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- 1. C - 1© 2011 Pearson Education, Inc. publishing as Prentice HallC Transportation ModelsPowerPoint presentation to accompanyHeizer and RenderOperations Management, 10ePrinciples of Operations Management, 8ePowerPoint slides by Jeff Heyl
- 2. C - 2© 2011 Pearson Education, Inc. publishing as Prentice HallOutline Transportation Modeling Developing an Initial Solution The Northwest-Corner Rule The Intuitive Lowest-Cost Method The Stepping-Stone Method Special Issues in Modeling Demand Not Equal to Supply Degeneracy
- 3. C - 3© 2011 Pearson Education, Inc. publishing as Prentice HallLearning ObjectivesWhen you complete this module youshould be able to:1. Develop an initial solution to atransportation models with thenorthwest-corner and intuitivelowest-cost methods2. Solve a problem with the stepping-stone method3. Balance a transportation problem4. Solve a problem with degeneracy
- 4. C - 4© 2011 Pearson Education, Inc. publishing as Prentice HallTransportation Modeling An interactive procedure that findsthe least costly means of movingproducts from a series of sourcesto a series of destinations Can be used tohelp resolvedistributionand locationdecisions
- 5. C - 5© 2011 Pearson Education, Inc. publishing as Prentice HallTransportation Modeling A special class of linearprogramming Need to know1. The origin points and the capacityor supply per period at each2. The destination points and thedemand per period at each3. The cost of shipping one unit fromeach origin to each destination
- 6. C - 6© 2011 Pearson Education, Inc. publishing as Prentice HallTransportation ProblemToFrom Albuquerque Boston ClevelandDes Moines $5 $4 $3Evansville $8 $4 $3Fort Lauderdale $9 $7 $5Table C.1
- 7. C - 7© 2011 Pearson Education, Inc. publishing as Prentice HallTransportation ProblemFort Lauderdale(300 unitscapacity)Albuquerque(300 unitsrequired)Des Moines(100 unitscapacity)Evansville(300 unitscapacity)Cleveland(200 unitsrequired)Boston(200 unitsrequired)Figure C.1
- 8. C - 8© 2011 Pearson Education, Inc. publishing as Prentice HallTransportation MatrixFromToAlbuquerque Boston ClevelandDes MoinesEvansvilleFort LauderdaleFactorycapacityWarehouserequirement300300300 200 200100700$5$5$4$4$3$3$9$8$7Cost of shipping 1 unit from FortLauderdale factory to Boston warehouseDes MoinescapacityconstraintCellrepresentinga possiblesource-to-destinationshippingassignment(Evansvilleto Cleveland)Total demandand total supplyClevelandwarehouse demandFigure C.2
- 9. C - 9© 2011 Pearson Education, Inc. publishing as Prentice HallNorthwest-Corner Rule Start in the upper left-hand cell (ornorthwest corner) of the table and allocateunits to shipping routes as follows:1. Exhaust the supply (factory capacity) of eachrow before moving down to the next row2. Exhaust the (warehouse) requirements ofeach column before moving to the nextcolumn3. Check to ensure that all supplies anddemands are met
- 10. C - 10© 2011 Pearson Education, Inc. publishing as Prentice HallNorthwest-Corner Rule1. Assign 100 tubs from Des Moines to Albuquerque(exhausting Des Moines’s supply)2. Assign 200 tubs from Evansville to Albuquerque(exhausting Albuquerque’s demand)3. Assign 100 tubs from Evansville to Boston(exhausting Evansville’s supply)4. Assign 100 tubs from Fort Lauderdale to Boston(exhausting Boston’s demand)5. Assign 200 tubs from Fort Lauderdale toCleveland (exhausting Cleveland’s demand andFort Lauderdale’s supply)
- 11. C - 11© 2011 Pearson Education, Inc. publishing as Prentice HallTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7FromNorthwest-Corner Rule100100100200200Figure C.3Means that the firm is shipping 100bathtubs from Fort Lauderdale to Boston
- 12. C - 12© 2011 Pearson Education, Inc. publishing as Prentice HallNorthwest-Corner RuleComputed Shipping CostTable C.2This is a feasible solutionbut not necessarily thelowest cost alternativeRouteFrom To Tubs Shipped Cost per Unit Total CostD A 100 $5 $ 500E A 200 8 1,600E B 100 4 400F B 100 7 700F C 200 5 $1,000Total: $4,200
- 13. C - 13© 2011 Pearson Education, Inc. publishing as Prentice HallIntuitive Lowest-Cost Method1. Identify the cell with the lowest cost2. Allocate as many units as possible tothat cell without exceeding supply ordemand; then cross out the row orcolumn (or both) that is exhausted bythis assignment3. Find the cell with the lowest cost fromthe remaining cells4. Repeat steps 2 and 3 until all unitshave been allocated
- 14. C - 14© 2011 Pearson Education, Inc. publishing as Prentice HallIntuitive Lowest-Cost MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100First, $3 is the lowest cost cell so ship 100 units fromDes Moines to Cleveland and cross off the first row asDes Moines is satisfiedFigure C.4
- 15. C - 15© 2011 Pearson Education, Inc. publishing as Prentice HallIntuitive Lowest-Cost MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100Second, $3 is again the lowest cost cell so ship 100 unitsfrom Evansville to Cleveland and cross off column C asCleveland is satisfiedFigure C.4
- 16. C - 16© 2011 Pearson Education, Inc. publishing as Prentice HallIntuitive Lowest-Cost MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100200Third, $4 is the lowest cost cell so ship 200 units fromEvansville to Boston and cross off column B and row Eas Evansville and Boston are satisfiedFigure C.4
