RELATÓRIO LINDO P3

Prévia do material em texto

Relatório do Lindo para Alguns Modelos da Lista
Questão 1: Problema de Fluxo de Custo Mínimo Genérico
No lindo:
min 3x17+20x12+9x37+30x34+40x72+10x75+2x54+10x57+4x56+4x65+8x62
s.t.
x12+x17<=50000
x37+x34<=60000
-x12-x72-x62<=-90000
-x34-x54<=-20000
x54+x56+x57-x75-x65=0
x65+x62-x56=0
x75+x72-x17-x37-x57=0
end
Solução:
LP OPTIMUM FOUND AT STEP 8
 OBJECTIVE FUNCTION VALUE
 1) 2660000.
 VARIABLE VALUE REDUCED COST
 X17 0.000000 5.000000
 X12 50000.000000 0.000000
 X37 60000.000000 0.000000
 X34 0.000000 9.000000
 X72 0.000000 18.000000
 X75 60000.000000 0.000000
 X54 20000.000000 0.000000
 X57 0.000000 20.000000
 X56 40000.000000 0.000000
 X65 0.000000 8.000000
 X62 40000.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 11.000000
 3) 0.000000 0.000000
 4) 0.000000 31.000000
 5) 0.000000 21.000000
 6) 0.000000 19.000000
 7) 0.000000 23.000000
 8) 0.000000 9.000000
 NO. ITERATIONS= 8
No lindo:
min x14 + 0.3x15 + 0.8x24 +4.3x25 + 2x34 + 4.6x35 + 0.5x45 + 3x56 +2.1x57 + 1.9x58 + 6x48 + 4.5x47 +0.2x46
st
x14 + x15 <= 900
x24 + x25 <= 1400
x34 + x35 <= 1000
-x46 -x56 <= -1100
-x47 -x57 <= -1000
-x48-x58 <= -1200
x57 +x58 +x56 -x45 -x15 -x25 -x35 = 0
x45 +x46 +x47 +x48 -x14 -x24 -x34 = 0
x14>=0
x15>=0
x24>=0
x25>=0
x34>=0
x35>=0
x45>=0
x56>=0
x57>=0
x58>=0
x48>=0
x47>=0
x46>=0
end
Solução:
 LP OPTIMUM FOUND AT STEP 10
 OBJECTIVE FUNCTION VALUE
 1) 8640.000
 VARIABLE VALUE REDUCED COST
 X14 0.000000 1.200000
 X15 900.000000 0.000000
 X24 1400.000000 0.000000
 X25 0.000000 3.000000
 X34 1000.000000 0.000000
 X35 0.000000 2.100000
 X45 1300.000000 0.000000
 X56 0.000000 3.300000
 X57 1000.000000 0.000000
 X58 1200.000000 0.000000
 X48 0.000000 3.600000
 X47 0.000000 1.900000
 X46 1100.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 2.200000
 3) 0.000000 1.200000
 4) 0.000000 0.000000
 5) 0.000000 2.200000
 6) 0.000000 4.600000
 7) 0.000000 4.400000
 8) 0.000000 2.500000
 9) 0.000000 2.000000
 10) 0.000000 0.000000
 11) 900.000000 0.000000
 12) 1400.000000 0.000000
 13) 0.000000 0.000000
 14) 1000.000000 0.000000
 15) 0.000000 0.000000
 16) 1300.000000 0.000000
 17) 0.000000 0.000000
 18) 1000.000000 0.000000
 19) 1200.000000 0.000000
 20) 0.000000 0.000000
 21) 0.000000 0.000000
 22) 1100.000000 0.000000
 NO. ITERATIONS= 10
No lindo:
min 5x12 + 3x13 + x24 + 4x23 + 6x32 +2x36 + 9x45 + 4x47 +2x54 +8x57 +7x25 + x35 +5x34 +5x56 + 7x65 +3x63 + 3x67
st
