INVESTIGACION DE OPERACIONES

Modelo Matemático Función Objetivo Variables de decisión y parámetros Restricciones

Caso: Optica Central

La óptica Central desea determinar cuanto debe producir para que sea óptimamente aprovechada (es decir, obtener el > beneficio). Ella posee 74 modelos de monturas. 74 Monturas Tornillos 15000 unid. Carey 4700 gr. Lentejas de silicona 1000 lent. Cada montura posee 6 tornillos, 5 gr. cobre 2 lentejas de silicona se posee 478 monturas en inventario final de periodo anterior. Su producción debe ser menor o igual a este. Por el comportamiento de mercado se sabe que la demanda de monturas al mes es de 1000 unidades.

De acuerdo al estudio de mercado se determino que del modelo Amadeus se debe producir una cantidad mayor a 40, del modelo Barón se debe producir a lo más 30 unidades

Los tiempos y requerimientos se mostraron en el siguiente cuadro. Var. Tiempo Dpta Tornillos Inst. carey Coloc. Siliconas Marca Cantidad Costo Unit Precio Unit. Utilidad X1 25 23 10 Amadeus 31 40.75 53.79 13.04 X2 18 20 8 Andrea Biagiotti 48 13.22 15.47 2.25 X3 Angel Eye 1 12 15 3 X4 5 Baglioni 17 7.25 9.52 2.27 X5 Barbinzon C/flex 11.00 4 X6 23m Baron 33 38.25 43.857 5.607 X7 23 m Belutti 40.00 49.98 9.98 X8 10 m Best 7.00 X9 15 m 16 6 Biaggio 13 X10 Bibi 9.00 X11 Broadway 10.00 X12 Camel 2 6.30 9 2.7 X13 Cameroon 5.20 8.33 3.12 X14 7 Carusso 11 7.75 9.25 X15 Cecilie 9.95 2.05

X16 10 12 5 Clare collection 2 7.00 3 X17 11 13 Clio 1 9.20 12.5 3.3 X18 20 23 Couple Rim 20.01 29.75 9.74 X19 28 25 Crispol 47.10 53 5.9 X20 Cross 4 8.0 8 X21 Cta 4.0 X22 Christiam Dior 4.10 3.9 X23 Dasic 16 5.30 8.33 3.03 X24 24 Dilen 23.40 35 11.6 X25 Dirary 7.0 X26 Donald duck 5.70 2.63 X27 Duck head 5.10 3.23 X28 Escape 6.0 X29 Europtics X30 Flemingo 5.20 3.13 X31 9 Flinistones p niños 23.10 11.9 X32 Frost 7.10 1.23 X33 Ferry Weber 30.20 49.98 19.78 X34 Gianni 11.20 15.17 3.97 X35 17 Giovanni 26 13.10 15 1.9 X36 18 Giovanni Ochialli 4.40 7 2.6

X37 8 10 4 Giro 1 3.50 4.5 X38 12 5 Goya lens 3 4.40 9.52 5.12 X39 11 13 Gratfitti 12.10 15 2.9 X40 17 18 Hermes 8.0 2 X41 Historie de Voir 5.10 8.33 3.23 X42 Hollayday 14 9.40 5.6 X43 16 7 Hollywood 8.10 5.9 X44 Jr. Optical 7.30 5.7 X45 6 Jazmin o Jazmine X46 9 Kenzo X47 Kirk 2.32 X48 Lectos Alicia 7.50 2.50 X49 Lector Nitro 2.20 3.80 X50 20 23 Logros 13.70 4.3 X51 Maniatan X52 Maru X53 Melissa 4.10 3.9 X54 Monc Blanc 3.20 2.8

X55 19 21 10 Myke 25 14.20 17.69 3.49 X56 11 13 5 Napoli 2 6.70 3.3 X57 12 14 Panorama 1 X58 8 4 Pascali 4.10 6 1.9 X59 9 Passport Ochiali 4.50 3.5 X60 Primicia 5.30 4.7 X61 Primmera X62 Profesor 3 X63 Reiz 5.10 8.33 3.23 X64 15 Revelato 12.67 5.97 X65 Rexon 20 4.20 4.13 X66 Roden 18 X67 17 Rover 11.30 16.66 5.36 X68 s/m 3.20 7 3.8 X69 Salón kids 3.10 6.54 X70 Stom X71 Sun 3.7 X72 Sziois 25.6 X73 Tribal 23 10.30 X74 30 u. Pacific 80.40 106 Total disponible 9800 10710 9500 62

