PROBLEMA ORIGINAL Maximizar el número de cajones que caben dentro de un estante de 90cm de alto. Las alturas de los cajones son 7.5cm, 10cm, 15cm, 20cm y 30cm. Si tenemos disponibles solamente 4 estantes, cual es el máximo numero de cajones a ocupar si tenemos solamente 8 cajones de 7.5cm, 13 cajones de 10cm, 24 cajones de 15cm, 13 cajones de 20cm y 3 cajones de 30cm. La suma de las alturas de los cajones no debe sobrepasar los 90cm, pues no habría espacio disponible para los cajones y tampoco puede ser menor a 90cm pues habría un desperdicio de espacio. max x11+x12+x13+x14+x21+x22+x23+x24+x31+x32+x33+x34+x41+x42+x43+x44+x51+x52+x53+x 54 subject to x11+x12+x13+x14<=8 x21+x22+x23+x24<=13 x31+x32+x33+x34<=24 x41+x42+x43+x44<=13 x51+x52+x53+x54<=3 7.5x11+10x21+15x31+20x41+30x51<=90 7.5x12+10x22+15x32+20x42+30x52<=90 7.5x13+10x23+15x33+20x43+30x53<=90 7.5x14+10x24+15x34+20x44+30x54<=90 end GIN 20 CORRIDA EN PROGRAMA LINDO LP OPTIMUM FOUND AT STEP 9 OBJECTIVE VALUE = 32.3333321 SET SET SET SET X31 TO <= X12 TO <= X34 TO >= X32 TO >= 0 AT 1 AT 6 AT 6 AT 1, BND= 2, BND= 3, BND= 4, BND= 32.33 32.33 32.33 32.00 NEW INTEGER SOLUTION OF 32.0000000 BOUND ON OPTIMUM: 32.33333 DELETE X32 AT LEVEL 4 DELETE X34 AT LEVEL 3 DELETE X12 AT LEVEL 2 DELETE X31 AT LEVEL 1 ENUMERATION COMPLETE. BRANCHES= TWIN= TWIN= TWIN= TWIN= AT BRANCH 4 PIVOTS= LAST INTEGER SOLUTION IS THE BEST FOUND RE-INSTALLING BEST SOLUTION... OBJECTIVE FUNCTION VALUE 1) 32.00000 32.33 32.33 32.33 32.33 12 15 19 25 4 PIVOT 25 25 VARIABLE VALUE X11 8.000000 X12 0.000000 X13 0.000000 X14 0.000000 X21 3.000000 X22 0.000000 X23 9.000000 X24 0.000000 X31 0.000000 X32 6.000000 X33 0.000000 X34 6.000000 X41 0.000000 X42 0.000000 X43 0.000000 X44 0.000000 X51 0.000000 X52 0.000000 X53 0.000000 X54 0.000000 REDUCED COST -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.000000 3) 1.000000 0.000000 4) 12.000000 0.000000 5) 13.000000 0.000000 6) 3.000000 0.000000 7) 0.000000 0.000000 8) 0.000000 0.000000 9) 0.000000 0.000000 10) 0.000000 0.000000 NO. ITERATIONS= 25 BRANCHES= 4 DETERM.= 1.000E 0 ACOMODO DE CAJONERAS max x11+x12+x13+x14+x21+x22+x23+x24+x31+x32+x33+x34+x41+x42+x43+x44+x51+x52+x53+x 54 subject to x11+x12+x13+x14<=8 x21+x22+x23+x24<=13 x31+x32+x33+x34<=24 x41+x42+x43+x44<=13 x51+x52+x53+x54<=3 7.5x11+10x21+15x31+20x41+30x51<=90 7.5x12+10x22+15x32+20x42+30x52<=90 7.5x13+10x23+15x33+20x43+30x53<=90 7.5x14+10x24+15x34+20x44+30x54<=90 x11-x12=0 x12-x13=0 x13-x14=0 x21-x22=0 x22-x23=0 x23-x24=0 x31-x32=0 x32-x33=0 x33-x34=0 x41-x42=0 x42-x43=0 x43-x44=0 x51-x52=0 x52-x53=0 x53-x54=0 end GIN 20 CORRIDA EN PROGRAMA LINDO LP OPTIMUM FOUND AT STEP 7 OBJECTIVE VALUE = 32.3333321 FIX ALL VARS.