1 / 29

INVESTIGACION DE OPERACIONES

INVESTIGACION DE OPERACIONES. Función Objetivo. Variables de decisión y parámetros. Modelo Matemático. Restricciones. Caso:. Optica Central. La óptica Central desea determinar cuanto debe producir para que sea óptimamente aprovechada (es decir, obtener el > beneficio). Ella posee

chenoa
Download Presentation

INVESTIGACION DE OPERACIONES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. INVESTIGACION DE OPERACIONES

  2. Función Objetivo Variables de decisión y parámetros Modelo Matemático Restricciones

  3. Caso: Optica Central

  4. 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.

  5. 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

  6. Los tiempos y requerimientos se mostraron en el siguiente cuadro.

  7. 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 .

  8. 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

  9. 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.

  10. 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

  11. En función de la oferta 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

  12. 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

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

  14. 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

  15. Departamento de carey 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

  16. 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

  17. 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

  18. WinQSB Resultados obtenidos por el

  19. 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.

More Related