x12 + x13 <= 1
-x67-x57-x47 <= -1
x24 + x23 +x25 -x12 -x32 = 0
x34 +x32 +x35 +x36 -x23 -x63 -x13 = 0
x45 + x47 -x34 -x54 -x24 = 0
x57 + x54 +x56 -x25 -x45 -x35 -x65 = 0
x67 +x65 +x63 -x36 -x56 = 0
end
Solução:
 LP OPTIMUM FOUND AT STEP 7
 OBJECTIVE FUNCTION VALUE
 1) 8.000000
 VARIABLE VALUE REDUCED COST
 X12 0.000000 2.000000
 X13 1.000000 0.000000
 X24 0.000000 0.000000
 X23 0.000000 4.000000
 X32 0.000000 6.000000
 X36 1.000000 0.000000
 X45 0.000000 11.000000
 X47 0.000000 0.000000
 X54 0.000000 0.000000
 X57 0.000000 2.000000
 X25 0.000000 8.000000
 X35 0.000000 2.000000
 X34 0.000000 4.000000
 X56 0.000000 2.000000
 X65 0.000000 10.000000
 X63 0.000000 5.000000
 X67 1.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 0.000000
 3) 0.000000 8.000000
 4) 0.000000 3.000000
 5) 0.000000 3.000000
 6) 0.000000 4.000000
 7) 0.000000 2.000000
 8) 0.000000 5.000000
 NO. ITERATIONS= 7
No lindo:
min x14 + 0.3x15 + 0.8x24 +4.3x25 + 2x34 + 4.6x35 + 0.5x45 + 3x56 +2.1x57 + 1.9x58 + 6x48 + 4.5x47 +0.2x46
st
x14 + x15 <= 900
x24 + x25 <= 1400
x34 + x35 <= 1000
-x46 -x56 <= -1100
-x47 -x57 <= -1000
-x48-x58 <= -1200
x57 +x58 +x56 -x45 -x15 -x25 -x35 = 0
x45 +x46 +x47 +x48 -x14 -x24 -x34 = 0
x45 <= 500
-x25 <= -200
x14>=0
x15>=0
x24>=0
x25>=0
x34>=0
x35>=0
x45>=0
x56>=0
x57>=0
x58>=0
x48>=0
x47>=0
x46>=0
end
LP OPTIMUM FOUND AT STEP 10
 OBJECTIVE FUNCTION VALUE
 1) 10380.00
 VARIABLE VALUE REDUCED COST
 X14 0.000000 3.100000
 X15 900.000000 0.000000
 X24 1200.000000 0.000000
 X25 200.000000 0.000000
 X34 1000.000000 0.000000
 X35 0.000000 0.200000
 X45 500.000000 0.000000
 X56 0.000000 5.200000
 X57 400.000000 0.000000
 X58 1200.000000 0.000000
 X48 0.000000 1.700000
 X47 600.000000 0.000000
 X46 1100.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 4.100000
 3) 0.000000 1.200000
 4) 0.000000 0.000000
 5) 0.000000 2.200000
 6) 0.000000 6.500000
 7) 0.000000 6.300000
 8) 0.000000 4.400000
 9) 0.000000 2.000000
 10) 0.000000 1.900000
 11) 0.000000 1.100000
 12) 0.000000 0.000000
 13) 900.000000 0.000000
 14) 1200.000000 0.000000
 15) 200.000000 0.000000
 16) 1000.000000 0.000000
 17) 0.000000 0.000000
 18) 500.000000 0.000000
 19) 0.000000 0.000000
 20) 400.000000 0.000000
 21) 1200.000000 0.000000
 22) 0.000000 0.000000
 23) 600.000000 0.000000
 24) 1100.000000 0.000000
 NO. ITERATIONS= 10
Questão 2: Problema do Transporte
No lindo
Modelo:
min 12x11+9x12+8x13+13x21+12x22+5x23+7x31+9x32+5x33+3x41+2x42+8x43
s.t.
