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TRABAJO OPERACIONES
PAPER AND MORE

Integrantes:
Fecha: Julio 2009
III,
Módulo III Executive MBA
DESARROLLO DE PREGUNTAS
I.

ANÁLISIS # 1

A.
i). ¿Qué punto de pedir-hasta da un 98% de porcentaje de en –inventario (servicio Tipo 1)?
De acuerdo a los resultados obtenidos en el análisis # 1, obtener un 98% de en-inventario (tipo
1), a las 77 unidades.

ii) ¿Un 98% de tasa de despacho (tipo 2)?
Para obtener la tasa de despacho deseada a un 98%, el order up-to-point, debe ser 69 unidades. iii) ¿Por qué no son iguales?
Por que la demanda no es uniforme, y dado que ambos indicadores miden distintos servicios los resultados van a ser distintos
Tipo 1
Tipo 2

Total de semanas en las cuales no hubo quiebre de stock, sobre las semanas totales.
El porcentaje de la demanda satisfecha desde el inventario en stock. Proporción de los despachos satisfechos desde el inventario iv) ¿Por qué hay una tendencia a que uno sea más alto que el otro?
Por que el tipo 1, es un indicador más ácido en el sentido que es más sensible dado que mide presencia en inventario (tipo binario si-no), durante un período definido de semanas. Sin embargo el tipo 2, existen muchas más posibilidades de acertar (98%,97%,96%,95%… etc.), porque los despachos son más que las semanas de inventario.

v) ¿Qué punto de pedir –hasta maximiza la utilidad neta sobre Great White?
En el nivel de inventario 57 unidades, se obtiene la máxima utilidad neta, pese a que no se logra el nivel de servicio deseado.
B.
i)

Costo de exceso para la SKU de Great White.

De acuerdo a los datos obtenidos, el precio del producto al por mayor US$20, y el costo de inventario del 25%, del costo al por mayor, y si consideramos que el número de periodos al año son
25 (300 días divididos en 12 días hábiles por período), el costo de exceso sería:
Costo de exceso = (25% * 20) / 25 = 0,2 dólares por resma ii) El costo de carencia para el SKU Great White sería
(21 -20) = 1 dólar por resma
Al considerar el margen de un venta pérdida, es un modelo más orientado al cliente, en el sentido que se considera un quiebre de stock como un venta pérdida, dado que el producto no tendría substitución y la venta se perdería. Consideramos que este modelo es más consistente con el modelo de negocios de P&M

iii)

El fractil critico sería:
=(1/(1+0,2) = 0,83 eq. 83% de tasa en-inventario (tipo 1)
Al revisar la tabla de Análisis #1 obtenemos que el punto de pedir hasta, más cercano al fractil critico, es entre 59 y 63 unidades (un 84% de in stock rate).

C) y D)
La política de inventario de pedir hasta, de 57 unidades considera la maximización de beneficios.
Este nivel de inventario otorga un nivel de servicio en inventario de 80% con una tasa de satisfacción de la demanda de un 93,8%, bajo un punto de vista financiero y de maximización de utilidades para un mono producto.
Sin embargo debiéramos considerar 2 características fundamentales de este negocio: Por una parte los clientes, de acuerdo a la opinión de Brown, son muy leales a Great White dado el nivel de satisfacción de la demanda y que frente a un quiebre de stock la venta se perdería. Y por otra parte el producto es un generador de tráfico de la tienda, por lo cual las políticas de inventario no debieran considerarse mirando solo este producto, y al considerar el costo no solo de la perdida de la venta de White, si no el costo de la menor venta general de las tiendas, generado por el menor tráfico. Por lo tanto, consideramos que el análisis realizado es un punto de partida, luego debe sensibilizarse con variables cualitativas del producto: como su peso especifico, que tipo de producto es y como funciona en la demanda global de la empresa.

II.

ANALISIS # 2
i)

Media: 40,24
Dev. St: 20,35

ii)

Histograma para Great White

Histograma
14

120,00%

12

100,00%

Frecuencia

10
80,00%
8
60,00%
6
40,00%

Frecuencia
% acumulado

4
20,00%

2

r..
.

