quantity Payoff Greatest Exected Payoff Associated with Order Quantity Order quantity for an item Ste 1: alculate the EOQ at the lowest rice ($.00)...00,000 0 EOQ 447. or 447 units This solution is infeasible. We cannot buy 447 units at a rice of $.00 each. Therefore, we calculate the EOQ at the next lowest rice ($.5)...5,000 0 EOQ 41.6 or 4 units Ste : alculate total costs at the feasible EOQ and at higher discount quantities. S PD Q , $.5 $0 $.5,000 4 $94. $94.79 $4, $4, , $.00 1, 000 $0 $ $00.00 $40.00 $4, $4, The order quantity should be 1,000 units. 5. Mac-in-the-Box, Inc. Ste 1: alculate the EOQ at the lowest rice ($400): , EOQ or 106 scanners This solution is infeasible. We cannot buy 106 scanners at a rice of $400 each. Therefore, we calculate the EOQ at the next lowest rice ($500). oyright 010 Pearson Education, Inc. Publishing as Prentice all.

3 310 PART 3 Managing Suly hains , EOQ or scanners Ste : alculate total costs at the feasible EOQ and at higher discount quantities. S PD Q 1,00.16 $500 $300 $ $3,800 $3,800 $600, 000 $607, ,00.16 $400 $300 $ $4, $, $480, 000 $487, The order quantity should be scanners. 6. University Bookstore Ste 1: alculate the EOQ at the lowest rice ($3.5), EOQ 6.45, or 6 This solution is infeasible; we cannot buy 6 encils at $3.5 a iece. Therefore, we calculate the EOQ at the next lowest rice ($3.50)., EOQ 18.1, or 18 Ste : alculate total costs at the feasible EOQ and at higher discount quantities. S PD Q 18,001 18, $ $ $8, $10 $3.50,500 $8,979.1, 001,500, 001 $ $1.49 $8, $10 $3.5,500 $9,11.98 The best order quantity is 18 units. oyright 010 Pearson Education, Inc. Publishing as Prentice all.

4 Secial Inventory Models SUPPLEMENT D Pfisher. The EOQ at the lowest rice ($49.00) remains infeasible and the EOQ at the next lowest rice ($50.5) remains at 79 ackages. The total annual cost of buying disosable surgical ackages also remains at $5, er year. Now we calculate the annual cost associated with ordering 500 at a time: $47.80 $64 $ $,0 $6.7 $3, $5,874.7 The quantity discount is not sufficient to cause Pfisher to buy the larger order quantity. 8. Bucks Grande major-league baseball In this roblem we assume the annual demand is based on a 5-week year. Ste 1: alculate the EOQ at the lowest rice ($48.50): EOQ.75 or 40 bats This solution is infeasible. We cannot buy 40 bats at a rice of $48.50 each. Therefore we calculate the EOQ at the next lowest rice ($51.00): EOQ or bats Ste : alculate total costs at the feasible EOQ and at higher discount quantities: S PD Q $51.00 $70 $ $ $ $10, 608 $11, $48.50 $70 $ $1,36.96 $ $10, 088 $11, a. It is less costly on an annual basis to buy bats at a time. b. The total annual costs associated with buying bats at a time are $11, c. Yes, if the rice is reduced to $45 at an order quantity of 180 bats. The Quantity Discount Solver from OM Exlorer is used to find the solution. oyright 010 Pearson Education, Inc. Publishing as Prentice all.

5 31 PART 3 Managing Suly hains Min. Amount Req'd for Lot Sizes Price/Unit Price Point $ $ $ or more $45.00 Annual demand 08 Order cost $70 olding cost (% of Price) 38% Best order quantity 180 EOQ or Req'd Price Point Order for Price Point Inventory ost Order ost Purchase ost Total ost $ $ $ $11,3 $1,005 $51.00 $ $ $10,608 $11,359 $48.50 $1,37 $ $10,088 $11,516 $ $1,5 $80.89 $9,360 $10,980 Therefore, Bucks Grande should urchase 180 bats at a time. 9. Sud s Bottling omany ELS d , ,31, , , 13 cases 10. Share utter oyright 010 Pearson Education, Inc. Publishing as Prentice all.

6 Secial Inventory Models SUPPLEMENT D 313 a. ELS d 100, , , 13 knives b. Total annual cost Q d D S Q 1, , , 13 $1, $1, 414. $,88.44 ELS 1, 13 c. TBO 50 days year days D 100, 000 ELS 1, 13 d. Production time/lot days 11. Bold Vision Inc. ELS d , , , toner cartridges oyright 010 Pearson Education, Inc. Publishing as Prentice all.

7 314 PART 3 Managing Suly hains oyright 010 Pearson Education, Inc. Publishing as Prentice all.