x11+x12+x13=10
x21+x22+x23=20
x31+x32+x33=10
x41+x42+x43=15
x11+x21+x31+x41=8
x12+x22+x32+x42=30
x13+x23+x33+x43=17
end
Solução:
LP OPTIMUM FOUND AT STEP 7OBJECTIVE FUNCTION VALUE
 1) 315.0000
 VARIABLE VALUE REDUCED COST
 X11 0.000000 5.000000
 X12 10.000000 0.000000
 X13 0.000000 6.000000
 X21 0.000000 3.000000
 X22 3.000000 0.000000
 X23 17.000000 0.000000
 X31 8.000000 0.000000
 X32 2.000000 0.000000
 X33 0.000000 3.000000
 X41 0.000000 3.000000
 X42 15.000000 0.000000
 X43 0.000000 13.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 3.000000
 3) 0.000000 0.000000
 4) 0.000000 3.000000
 5) 0.000000 10.000000
 6) 0.000000 -10.000000
 7) 0.000000 -12.000000
 8) 0.000000 -5.000000
 NO. ITERATIONS= 7 
(D) No lindo:
min 12x11+9x12+8x13+13x21+12x22+5x23+7x31+9x32+5x33+3x41+8x43 + 50x42
st
x11+x12+x13=10
x21+x22+x23=20
x31+x32+x33=10
x41+x42+x43=15
x11+x21+x31+x41=8
x12+x22+x32+x42=30
x13+x23+x33+x43=17
x42 = 0
end
 LP OPTIMUM FOUND AT STEP 6
 OBJECTIVE FUNCTION VALUE
 1) 430.0000
 VARIABLE VALUE REDUCED COST
 X11 0.000000 15.000000
 X12 10.000000 0.000000
 X13 0.000000 6.000000
 X21 0.000000 13.000000
 X22 10.000000 0.000000
 X23 10.000000 0.000000
 X31 0.000000 10.000000
 X32 10.000000 0.000000
 X33 0.000000 3.000000
 X41 8.000000 0.000000
 X43 7.000000 0.000000
 X42 0.000000 35.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 0.000000
 3) 0.000000 -3.000000
 4) 0.000000 0.000000
 5) 0.000000 -6.000000
 6) 0.000000 3.000000
 7) 0.000000 -9.000000
 8) 0.000000 -2.000000
 9) 0.000000 0.000000
 NO. ITERATIONS= 6
Questão 3: Problema da Designação
No Lindo:
Min 4000x11 + 5000x12 + 4500x13 + 3800x21 + 4000x22 + 4000x24 + 3000x31 + 2000x33 + 4500x34 + 3500x41 + 4000x43 + 5000x44
s.t.
x11 + x12 + x13 = 1
x21 + x22 + x24 = 1
x31 + x33 + x34 = 1
x41 + x43 + x44 = 1
x11 + x21 + x31 + x41 = 1
x12 + x22 = 1
x13 + x33 + x43 = 1
x24 + x34 + x44 = 1
end
int12
Solução:
LP OPTIMUM FOUND AT STEP 6
 OBJECTIVE FUNCTION VALUE
 1) 14500.00
 VARIABLE VALUE REDUCED COST
 X11 0.000000 0.000000
 X12 1.000000 0.000000
 X13 0.000000 1500.000000
 X21 0.000000 800.000000
 X22 0.000000 0.000000
 X24 1.000000 0.000000
 X31 0.000000 0.000000
 X33 1.000000 0.000000
 X34 0.000000 500.000000
 X41 1.000000 0.000000
 X43 0.000000 1500.000000
 X44 0.000000 500.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 -1000.000000
 3) 0.000000 0.000000
 4) 0.000000 0.000000
 5) 0.000000 -500.000000
 6) 0.000000 -3000.000000
 7) 0.000000 -4000.000000
 8) 0.000000 -2000.000000
 9) 0.000000 -4000.000000
 NO. ITERATIONS= 6
(C) No lindo:
(C) No lindo:
 Min 4000x11 + 5000x12 + 4500x13 + 3800x21 + 4000x22 + 4000x24 + 3000x31 + 2000x33 + 4500x34 + 3500x41 + 4000x43 + 5000x44
s.t.
x11 + x12 + x13 <= 2
x21 + x22 + x24 <= 2
x31 + x33 + x34 <= 2
x41 + x43 + x44 <= 2
x11 + x21 + x31 + x41 = 1
x12 + x22 = 1
x13 + x33 + x43 = 1
x24 + x34 + x44 = 1
end
int12 
 LP OPTIMUM FOUND AT STEP 5
 OBJECTIVE FUNCTION VALUE
 1) 13000.00