80 y m

ay o 70

60

50

40

30

20

0,00%
10

0

Clase

iii) Comparación frecuencias acumulativas del histograma Great White, con un histograma de frecuencia normal

Histograma
Anexo 1

Histograma
14

120,00%

12

100,00%

120,00%

100,00%

20,00%

10

Frecuencia

25,00%

80,00%

8
60,00%
6

80,00%

Frecuencia
% acumulado

15,00%
60,00%

40,00%
4

10,00%

80 m ay or .. . y 70

60

50

40

30

0,00%
20

20,00%

0
10

2

40,00%

Clase

5,00%

20,00%

0,00%

0,00%
10

20

30

40

50

60

70

80

More than
80

La distribución normal posee ciertas propiedades importantes que conviene destacar:
i.

Tiene una única moda, que coincide con su media y su mediana.

Frequency
Cumulative

ii. iii. iv.

Es simétrica con respecto a su media . Según esto, para este tipo de variables existe una probabilidad de un 50% de observar un dato mayor que la media, y un 50% de observar un dato menor.
La distancia entre la línea trazada en la media y el punto de inflexión de la curva es igual a una desviación típica ( ). Cuanto mayor sea
, más aplanada será la curva de la densidad. El área bajo la curva comprendido entre los valores situados aproximadamente a dos desviaciones estándar de la media es igual a 0.95. En concreto, existe un 95%

Si utilizamos los parámetros mencionados para evaluar el Histograma de Great White, podemos evidenciar que su curva de acerca a una distribución normal dado que:
1. Los parámetros de moda, mediana, y media son cercanos
Moda
Mediana
Media

37,00
41,00
40,24

2. De acuerdo a los datos de la frecuencia, existe un 46% de probalidades que los datos sean menores y un 54% que sean mayores que la media
Utilizando otros parámetros de comparación de distribución normal, denominado CURTOSIS y
Fischer. El cual establece que: “Cuando la distribución de los datos cuenta con un coeficiente de asimetría (g1 = ±0.5) y un coeficiente de Curtosis de (g2 = ±0.5), se le denomina Curva Normal. Este criterio es de suma importancia ya que para la mayoría de los procedimientos de la estadística de inferencia se requiere que los datos se distribuyan normalmente”.
G1 FIsher
Es asimétrica positiva (que la mayor cantidad de datos esta a la izq. de la media). De acuerdo al parámetro Fischer, la asimetría de nuestra es: 0, 03, con respecto a 0.
Se utilizo la siguiente fórmula:

G2 Curtosis
El histograma de Great White sigue una distribución normal, dado que g2 es igual a 0,57 resultado obtenido de la siguiente fórmula:

Conclusión: si tuvieses más datos de la demanda (más 1 año), la distribución tendería a ser una normal. 3. y 4. Tenemos que:
Media
Desv.est.

40,24
20,3546

61
81

20
(0)

σ


66%
98%

A un σ tenemos cubierto el 66% de los datos, comparado con un 68% correspondiente a una distribución normal, y 2 σ tenemos un 98% de los datos, siendo un 95% para una distribución normal1 D.
Sobre la base de los datos entregados por las tablas del análisis #2 letra b y c, obtenemos lo siguiente: Con un fractil crítico de 83%, el nivel de inventario de pedir hasta corresponde a 60 unidades. Y con este nivel de inventario podemos entregar un nivel de servicio de 95,5%, siendo este el punto de mayor maximización de utilidades.
Si mantenemos los parámetros indicados por Browne, de 98% de Fill rate, el nivel de inventario que debiera ser de 68 unidades, equivalente a un 91% de orden up to point.

1

Las definiciones utilizadas han sido extraídas de los libros Estadística para administradores escrito por Alan Wester de la editorial McGraw-Hill y el libro Estadística y Muestreo escrito por Ciro
Martínez editorial Ecoe editores (Octava edición).

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