PREDICCIÓN DE LA DEMANDA DE SEMICONDUCTORES PARA …oa.upm.es/46890/1/TFG_DARIO_KHAMBATTA_MORENO.pdf · aplicados a un nivel superior, en este caso departamentos. Se muestran las

UNIVERSIDAD POLITÉCNICA DE MADRID

ESCUELA TÉCNICA SUPERIOR DE INGENIEROS INDUSTRIALES

TRABAJO DE FIN DE GRADO

PREDICCIÓN DE LA DEMANDA DE

SEMICONDUCTORES PARA CLIENTES

AUTOMOVILÍSTICOS

Darío Khambatta Moreno

Predicción de la demanda de semiconductores para clientes automovilísticos

2 Escuela Técnica Superior de Ingenieros Industriales (UPM)


Darío Khambatta Moreno 3

Resumen

En este Trabajo de Fin de Grado se trata el problema de la predicción de demanda a

nivel cliente mediante el uso de una base de datos poco extensa en el marco de Infineon

Technologies AG, empresa colaboradora en este Trabajo. Es el primer análisis de

predicción realizado a este nivel en la citada empresa y su importancia es crítica porque

aporta nuevos resultados que son comparados con los actuales métodos de predicción

aplicados a un nivel superior, en este caso departamentos. Se muestran las metodologías

aplicadas hasta el momento en la compañía y, considerando también nuevos modelos, la

regresión múltiple es elegida como la mejor técnica de predicción para aplicar. La

escasez de datos relevantes a nivel cliente fue el asunto más problemático para la

realización de este Trabajo, pero la definición de las denominadas gráficas “EDI Crawl

Charts” lo resolvieron. Se explica, además, un procedimiento general para predecir la

demanda de los clientes a través de la regresión lineal, a la vez que se muestran los

modelos de regresión definitivos para diferentes tipos de clientes. Finalmente, este

documento presenta la herramienta “EDI Order Development Crawl Chart Tool”, la

cual integra los modelos de predicción finales en Excel, habilitando así su uso para los

planificadores de la cadena de suministro.

Palabras clave: predicción de demanda, semiconductores, regresión múltiple, Crawl

Charts.





Tabla de contenido 1 Introducción ................................................................................................................. 7

1.1 Motivación e impacto .............................................................................................. 7

1.2 Definición del problema .......................................................................................... 7

1.3 Objetivos .................................................................................................................. 8

1.4 Impacto medioambiental .......................................................................................... 8

2 Desarrollo del Trabajo ................................................................................................. 9

2.1 Predicción de la demanda en la industria de los semiconductores .......................... 9

2.2 Infineon Technologies AG ..................................................................................... 12

2.3 Metodología ........................................................................................................... 13

2.3.1 Representación de los datos ......................................................................... 13

2.3.2 Selección del método de predicción ............................................................. 18

2.4 Resultados .............................................................................................................. 21

2.5 Integración de los resultados en los Crawl Charts ................................................. 32

3 Conclusiones .............................................................................................................. 33

4 Información sobre el Trabajo .................................................................................... 34

4.1 Universidad de destino ........................................................................................... 34

4.2 Presupuesto ............................................................................................................ 34

4.3 Planificación temporal ........................................................................................... 35

TRABAJO EN LA UNIVERSIDAD DE DESTINO ...................................................... 37





1. Introducción

1.1 Motivación e impacto

La industria de los semiconductores es una industria de tecnología puntera y necesita

seguir el ritmo de las tendencias más innovadoras, reducir el tiempo de ciclo del producto

y afrontar la nueva y fuerte competencia asiática. A la vez que supera dichos desafíos, las

empresas fabricantes de semiconductores tienen también que satisfacer una demanda

flexible aparte de dar un servicio de calidad a través de plazos más cortos.

La predicción de la demanda en la industria de los semiconductores es crítica debido a

los altos costes de producción, los largos tiempos requeridos para la fabricación y la alta

volatilidad del mercado.

Siguiendo la política “More-than-Moore”, la industria de los semiconductores trata de

diseñar nuevas formas de innovación que difieren de que meramente atañen al

semiconductor en sí. Es por ello, que la realización de una predicción de demanda cada

vez más precisa puede hacer destacar a las empresas de esta industria.

1.2 Definición del problema

El propósito de este Trabajo es la realización de la primera predicción en Infineon

Technologies AG a nivel cliente, con el objetivo de descubrir si el análisis en esta

granularidad lleva a una predicción más precisa y a un entendimiento mejor del

comportamiento del cliente que la realizada a nivel de departamentos

De las cinco diferentes divisiones de Infineon, la más grande en términos de beneficios y

también la más estable es la división de automoción. En consecuencia, se puede asegurar

que la creación de un modelo de predicción para los clientes de esta división será

suficientemente significativa y representativa a la hora de analizar clientes decisivos.