Amadeus Andrea Biagiotti Angel Eye Baglioni Barbinzon C/flex Baron Belutti Best Biaggio Bibi Broadway Camel Cameroon Carusso Cecilie Clare collection Clio Couple Rim Crispol Cross Cta Christiam Dior Dasic Dilen Dirary Donald duck Duck head Escape Europtics Flemingo Flinistones p niños Frost Ferry Weber Gianni Giovanni Giovanni Ochialli Giro Goya lens Gratfitti Hermes Historie de Voir Hollayday Hollywood Jr. Optical Jazmin o Jazmine Kenzo Kirk Lectos Alicia Lector Nitro Logros Maniatan Maru Melissa Monc Blanc Myke Napoli Panorama Pascali Passport Ochiali Primicia

Primmera Profesor Reiz Revelato Rexon Roden Rover s/m Salón kids Stom Sun Sziois Tribal u. Pacific

Función objetivo: Maximizar la utilidad. Max Z = Maximizar la utilidad Max Z = 13.04X1 + 2.25 X2 + 3 X3+ 2.27 X4+ 4 X5+ 5.607 X6+ 9.98 X7+ 3 X8+ 4 X9+ 3 X10+ 5 X11+ 2.7 X12+ 3.12 X13+ 9.25 X14+ 2.05 X15+ 3 X16+ 3.3 X17+ 9.74 X18+ 5.9 X19+ 3 X20+4 X21+ 39X22+ 3.03 X23+ 11.6 X24+ 3 X25+ 2.63 X26+ 3.23 X27+ 4 X28+ 4 X29+ 3.13 X30+ 11.9 X31+ 1.23 X32+ 19.78 X33+ 3.97 X34+ 1.9 X35+ 2.6 X36+ 4.5 X37+ 5.12 X38+ 2.9 X39+ 2 X40+ 3.23 X41+ 5.6 X42+ 3.9 X43+ 5.7 X44+ 3.23 X45+ 3.23 X46+ 3.23 X47+ 2.50 X48+ 3.80 X49+ 4.3 X50+ 3.23 X51+ 3.23 X52+ 3.9 X53+ 2.8 X54+ 3.49 X55+ 3.3 X56+ 3.3 X57+ 1.9 X58+ 3.5 X59+ 4.7 X60+ 4.7 X61+ 4.7 X62+ 3.23 X63+ 5.97 X64+ 4.13 X65+ 4.13 X66+ 5.36 X67+ 3.8 X68+ 3.44 X69+ 3.8 X70+ 3.8 X71+ 3.8 X72+ 3.7 X73+ 25.6 X74 .

Material prima: Tornillos 6X1 + 6X2 + 6X3 + 6X4 + 6X5 + 6X6 + 6X7 + 6X8+ 6X9+ 6X10 + 6X11 + 6X12 + 6X13 + 6 X14 + 6X15n + 6X16 + 6X17 + 6X18 + 6X19 + 6X20 + 6X21+ 6X22 + 6X23+ 6X24 + 6X25 + 6 X26 + 6X27 + 6X28 + 6X29 + 6X30 + 6X31+ 6X32 + 6X33 + 6X34 + 6X35 + 6X36 + 6 X37 + 6X38 + 6X39 + 6X40+ 6X41 + 6X42 + 6X43 + 6X44 + 6X45 + 6X46 + 6X47 + 6X48 + 6X49 + 6X50 + 6X51 + 6X52 + 6X53 + 6X54 + 6X55 + 6X56 + 6X57 + 6X58 + 6X59 + 6 X60 + 6X61 + 6X62 + 6X63 + 6X64 + 6X65 + 6X66 + 6X67 + 6X68 + 6X69 + 6X70 + 6X71 +6 X72 + 6X73 + 6X74  1600 unidades Restriccion

Restriccion M.P en Carey 5X1 + 5X2 + 5X3 + 5X4 + 5X5 + 5X6 + 5X7 + 5X8+ 5X9+ 5X10 + 5X11 + 5X12 + 5X13 + 5X14 + 5X15n + 5X16 + 5X17 + 5X18 + 5X19 + 5X20 + 5X21+ 5X22 + 5X23+ 5X24 + 5X25 + 5X26 + 5X27 + 5X28 + 5X29 + 5X30 + 5X31+ 5X32 + 5X33 + 5X34 + 5X35 + 5X36 + 5 X37 + 5X38 + 5X39 + 5X40+ 5X41 + 5X42 + 5X43 + 5X44 + 5X45 + 5X46 + 5X47 + 5X48 + 5X49 + 5X50 + 5X51 + 5X52 + 5X53 + 5X54 + 5X55 + 5X56 + 5X57 + 5X58 + 5X59 + 5X60 + 5X61 + 5X62 + 5X63 + 5X64 + 5X65 + 5X66 + 5X67 + 5X68 + 5X69 + 5X70 + 5X71 +5 X72 + 5X73 + 5X74  4700 Gr.

