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How to Use Solver Spanish

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Instrucciones de EXCEL Solver

Octubre de 2000

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La opción Solver de EXCEL sirve para resolver problemas de optimización lineal y no lineal; también se pueden indicar restricciones enteras sobre las variables de decisión. Con Solver es posible resolver problemas que tengan hasta 200 variables de decisión, 100 restricciones explícitas y 400 simples (cotas superior e inferior o restricciones enteras sobre las variables de decisión). Para acceder a Solver, seleccione Tools en el menú principal y luego Solver. La ventana con los parámetros de Solver aparecerá tal y como se muestra a continuación:

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Cuadro de diálogo de los parámetros de Solver
La ventana Solver Parameters se utiliza para describir el problema de optimización a EXCEL. El campo Set Target Cell contiene la celda donde se encuentra la función objetiva correspondiente al problema en cuestión. Si desea hallar el máximo o el mínimo, seleccione Max o Min. Si la casilla Value of está seleccionada, Solver tratará de hallar un valor de la celda igual al valor del campo que se encuentra a la derecha de la selección. El cuadro de diálogo By Changing Cells contendrá la ubicación de las variables de decisión para el problema. Por último, las restricciones se deben especificar en el campo Subject to the Constraints haciendo clic en Add. El botón Change permite modificar las restricciones recién introducidas y Delete sirve para borrar las restricciones precedentes. Reset All borra el problema en curso y restablece todos los parámetros a sus valores por defecto. Con el botón Options se accede a las opciones de Solver (ver más adelante). El botón Guess carece de interés para nuestros fines y no se tratará en estas instrucciones. A continuación, y para mayor claridad, se señalan las partes más importantes del cuadro de diálogo de los parámetros de Solver.

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Al hacer clic en el botón Add, aparece la ventana Add Constraint.

Si hace clic en el campo Cell Reference podrá especificar la ubicación de una celda (por lo general, una celda con una fórmula). Introduzca el tipo de restricción haciendo clic en la flecha del campo central desplegable (=, =, int, donde int se refiere a un número entero, o bin, donde bin se refiere a binario). El campo Constraint puede llevar una fórmula de celdas, una simple referencia a una celda o un valor numérico. El botón Add añade la restricción especificada al modelo existente y vuelve a la ventana Add Constraint. El botón OK añade la restricción al modelo y vuelve a la ventana Solver

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Dialog. Nota: Solver no asume la no negatividad de las variables de decisión. En la ventana de opciones puede especificar que las variables han de ser no negativas.

Si en la ventana de los parámetros de Solver hacemos clic en el botón Options, aparece la ventana siguiente:

Max Time permite especificar el número de segundos antes de que Solver se detenga. El campo Iterations, al igual que el campo anterior, permite especificar el número máximo de iteraciones (pasos del algoritmo solver) antes de que el programa se detenga. Precision es el grado de exactitud del algoritmo solver (por ejemplo, lo cerca que tiene que estar el valor del lado derecho de una restricción antes de que se considere igual al lado izquierdo). El campo Tolerance se utiliza para programas enteros. Especifica un porcentaje dentro del cual se garantiza la optimalidad de la solución. Si intenta hallar la solución óptima, ponga el valor cero en este campo, aunque tal vez desee establecer un valor más alto si el tiempo de ejecución es demasiado largo (siempre que le interese aceptar una solución dentro de ese porcentaje de optimalidad). Si su modelo es un programa lineal o un programa entero lineal, le aconsejamos que seleccione la casilla Assume Linear Model. De este modo, el programa utiliza el algoritmo simplex en lugar de un algoritmo no lineal más largo y complicado (Generalized Reduced

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Gradient Meted). Seleccione la casilla Assume Non-Negative si desea que todos los valores de las celdas cambiantes sean ≥ 0. Seleccione Show Iterations Results si le interesa ver la información iteración por iteración (esto ralentiza mucho el tiempo de procesamiento). Use Automatic Scaling es útil si el modelo que utiliza tiene una escala defectuosa (si las entradas son de órdenes de magnitud completamente diferentes). Por último, la parte inferior de la ventana contiene las opciones para el algoritmo no lineal, a saber, cómo calcula la no linealidad, cómo se calculan las tasas de cambio y el tipo de técnica de búsqueda empleado. En términos generales, los valores por defecto de la mayoría de estos parámetros son perfectamente válidos. Es importante acordarse de seleccionar Assume Linear Model si se trata de un programa lineal o un programa lineal entero. Seleccione la casilla Assume NonNegativity si desea que las celdas cambiantes adopten sólo valores no negativos. Del mismo modo, si intenta obtener la solución óptima de un programa entero, no olvide establecer un 0% en el campo Tolerance.