Además, esta estabilidad hace que la predicción sea más factible.

Se tratan pues, dos cuestiones de investigación principales. Por un lado, el análisis de

diferentes métodos que puedan mejorar las actuales predicciones a nivel cliente. Por otro

lado, se compararán los patrones de demanda de dos clientes con diferentes estrategias, a

corto y largo plazo, con respecto a la predicción.



1.3 Objetivos

Para comenzar, los objetivos básicos de este Trabajo son la comprensión de la

importancia de una predicción precisa en la cadena de suministro de la industria de los

semiconductores y la comprensión de la aplicación de los denominados “Crawl Charts”.

En este documento se analiza la diferencia en cuanto a predicción de la demanda de los

clientes con diferentes comportamientos en la demanda. Esto se consigue, a su vez,

analizando y comparando diferentes métodos de predicción y definiendo para cada cliente

un modelo específico que pueda minimizar en la medida de lo posible los intervalos de

predicción.

1.4 Impacto medioambiental

Este Trabajo en colaboración con Infineon, se encierra en el marco de IMPRES (Infineon

Integrated Management Program for Environment, Energy, Safety and Health), que ha

sido certificado acorde con ISO 14001 y OHSAS 18001. Adicionalmente, ha sido

certificada según ISO 50001, la gestión de la energía de los principales sitios de

producción europeos, además de la sede corporativa.

La industria de los semiconductores, debido a su rápida evolución, hace que sus productos

estén obsoletos en cortos periodos de tiempo, por lo que una predicción de demanda

precisa reduciría los stocks de dichos productos, reduciendo, a su vez, las emisiones de

CO2 derivadas de la producción y el gasto energético.



2. Desarrollo del Trabajo

2.1 Predicción de la demanda en la industria de los semiconductores

La predicción es el proceso de estimación dentro de la cadena de suministro en situaciones

futuras desconocidas, bajo riesgo e incertidumbre. Asimismo, la demanda aparece cuando

un cliente final solicita un cierto número de productos en una fecha determinada. Hay tres

dimensiones a través de las cuales el proveedor consigue agregar la demanda. Estas tres

dimensiones clave son: los productos, el tiempo y la localización. Por ejemplo, el cliente

A demandará el producto B el próximo mes, por lo que el proveedor tiene que producir

B antes de esa fecha y situarla y entregarla al cliente A. Esto significa que esas tres

dimensiones clave son la información básica para cualquier decisión en su respectivo

nivel organizacional. Consecuentemente, la planificación y la predicción están basadas

en este enfoque, ya que son la extrapolación en diferentes horizontes temporales.

Figura 1. Marco para la predicción. Fuente: Vollmann (2008)

Como se observa en la imagen anterior, dependiendo a qué granularidad se aplicará la

predicción, se tienen diferentes características, como son la frecuencia de predicción,

horizonte temporal o el coste del procesamiento y obtención de datos.

Partiendo de los datos históricos y a través de una metodología de predicción concreta, es

posible predecir los futuros pedidos de los clientes. El plan de producción adecuado será

organizado según estas predicciones. Los fabricantes predecirán con el objetivo de

asegurar que la producción consigue el suficiente nivel para satisfacer la demanda de sus

clientes.



Las predicciones aportan también un análisis intensivo del comportamiento del cliente y

esta información es crucialmente útil para tener un mejor control de las existencias y de

la capacidad. Es también importante la colaboración entre proveedor y cliente en cuanto

a la predicción con el objetivo de conseguir intervalos de predicción más precisos, ya que

la información es compartida y, de esta manera, la información usada no es tan limitada

como la que pueden tener por separado cada uno de los colaboradores de la cadena de

suministro.

Cuando esta colaboración no ocurre, se experimenta el llamado “efecto látigo” o

“bullwhip effect”. El efecto látigo se refiere la tendencia de los pedidos a aumentar en

variabilidad a la vez que escala en la cadena de suministro (Lee, Padmanabhan, & Whang,

1997).

Observando los datos históricos, se puede establecer también dos nuevos componentes

claves que influyen en las predicciones. Estos dos componentes son la estacionalidad y la

tendencia. Por un lado, la estacionalidad es la característica de una serie temporal que

indica cualquier cambio predecible o patrón que se repite cada periodo de un año o menos.