Materia prima en lentejas de silicona 2X1 + 2X2 + 2X3 + 2X4 + 2X5 + 2X6 + 2X7 + 2X8+ 2X9+ 2X10 + 2X11 + 2X12 + 2X13 + 2X14 + 2X15n + 2X16 + 2X17 + 2X18 + 2X19 + 2X20 + 2X21+ 2X22 + 2X23+ 2X24 + 2X25 + 2X26 + 2X27 + 2X28 + 2X29 + 2X30 + 2X31+ 2X32 + 2X33 + 2X34 + 2X35 + 2X36 +2 X37 + 2X38 + 2X39 + 2X40 + 2X41 + 2X42 + 2X43 + 2X44 + 2X45 + 2X46 + 2X47 + 2X48 + 2X49 + 2X50 + 2X51 + 2X52 + 2X53 + 2X54 + 2X55 + 2X56 + 2X57 + 2X58 + 2X59 + 2X60 + 2X61 + 2X62 + 2X63 + 2X64 + 2X65 + 2X66 + 2X67 + 2X68 + 2X69 + 2X70 + 2X71 + 2X72 + 2X73 + 2X74  1000 unidades. Restriccion

En función de la oferta Restriccion X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8+ X9+ X10 + X11 + X12 + X13 + X14 + X15n + X16 + X17 + X18 + X19 + X20 + X21+ X22 + X23+ X24 + X25 + X26 + X27 + X28 + X29 + X30 + X31+ X32 + X33 + X34 + X35 + X36 + X37 + X38 + X39 + X40 + X41 + X42 + X43 + X44 + X45 + X46 + X47 + X48 + X49 + X50 + X51 + X52 + X53 + X54 + X55 + X56 + X57 + X58 + X59 + X60 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X70 + X71 + X72 + X73 + X74  474 monturas. Restriccion

En función de la demanda. X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8+ X9+ X10 + X11 + X12 + X13 + X14 + X15n + X16 + X17 + X18 + X19 + X20 + X21+ X22 + X23+ X24 + X25 + X26 + X27 + X28 + X29 + X30 + X31+ X32 + X33 + X34 + X35 + X36 + X37 + X38 + X39 + X40 + X41 + X42 + X43 + X44 + X45 + X46 + X47 + X48 + X49 + X50 + X51 + X52 + X53 + X54 + X55 + X56 + X57 + X58 + X59 + X60 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X70 + X71 + X72 + X73 + X74  1000 monturas. Restriccion

De acuerdo a estudio de mercado X1  40 X6  30 Restriccion

Departamento de tornillos 25X1 + 18X2 + 18X3 + 10X4 + 18X5 + 23X6 + 23X7 + 10X8+ 15X9+ 12X10 + 18X11 + 10X12 + 10X13 + 16X14 + 11X15n + 10X16 + 11X17 + 20X18 + 28X19 + 10X20 + 10X21+ 10X22 + 10X23+ 10X24 + 24X25 + 11X26 + 10X27 + 10X28 + 12X29 + 12X30 + 9X31+ 24X32 + 10X33 + 28X34 + 16X35 + 17X36 + 8X37 + 10X38 + 11X39 + 17X40 + 11X41 + 10X42 + 13X43 + 14X44 + 9X45 + 10X46 + 10X47 + 10X48 + 8X49 + 20X50 + 9X51 + 9X52 + 10X53 + 8X54 + 19X55 + 11X56 + 12X57 + 8X58 + 9X59 + 10X60 + 11X61 + 12X62 + 9X63 + 13X64 + 10X65 + 10X66 + 17X67 + 8X68 + 7X69 + 8X70 + 9X71 + 8X72 + 15X73 + 30X74  9800. Restriccion