Un ejemplo: la empresa Colorado Cattle Company1 La empresa Colorado Cattle Company (CCC) puede comprar tres tipos de ingredientes alimentarios sin procesar a un distribuidor mayorista. El ganado de la empresa tiene ciertas necesidades alimenticias con respecto a las grasas, proteínas, calcio y hierro. Cada vaca requiere al menos 10 unidades de calcio, no más de 7,5 unidades de grasa, al menos 12 unidades de hierro y al menos 15 unidades de proteína al día. La tabla siguiente indica la cantidad de grasa, proteína, calcio y hierro por cada libra de los tres ingredientes

Este problema se extrajo de Camm, J.D. y Evans, J.R., Management Science, Modeling , Analysis, and Interpretation, South-Western Publishing Co., Cincinnati, Ohio, 1996.

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7 alimentarios. El alimento de grado 1 cuesta 0,25 dólares; el de grado 2, 0,10 dólares; y el de grado 3, 0, 08 por libra. El ganado se puede alimentar con una mezcla de los tres tipos de alimento sin procesar. CCC está interesada en alimentar al ganado del modo más barato posible. -------------------------------------------------------------------------------------------------------------Datos de Colorado Cattle Company Ingredientes alimentarios (Unidades por libra) Grado 1 Calcio Hierro Proteínas Grasa 0,7 0,9 0,8 0,5 Grado 2 0,8 0,8 1,5 0,6 Grado 3 0 0,8 0,9 0,4

------------------------------------------------------------------------------------------------------------------A continuación se formula el modelo de programación lineal del problema: Sea grado 1 = cantidad diaria (en libras) de grado 1 utilizada en alimentar una vaca grado 2 = cantidad diaria (en libras) de grado 2 utilizada en alimentar una vaca grado 3 = cantidad diaria (en libras) de grado 1 utilizada en alimentar una vaca

Minimizar 0,25 grado 1 + 0,1 grado 2 + 0,08 grado 3 sujeto a 0,7 grado 1 + 0,8 grado 2 + 0 grado 3 ≥10 0,9 grado 1 + 0,8 grado 2 + 0,8 grado 3 ≥ 12 0,8 grado 1 + 1,5 grado 2 + 0,9 grado 3 ≥ 15 (Calcio) (Hierro) (Proteínas)

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0,5 grado 1 + 0,6 grado 2 + 0,4 grado 3 ≤ 7,5 grado 1, grado 2, grado 3 ≥ 0 A continuación se muestra una hoja EXCEL con el modelo de este escenario: (Grasa)

Las fórmulas de celda en esta hoja todas tienen lugar en la sección Model Outputs (esto es, restricciones).

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La función SUMPRODUCT lleva a cabo el producto escalar. Por ejemplo, la cantidad de calcio utilizada es SUMPRODUCT(B7:D7,B15:D15) = ( B7*B15 + C7*C15 + D7*D15 ). Siga los siguientes pasos para crear el modelo de PL que se muestra más abajo: 1. 2. 3. 4. Vaya a Tools - Solver. Haga clic en el campo Set Target Cell y escriba B26. Haga clic en Min. Haga clic en el campo By Changing Cells y, en la hoja de cálculo, haga clic y arrastre el ratón de B15 a D15 (o escriba B15:D15). Haga clic en el botón Add para acceder a la ventana Add Constraint. Para introducir las restricciones necesarias mínimas: haga clic en Cell Reference e introduzca B20:B22, seleccione el tipo >= y, a continuación, vaya al campo Constraint e introduzca F7:F9. Haga clic en Add. Para introducir las restricciones máximas permitidas: haga clic en Cell Reference e introduzca B24, seleccione el tipo =$F$7 Obligatorio 12 $B$21>=$F$8 Obligatorio 15,1 $B$22>=$F$9 Opcional 7,5 $B$24

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