Por otro lado, las tendencias se caracterizan por una pendiente creciente o decreciente.

La industria de los semiconductores es conocida por ser una de las industrias más

dinámicas del mundo. Debido a esta alta dinámica mercantil, los semiconductores tienen

un ciclo de vida corto, como señaló Moore (1965). Moore, cofundador de Intel, predijo

que el número de transistores por microprocesador se doblaría cada cierto periodo de

tiempo, entre 18 y 24 meses, dando así una fecha final para el desarrollo total de los

semiconductores. Esta es la llamada ley de Moore y, como se puede observar en la

siguiente gráfica, es una aproximación que se adecua bastante a los datos reales. Por ende,

los fabricantes de semiconductores tienen que innovar continuamente para concebir

productos más avanzados y baratos.



Figura 2. Ley de Moore para los microprocesadores. Fuente:

http://www.cmg.org/measureit/issues/mit41/m_41_2.html (04.06.2010)

Una de las características principales de la industria de los semiconductores es la alta

volatilidad. Aunque a largo plazo, el mercado aumenta constantemente, excepto por la

caída en 2009, consecuencia de la crisis financiera mundial, se pueden observar grandes

fluctuaciones en la demanda en los últimos 40 años, yendo desde +70% a -40%.

Figura 3. Los ingresos en billones de dólares americanos y la tasa de crecimiento del Mercado

global de los semiconductores. Fuente: The World Semiconductor Trade Statistics (WSTS) for

historical data: Infineon Intern (28.04.2010)



2.2 Infineon Technologies AG

Esta empresa se dedica al diseño, desarrollo, fabricación y marketing de semiconductores

y sistemas completos (MarketLine, 2015). Infineon opera en cinco distintos segmentos

de negocio: microprocesadores y seguridad, gestión de la potencia, automoción, control

de potencia industrial y otros sistemas operativos.

Todos los datos usados y los resultados obtenidos en este Trabajo son de aplicación

exclusiva en el departamento de automoción (ATV). Este segmento se centra en

semiconductores de potencia, sensores, controladores y semiconductores discretos. Estos

productos son usados en diferentes aplicaciones como la apertura del vehículo sin llaves,

la gestión de la seguridad o el control de las ventanillas.

La estructura de la cadena de suministro de Infineon Technologies está basado en el

modelo SCOR® (Supply Chain Operations Reference Model), que es un modelo de

referencia de procesos creado por el Asociación APICS. El modelo SCOR® divide la

cadena de suministro en cinco secciones: Planificación, Fuente, Hacer, Repartir y

Devolver, como se ve en la siguiente imagen.

Figura 4. Cadena de Suministro según SCOR. Fuente: Infineon Technologies Intern

Este Trabajo se centrará en la sección de Planificación, la cual contempla la gestión de

pedidos, la gestión de demanda, la planificación de la capacidad y la gestión de la

producción. El objetivo principal de este Trabajo es recoger los datos históricos de los

pedidos de cada uno de los clientes y proporcionar una predicción del número total de



productos al final de cada trimestre. Este valor predicho puede ser usado tanto por el

departamento financiero como por los planificadores de la cadena de suministro, los

cuales pueden gestionar la producción teniendo en cuenta el valor aproximado dado.

2.3 Metodología

2.3.1 Representación de los datos

El “CEBIS Order Development Crawl Chart” es una gráfica que refleja la evolución del

negocio mostrando los beneficios trimestrales acumulados del pasado y la perspectiva del

beneficio más probable basado en los pedidos en mano, la predicción del cliente y los

beneficios anteriores. Los pedidos en mano son aquellos realizados por el cliente y

confirmados por Infineon. Estas gráficas comprenden desde la semana -26 (26 semanas

antes de que comience el trimestre) hasta la semana 14, que significa el fin de trimestre.

La semana 0 simboliza el inicio del trimestre y con él los pedidos en mano comienzan a

transformarse también en beneficios, por lo que, tras el inicio del trimestre, aparece una

mezcla de pedidos y beneficios. Los datos utilizados para la realización de estas gráficas

se recogen de la base de datos interna para los informes de Infineon, llamada CEBIS.

Figura 5. CEBIS Crawl Charts. Fuente: Knezevic (2016)

Actualmente, el método de predicción usado en la división automovilística se llama

“análisis Quarter-on-Quarter”. Este método se basa en que el cambio porcentual de los

pedidos en comparación con los trimestres anteriores producirá el mismo cambio en el

beneficio final. Por ejemplo, si para la semana -13 la cantidad de pedidos aumenta un



20% con respecto al trimestre anterior, el beneficio esperado para el final del actual

trimestre, semana 14, será también 20% mayor que el beneficio del trimestre pasado.