- 17. C - 17© 2011 Pearson Education, Inc. publishing as Prentice HallIntuitive Lowest-Cost MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100200300Finally, ship 300 units from Albuquerque to FortLauderdale as this is the only remaining cell to completethe allocationsFigure C.4
- 18. C - 18© 2011 Pearson Education, Inc. publishing as Prentice HallIntuitive Lowest-Cost MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100200300Total Cost = $3(100) + $3(100) + $4(200) + $9(300)= $4,100Figure C.4
- 19. C - 19© 2011 Pearson Education, Inc. publishing as Prentice HallIntuitive Lowest-Cost MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100200300Total Cost = $3(100) + $3(100) + $4(200) + $9(300)= $4,100Figure C.4This is a feasible solution,and an improvement overthe previous solution, butnot necessarily the lowestcost alternative
- 20. C - 20© 2011 Pearson Education, Inc. publishing as Prentice HallStepping-Stone Method1. Select any unused square to evaluate2. Beginning at this square, trace aclosed path back to the original squarevia squares that are currently beingused3. Beginning with a plus (+) sign at theunused corner, place alternate minusand plus signs at each corner of thepath just traced
- 21. C - 21© 2011 Pearson Education, Inc. publishing as Prentice HallStepping-Stone Method4. Calculate an improvement index byfirst adding the unit-cost figures foundin each square containing a plus signand subtracting the unit costs in eachsquare containing a minus sign5. Repeat steps 1 though 4 until you havecalculated an improvement index forall unused squares. If all indices are ≥0, you have reached an optimalsolution.
- 22. C - 22© 2011 Pearson Education, Inc. publishing as Prentice Hall$5$8 $4$4+ -+-Stepping-Stone MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100100200200+--+1100201 9999100200Figure C.5Des Moines-Boston index= $4 - $5 + $8 - $4= +$3
- 23. C - 23© 2011 Pearson Education, Inc. publishing as Prentice HallStepping-Stone MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100100200200Figure C.6Start+-+-+-Des Moines-Cleveland index= $3 - $5 + $8 - $4 + $7 - $5 = +$4
- 24. C - 24© 2011 Pearson Education, Inc. publishing as Prentice HallStepping-Stone MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100100200200Evansville-Cleveland index= $3 - $4 + $7 - $5 = +$1(Closed path = EC - EB + FB - FC)Fort Lauderdale-Albuquerque index= $9 - $7 + $4 - $8 = -$1(Closed path = FA - FB + EB - EA)
- 25. C - 25© 2011 Pearson Education, Inc. publishing as Prentice HallStepping-Stone Method1. If an improvement is possible, choosethe route (unused square) with thelargest negative improvement index2. On the closed path for that route,select the smallest number found inthe squares containing minus signs3. Add this number to all squares on theclosed path with plus signs andsubtract it from all squares with aminus sign
- 26. C - 26© 2011 Pearson Education, Inc. publishing as Prentice HallStepping-Stone MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100100100200200Figure C.7++--1. Add 100 units on route FA2. Subtract 100 from routes FB3. Add 100 to route EB4. Subtract 100 from route EA
- 27. C - 27© 2011 Pearson Education, Inc. publishing as Prentice HallStepping-Stone MethodTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300100700$5$5$4$4$3$3$9$8$7From100200100100200Figure C.8Total Cost = $5(100) + $8(100) + $4(200) + $9(100) + $5(200)= $4,000
- 28. C - 28© 2011 Pearson Education, Inc. publishing as Prentice HallSpecial Issues in Modeling Demand not equal to supply Called an unbalanced problem Common situation in the real world Resolved by introducing dummysources or dummy destinations asnecessary with cost coefficients ofzero
- 29. C - 29© 2011 Pearson Education, Inc. publishing as Prentice HallSpecial Issues in ModelingFigure C.9NewDes MoinescapacityTo (A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouserequirement 300 200 200Factorycapacity300300250850$5$5$4$4$3$3$9$8$7From5020025050150Dummy150000150Total Cost = 250($5) + 50($8) + 200($4) + 50($3) + 150($5) + 150(0)= $3,350
- 30. C - 30© 2011 Pearson Education, Inc. publishing as Prentice HallSpecial Issues in Modeling Degeneracy To use the stepping-stonemethodology, the number ofoccupied squares in any solutionmust be equal to the number ofrows in the table plus the numberof columns minus 1 If a solution does not satisfy thisrule it is called degenerate
- 31. C - 31© 2011 Pearson Education, Inc. publishing as Prentice HallTo Customer1Customer2Customer3Warehouse 1Warehouse 2Warehouse 3Customerdemand 100 100 100Warehousesupply12080100300$8$7$2$9$6$9$7$10$10FromSpecial Issues in Modeling0 1001008020Figure C.10Initial solution is degeneratePlace a zero quantity in an unused square andproceed computing improvement indices
- 32. C - 32© 2011 Pearson Education, Inc. publishing as Prentice HallAll rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise, without the prior written permission of the publisher.Printed in the United States of America.

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