 VARIABLE VALUE REDUCED COST
 X11 0.000000 500.000000
 X12 0.000000 0.000000
 X13 0.000000 2000.000000
 X21 0.000000 1300.000000
 X22 1.000000 0.000000
 X24 1.000000 0.000000
 X31 1.000000 0.000000
 X33 1.000000 0.000000
 X34 0.000000 0.000000
 X41 0.000000 0.000000
 X43 0.000000 1500.000000
 X44 0.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 2.000000 0.000000
 3) 0.000000 1000.000000
 4) 0.000000 500.000000
 5) 2.000000 0.000000
 6) 0.000000 -3500.000000
 7) 0.000000 -5000.000000
 8) 0.000000 -2500.000000
 9) 0.000000 -5000.000000
 NO. ITERATIONS= 5
Questão 4: Problema do Caminho Mínimo entre Dois Pontos
No Lindo:
Min 2x13 + 1x12+ 4x36+ 1x35+ 1x23 + 2x25 + 5x24 + 3x56 + 7x57 + 3x45 + 6x46 + 8x47 + 5x67 + 2x68 + 6x78 
s.t
x12 + x13 = 1
x23 + x25 + x24 - x12 = 0
x36 + x35 - x13 - x23 = 0
x45 + x46 + x47 - x24= 0
x56 + x57 - x35 - x25 - x45 = 0
x68 + x67 - x36 - x56 - x46 = 0
x78 - x57 + x47 + x67 = 0
-x68 - x78 = -1
end
int15
Solução:
LP OPTIMUM FOUND AT STEP 3
 OBJECTIVE FUNCTION VALUE
 1) 8.000000
 VARIABLE VALUE REDUCED COST
 X13 1.000000 0.000000
 X12 0.000000 0.000000
 X36 0.000000 0.000000
 X35 1.000000 0.000000
 X23 0.000000 0.000000
 X25 0.000000 0.000000
 X24 0.000000 0.000000
 X56 1.000000 0.000000
 X57 0.000000 0.000000
 X45 0.000000 6.000000
 X46 0.000000 6.000000
 X47 0.000000 20.000000
 X67 0.000000 17.000000
 X68 1.000000 0.000000
 X78 0.000000 8.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 -2.000000
 3) 0.000000 -1.000000
 4) 0.000000 0.000000
 5) 0.000000 4.000000
 6) 0.000000 1.000000
 7) 0.000000 4.000000
 8) 0.000000 8.000000
 9) 0.000000 6.000000
 NO. ITERATIONS= 3 
(B) No lindo:
Min 5x12 + x13 + 2x32 +7x24 +6x26 + 6x34 +7x35 +4x46 + 7x43+ 6x47 +5x56 + 9x57 +4x54 + 7x62 +2x67 +x25
s.t.
x12 + x13 = 1
x26 + x24 + x25 - x12 -x32 -x62 = 0
x34 +x35 +x32 -x13 -x43 = 0
x46 +x47 +x43 -x54 -x24 -x34 = 0
x56 +x57 +x54 -x25 -x35 = 0
x67 + x62 -x56 -x46 -x26 = 0
-x67 -x57 -x47 = -1
end
int15
Solução:
LP OPTIMUM FOUND AT STEP 6
 OBJECTIVE FUNCTION VALUE
 1) 11.00000
 VARIABLE VALUE REDUCED COST
 X12 0.000000 2.000000
 X13 1.000000 0.000000
 X32 1.000000 0.000000
 X24 0.000000 5.000000
 X26 1.000000 0.000000
 X34 0.000000 2.000000
 X350.000000 4.000000
 X46 0.000000 0.000000
 X43 0.000000 11.000000
 X47 0.000000 0.000000
 X56 0.000000 0.000000
 X57 0.000000 2.000000
 X54 0.000000 3.000000
 X62 0.000000 13.000000
 X67 1.000000 0.000000
 X25 0.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 -3.000000
 3) 0.000000 0.000000
 4) 0.000000 -2.000000
 5) 0.000000 2.000000
 6) 0.000000 1.000000
 7) 0.000000 6.000000
 8) 0.000000 8.000000
 NO. ITERATIONS= 6
Questão 6
Min 1x01 + 2x02 + 3x14 + 4x04 + 5x06 + 6x05 + 7x23 + 8x34 + 9x26 + 10x37 + 11x46 + 12x25 + 13x49 + 14x79 + 15x67 + 16x65+ 17x58 + 18x511 + 19x610 + 20x78 + 21x710 + 22x810 + 23x811
24x1011+ 25x815 + 26x910 + 27x912 + 28x915 + 29x1215 + 30x1013 + 1x1113 + 2x1312 + 3x1315 + 4x1115 + 5x1314 + 6x1114 + 7x1415
s.t.