Matemáticamente, el análisis Quarter-on-Quarter (QoQ) es:

𝑅𝐸𝑉𝑞 = REVq−1 ∗𝑂𝑂𝐻𝑡,𝑞

𝑂𝑂𝐻𝑡,𝑞−1

Donde R𝐸𝑉𝑞 es el beneficio final del trimestre, 𝑅𝐸𝑉q-1 es el del trimestre anterior y OOH

significa pedidos en mano para la semana t. En consecuencia, semana a semana se puede

conseguir una predicción del beneficio final.

Sin embargo, este método no es aplicable a nivel cliente, ya que la base de datos CEBIS

sólo guarda la información del último año, lo que resulta en 4 datos puntuales para cada

semana. Consecuentemente, para conseguir un modelo de predicción fiable, se necesitan

recoger más datos. Por ello, se usa la base de datos EDI (Electronic Data Interchange).

El EDI es una interfaz electrónica para intercambiar información entre dos empresas, que

en este caso son Infineon y el cliente. En ella, el cliente hace los pedidos de compra, da

una predicción estimada y recibe confirmaciones y notificaciones de envíos. En el EDI,

los datos de los pedidos hechos por un cliente desde el tercer trimestre, expresado en año

fiscal, están disponibles en términos de unidades de producto. Debido a la gran cantidad

de datos necesarios para extraer dicha información, el EDI fue transferido primero desde

el software especializado a un archivo de texto y de ahí a diferentes libros de Excel, 5 por

cada año de datos, por la limitación de la memoria de procesamiento de Excel. Los

parámetros utilizados para la obtención de la información final fueron: Nombre del

Cliente, Pedidos en piezas, Semana de entrega y Diferencia en Semanas entre el Pedido

y la Entrega.

En este Trabajo se analizarán dos clientes, uno con una estrategia de demanda a corto

plazo, A, y otro a corto, B. Los gráficos que se presentan a continuación muestran dicha

diferencia en el comportamiento de los dos clientes.



Figura 6. Pedidos en EDI para el cliente A

Figura 7. Pedidos en EDI para el cliente B

A partir de estos datos, se puede realizar una aproximación a los CEBIS Crawl Charts,

obteniendo una curva acumulativa en la que cada una representa el valor de la suma de

los pedidos de las semanas anteriores y la de la semana actual. Estos Crawl Charts

modificado, de ahora en adelante EDI Crawl Charts, al final del trimestre representan el

valor de la cantidad total de pedidos realizados por un cliente.



Figura 8. EDI Crawl Charts para el cliente A

Figura 9. EDI Crawl Charts para el cliente B

Las diferencias principales entre estos Crawl Charts propios, EDI, y los ya establecidos,

CEBIS, son que no se consideran las cancelaciones ni los pedidos realizados antes de la

semana -26. Al no incluir las cancelaciones, los EDI Crawl Charts no sufren ningún

cambio en la pendiente, que haga que los pedidos desciendan cuando comienza el

cuatrimestre y el cliente decide si continúa o no con los pedidos planeados. Se puede

apreciar este comportamiento en las gráficas normalizadas, como las siguientes:



Figura 10. CEBIS Crawl Charts normalizados para la división automovilística. Fuente: Knezevic

(2016)

Figura 11. EDI Crawl Charts normalizados para los clientes A y B

De estos Crawl Charts normalizados, se puede apreciar un hecho diferencial: la ordenada

en el origen. Mientras que en los CEBIS Crawl Charts muestran una ordenada en el origen

(Figura 15), entre 0.5 y 0.8, como consecuencia de los pedidos anteriores a la semana -

26, la ausencia de estos datos en EDI, hace que los EDI Crawl Charts empiecen casi desde

el origen (figura 16).

Además, se puede distinguir otra característica entre el cliente A y el cliente B con

respecto a su comportamiento en los pedidos. Las curvas del cliente B en los EDI Crawl

Charts normalizados se asemejan a una función linear y los diferentes trimestres se

superponen más que los del cliente A.

Los EDI Crawl Charts no incluyen la semana cero y terminan en la semana +12. Esto se

debe a que se considera la semana 1 como el inicio y el final en la semana 13. De esta

Customer A Customer B



manera, la semana 0 de los CEBIS Crawl Charts es la semana 1 de los EDI Crawl Charts

y la semana 13 de los CEBIS Crawl Charts es la semana 12 de los EDI Crawl Charts.