( 1) WITH RC > 4.00000 SET X24 TO <= 3 AT 1, BND= 32.00 NEW INTEGER SOLUTION OF 32.0000000 BOUND ON OPTIMUM: 32.00000 DELETE X24 AT LEVEL 1 ENUMERATION COMPLETE. BRANCHES= TWIN=-0.1000E+31 AT BRANCH 1 PIVOTS= LAST INTEGER SOLUTION IS THE BEST FOUND RE-INSTALLING BEST SOLUTION... OBJECTIVE FUNCTION VALUE 1) 32.00000 VARIABLE VALUE X11 2.000000 X12 2.000000 X13 2.000000 X14 2.000000 X21 3.000000 X22 3.000000 X23 3.000000 X24 3.000000 X31 3.000000 X32 3.000000 X33 3.000000 REDUCED COST -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 10 1 PIVOT 10 10 X34 X41 X42 X43 X44 X51 X52 X53 X54 ROW 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 SLACK OR SURPLUS DUAL PRICES 0.000000 0.000000 1.000000 0.000000 12.000000 0.000000 13.000000 0.000000 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 NO. ITERATIONS= 10 BRANCHES= 1 DETERM.= 1.000E 0 ACOMODO DE RESTO DE CAJONERAS max x11+x12+x13+x14+x15+x16+x21+x22+x23+x24+x25+x26+x31+x32+x33+x34+x35+x36+x41+x 42+x43+x44+x45+x46 subject to x11+x12+x13+x14+x15+x16<=1 x21+x22+x23+x24+x25+x26<=12 x31+x32+x33+x34+x35+x36<=13 x41+x42+x43+x44+x45+x46<=3 10x11+15x21+20x31+30x41<=90 10x12+15x22+20x32+30x42<=90 10x13+15x23+20x33+30x43<=90 10x14+15x24+20x34+30x44<=90 10x15+15x25+20x35+30x45<=90 10x16+15x26+20x36+30x46<=90 end GIN 24 CORRIDA EN PROGRAMA LINDO LP OPTIMUM FOUND AT STEP 12 OBJECTIVE VALUE = 29.0000000 SET SET SET SET SET SET SET X25 TO <= X35 TO <= X32 TO <= X36 TO <= X35 TO >= X46 TO >= X25 TO <= 2 AT 1 AT 1 AT 4 AT 1 AT 1 AT 0 AT 1, BND= 2, BND= 3, BND= 4, BND= 5, BND= 6, BND= 7, BND= 29.00 29.00 29.00 29.00 29.00 29.00 29.00 NEW INTEGER SOLUTION OF 29.0000000 BOUND ON OPTIMUM: 29.00000 DELETE X25 AT LEVEL 7 DELETE X46 AT LEVEL 6 DELETE X35 AT LEVEL 5 DELETE X36 AT LEVEL 4 DELETE X32 AT LEVEL 3 DELETE X35 AT LEVEL 2 DELETE X25 AT LEVEL 1 ENUMERATION COMPLETE. BRANCHES= TWIN= 29.00 34 TWIN= 29.00 37 TWIN= 29.00 39 TWIN=-0.1000E+31 39 TWIN= 29.00 48 TWIN= 29.00 52 TWIN= 29.00 56 AT BRANCH 6 PIVOTS= LAST INTEGER SOLUTION IS THE BEST FOUND RE-INSTALLING BEST SOLUTION... OBJECTIVE FUNCTION VALUE 1) 29.00000 VARIABLE VALUE X11 0.000000 X12 0.000000 X13 0.000000 X14 0.000000 X15 1.000000 X16 0.000000 X21 2.000000 X22 6.000000 X23 2.000000 X24 2.000000 REDUCED COST -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 6 PIVOT 56 56 X25 X26 X31 X32 X33 X34 X35 X36 X41 X42 X43 X44 X45 X46 ROW 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 0.000000 0.000000 3.000000 0.000000 3.000000 3.000000 1.000000 3.000000 0.000000 0.000000 0.000000 0.000000 2.000000 1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 SLACK OR SURPLUS DUAL PRICES 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 NO. ITERATIONS= 56 BRANCHES= 6 DETERM.= 1.000E 0