x01 + x02 + x04 + x06 + x05 = 1
x14 - x01 = 0
x26 + x25 + x23 - x02 = 0
x37 + x34 - x23 = 0
x49 + x46 - x14 -x04 - x34 = 0
x58 + x511 -x05 -x25 - x65 = 0
x68 +x610 +x67 -x06 - x46 - x26 = 0
x710 + x79 + x78 - x37 - x67 = 0
x915 + x912 + x910 - x49 - x79 = 0
x1011 + x1013 - x810 - x610 - x710 - x910 = 0
x811 + x815 +x810 - x58 - x78 = 0
x1113 + x1115 + x1114 - x1011 -x811 - x511 = 0
x1215 - x912 - x1312 = 0
x1315 + x1314 + x1312 -x1013 - x1113 = 0
x1415 -x1314 -x1114 = 0 
-x1215 - x915 - x1315 - x815 - x1115 - x1415 = -1 
end
int15
 LP OPTIMUM FOUND AT STEP 5
 OBJECTIVE FUNCTION VALUE
 1) 28.00000
 VARIABLE VALUE REDUCED COST
 X01 0.000000 0.000000
 X02 0.000000 0.000000
 X14 0.000000 17.000000
 X04 0.000000 17.000000
 X06 0.000000 15.000000
 X05 1.000000 0.000000
 X23 0.000000 0.000000
 X34 0.000000 30.000000
 X26 0.000000 21.000000
 X37 0.000000 31.000000
 X46 0.000000 8.000000
 X25 0.000000 8.000000
 X49 0.000000 0.000000
 X79 0.000000 2.000000
 X67 0.000000 17.000000
 X65 0.000000 0.000000
 X58 0.000000 15.000000
 X511 1.000000 0.000000
 X610 0.000000 0.000000
 X78 0.000000 0.000000
 X710 0.000000 0.000000
 X810 0.000000 21.000000
 X811 0.000000 7.000000
 X1011 0.000000 9.000000
 X815 0.000000 5.000000
 X910 0.000000 17.000000
 X912 0.000000 28.000000
 X915 0.000000 0.000000
 X1215 0.000000 0.000000
 X1013 0.000000 14.000000
 X1113 1.000000 0.000000
 X1312 0.000000 28.000000
 X1315 1.000000 0.000000
 X1115 0.000000 0.000000
 X1314 0.000000 9.000000
 X1114 0.000000 9.000000
 X1415 0.000000 0.000000
 X68 0.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 10.000000
 3) 0.000000 11.000000
 4) 0.000000 12.000000
 5) 0.000000 19.000000
 6) 0.000000 -3.000000
 7) 0.000000 16.000000
 8) 0.000000 0.000000
 9) 0.000000 -2.000000
 10) 0.000000 10.000000
 11) 0.000000 19.000000
 12) 0.000000 18.000000
 13) 0.000000 34.000000
 14) 0.000000 9.000000
 15) 0.000000 35.000000
 16) 0.000000 31.000000
 17) 0.000000 38.000000
 NO. ITERATIONS= 5
Questão 8: Problema do Fluxo Máximo (Caminho de Aumento)
No Lindo:
Max x48 + x68 + x78
s.t.
x12+x13+x14-x48-x68-x78=0
x23+x24-x12=0
x36+x35-x13-x23=0
x48+x46-x24-x14=0
x57-x35=0
x67+x68-x36-x46=0
x78-x57-x67=0
x12<=12
x13<=11 
x14<=3 
x23<=2 
x24<=9 
x36<=5 
x35<=9 
x57<=10 
x46<=3 
x48<=10 
x67<=4 
x68<=6 
x78<=6
end
Solução:
LP OPTIMUM FOUND AT STEP 2
 OBJECTIVE FUNCTION VALUE
 1) 22.00000
 VARIABLE VALUE REDUCED COST
 X48 10.000000 0.000000
 X68 6.000000 0.000000
 X78 6.000000 0.000000
 X12 11.000000 0.000000
 X13 8.000000 0.000000
 X14 3.000000 0.000000
 X23 2.000000 0.000000
 X24 9.000000 0.000000
 X36 4.000000 0.000000
 X35 6.000000 0.000000
 X46 2.000000 0.000000
 X57 6.000000 0.000000
 X67 0.000000 0.000000
 ROW SLACK OR SURPLUS DUAL PRICES
 2) 0.000000 0.000000
 3) 0.000000 0.000000
 4) 0.000000 0.000000
 5) 0.000000 0.000000
 6) 0.000000 0.000000
 7) 0.000000 0.000000
 8) 0.000000 0.000000
 9) 1.000000 0.000000
 10) 3.000000 0.000000
 11) 0.000000 0.000000
 12) 0.000000 0.000000
 13) 0.000000 0.000000
 14) 1.000000 0.000000
 15) 3.000000 0.000000
 16) 4.000000 0.000000
 17) 1.000000 0.000000
 18) 0.000000 1.000000
 19) 4.000000 0.000000
 20) 0.000000 1.000000
 21) 0.000000 1.000000
 NO. ITERATIONS= 2