Departamento de carey Restriccion 23X1 + 20X2 + 20X3 + 15X4 + 20X5 + 25X6 + 25X7 + 12X8+ 16X9+ 3X10 + 20X11 + 12X12 + 12X13 + 17X14 + 13X15n + 12X16 + 13X17 + 33X18 + 25X19 + 12X20 + 12X21+ 12X22 + 12X23+ 12X24 + 25X25 + 13X26 + 12X27 + 12X28 + 13X29 + 13X30 + 10X31+ 25X32 + 12X33 + 25X34 + 17X35 + 18X36 + 10X37 + 12X38 + 13X39 + 18X40 + 13X41 + 12X42 + 17X43 + 15X44 + 16X45 + 10X46 + 12X47 + 12X48 + 10X49 + 23X50 + 10X51 + 10X52 + 12X53 + 10X54 + 21X55 + 13X56 + 14X57 + 10X58 + 10X59 + 13X60 + 13X61 + 14X62 + 10X63 + 15X64 + 12X65 + 12X66 + 20X67 + 9X68 + 9X69 + 9X70 + 10X71 + 9X72 + 17X73 + 25X74  10710. Restriccion

Depart de colocación de siliconas. 10X1 + 8X2 + 8X3 + 5X4 + 8X5 + 10X6 + 10X7 + 5X8+ 6X9+ 7X10 + 8X11 + 5X12 + 5X13 + 7X14 + 5X15n + 5X16 + 5X17 + 10X18 + 10X19 + 5X20 + 5X21+ 5X22 + 5X23+ 5X24 + 10X25 + 5X26 + 5X27 + 5X28 + 5X29 + 5X30 + 4X31+ 10X32 + 5X33 + 10X34 + 8X35 + 8X36 + 4X37 + 5X38 + 5X39 + 8X40 + 5X41 + 5X42 + 7X43 + 5X44 + 6X45 + 4X46 + 5X47 + 5X48 + 4X49 + 10X50 + 4X51 + 4X52 + 5X53 + 4X54 + 10X55 + 5X56 + 5X57 + 4X58 + 4X59 + 5X60 + 5X61 + 5X62 + 4X63 + 6X64 + 5X65 + 5X66 + 8X67 + 4X68 + 4X69 + 4X70 + 4X71 + 4X72 + 7X73 + 10X74  9500. Restriccion

No negatividad Restriccion X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8+ X9+ X10 + X11 + X12 + X13 + X14 + X15n + X16 + X17 + X18 + X19 + X20 + X21+ X22 + X23+ X24 + X25 + X26 + X27 + X28 + X29 + X30 + X31+ X32 + X33 + X34 + X35 + X36 + X37 + X38 + X39 + X40 + X41 + X42 + X43 + X44 + X45 + X46 + X47 + X48 + X49 + X50 + X51 + X52 + X53 + X54 + X55 + X56 + X57 + X58 + X59 + X60 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X70 + X71 + X72 + X73 + X74  0. No negatividad Restriccion

WinQSB Resultados obtenidos por el Objective Function (Max.) = 1.019.482,00 Left Hand Right Hand Slack Shadow Allowable Constraint Side Direction or Surplus Price Min. RHS Max. RHS 1 C1 2.844,00 <= 16.000,00 13.156,00 M 2 C2 2.370,00 4.700,00 2.330,00 3 C3 948 1.000,00 52 4 C4 474 1.978,00 70 500 5 C5 526 6 C6 40 >= -674 311,3333 7 C7 30 3.629,00 343,0769 8 C8 5.730,00 9.800,00 4.070,00 9 C9 6.518,00 10.710,00 4.192,00 10 C10 2.720,00 9.500,00 6.780,00

Análisis de resultados La solución óptima es de s/.1.019.482,00 Sobran 13.156,00 unidades de tornillos, 2.330,00 unidades de Carey, 52 lentejas de Silicona. 526 monturas en función de la demanda, 4.070,00 minutos en el departamento de tornillo, 4.192,00 minutos en el departamento de colocación de Carey 6.780,00 minutos en el departamento de colocación de Silicona.

MARCA DE MONTURAS UNIDADES A PRODUCIR Amadeus 40 Andrea Biagiotti Angel Eye Baglioni Barbinzon C/flex Baron 30 Belutti Best Biaggio Bibi Broadway Camel Cameroon Carusso Cecilie Clare collection Clio Couple Rim

Crispol Cross Cta Christiam Dior Dasic Dilen Dirary Donald duck Duck head Escape Europtics Flemingo Flinistones p niños Frost Ferry Weber 404 Gianni Giovanni Giovanni Ochialli Giro

Goya lens Gratfitti Hermes Historie de Voir Hollayday Hollywood Jr. Optical Jazmin o Jazmine Kenzo Kirk Lectos Alicia Lector Nitro Logros Maniatan Maru Melissa Monc Blanc Myke Napoli Panorama

Pascali Passport Ochiali Primicia Primmera Profesor Reiz Revelato Rexon Roden Rover s/m Salón kids Stom Sun Sziois Tribal u. Pacific