Introduction to Operations Research - VTK Gent

1 Introduction to Operations ResearchANSWERST ransportation, Assignment, and Transshipment ProblemsProf. dr. E-H. RezendeAmaralExercise 1 Optimize using the stepping stone algorithm.(MODI Modified Distribution Method)Exercise 1xij: units produced in month ito meet the demand of month jBalanced Transportation Problem:JFMD ummySupplyRow PenaltyJ40042044000305F425420440001020M4 20415410001520 Demand0000 Column Penaltyx5xxExercise 1 Vogel s method:Exercise 1 JFMD ummySupplyRow PenaltyJ40042025440000305F25425420254400 01020M254204154105001520 Demand0000 Column Penaltyx5xxJ M: +440 -410 + 415 -420 = 25J D: +0 -0 + 420 -420 = 0F J: +425 -400 + 420 -420 = 25F M: +440 -410 + 415 -420 = 25M J: +420 -415 + 420 -400 = 25M D: +0 -0 + 420 -415 = 5 Stepping stone.

2 All indices 0 Solution is optimalExercise 1 JFMD ummySupplyRow PenaltyJ40042044000305F425420440001020M4 20415410001520 Demand0000 Column Penaltyx5xxTransportation Simplex (MODI):( Iij) = cij= cij ui vjExercise 2 Answer: -200 word processing files should be stored on the hard disk-100 word processing files in the computer memory-100 packaged programs on tape-100 data files on 3 Exercise 3 Hungarian Method:Exercise 3 Hungarian Method:-1+1 Exercise 3 Hungarian Method:Exercise 3 Hungarian Method:Exercise 3 Hungarian Method -Two solutionsExercise 3 Hungarian Method -Two solutionsExercises 5 + 6 Exercises 5 + 6557337 Total cost: 98 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 73-1#; 4-2#; 5-3#; 1-4*; 6-5#; 7-6#; 2-7*#starts in NY; * starts in ChicagoExercise 7+2+5+3+5+5+3+23-1#; 4-2#; 5-3#; 1-4*; 6-5#; 7-6#; 2-7*Exercise 8 Exercise 81P1S2P2S3P3 SSupply1220011352- - 2233353- - - - 3335 DUMMY- 0- 0- 05 Demand201515202515xi-jk: units produced in month ito meet the demand of month jfrom customer type ki {1,2,3,D}j {1,2,3}k {P,S}Exercise 10 Exercise 10 Exercise 10 Extra Exercis