2.3.2 Selección del método de predicción

A la hora de elegir el método de predicción, se consideran dos principales opciones: los

modelos autorregresivos integrados de media móvil (ARIMA) y los modelos de patrones

estacionales estables (SSPM). La razón por la que se consideran solo estos dos modelos

es porque ambos son una agregación de diferentes modelos.

ARIMA es una combinación de modelos diferenciación con autorregresión y media móvil

basado en una serie temporal, cuya fórmula es:

𝑦𝑡′ = 𝑐 + 𝜑1𝑦𝑡−1

′ + ⋯ + 𝜑𝑝𝑦𝑡−𝑝′ + 𝜃1𝑒𝑡−1 + ⋯ + 𝜃𝑞𝑒𝑡−𝑞 + 𝑒𝑡 (1)

y’t series diferenciadas; c constante; et ruido blanco; φ parámetro autorregresivo; θ el

parámetro de media móvil.

Los modelos ARIMA no estacionales dependen de tres diferentes parámetros, p,d y q,

donde p es el orden de la parte autorregresiva, d es el grado de la primera diferenciación

involucrada y q es el orden de la parte de la media móvil.

Los modelos ARIMA cubren la mayoría de los modelos de predicción para series

temporales. Estas series deben ser estacionarias o ser hechas estacionarias mediante

diferenciación. Estacionario significa que la serie no tiene tendencia y que varía entorno

a su media con una amplitud constante y, por lo tanto, sus autocorrelaciones se mantienen

constantes también.

Cumpliendo los requisitos anteriores, se consiguen los diferentes modelos con los valores

de p, d y q. De esta manera, el modelo más sencillo, ARIMA(0,0,0), sería simple ruido

blanco y ARIMA(0,1,0), camino aleatorio. Los modelos del tipo ARIMA(p,0,0) serían

autorregresiones y los ARIMA(0,0,q), medias móviles.

Aplicando la función auto.arima() en el software estadístico R, se obtienen los mejores

modelos ARIMA partiendo de los datos de los EDI Crawl Charts. Se minimizan el

Criterio de Información de Akaike Corregido (AICc), que se explicará más adelante, y la

Máxima Verosimilitud para obtener el modelo más preciso. Cuanto menor es el valor de

estas dos medidas, mejor el modelo ARIMA.



La función sigue el algoritmo de Hyndman-Khandakar, que consiste en la modelación del

número de diferencias, d, a través de los tests de Kwiatkowski-Phillips-Schmidt-Shin

(KPSS) y de los valores de p y q usando la selección por pasos (Stepwise Procedure) para

obtener el mínimo AICc (Hyndman & Athanasopoulos, 2013).

Empleando esta función para los clientes elegidos, se consigue para el cliente A un

modelo ARIMA(1,1,0) con deriva, el cual es un modelo autorregresivo de primer orden

de diferenciación. Se pueden apreciar los intervalos de predicción del 80% y el 90% en

la siguiente gráfica:

Figura 12. Predicción ARIMA(1,1,0) con deriva para el cliente A

En cuanto al cliente B, auto.arima() devuelve el modelo ARIMA(0,1,0), que es un modelo

de predicción de camino aleatorio.

Figura 13. Predicción ARIMA(0,1,0) para el cliente A



Sin embargo, Alba y Mendoza (2001), demostraron que mientras que los modelos

ARIMA precisan de más de 50 observaciones, 100 para algunos autores, para ser

aplicados con exactitud, los modelos SSPM pueden trabajar con muestras más pequeñas.

Como en este caso, se tienen 12 observaciones, SSPM es el método que debe ser elegido.

En este Trabajo, se demuestra que los datos utilizados cumplen con los requisitos de los

modelos SSPM, y que de entre ellos, el que resulta en intervalos de predicción más

precisos es la regresión lineal.

Tras comprobarse el cumplimiento de las hipótesis necesarias para la aplicación de la

regresión lineal, se concluye que el objetivo ideal es la obtención de un modelo de

regresión para cada cliente. Las mismas variables serán consideradas para las diferentes

semanas, para así evitar una alta complejidad. El cálculo de la predicción seguirá el

siguiente diagrama de flujo:

Figura 14. Procedimiento para la predicción con regresión lineal

La selección de todas las variables posibles se realizará en una sola ocasión y el resultado

es el siguiente:

Pedidos en Mano de los clientes en piezas (OOH).



Pedidos en Mano + Ingresos de la división automovilística en piezas

(OOHUMatv).

Pedidos en Mano + Ingresos de Infineon Technologies en piezas (OOHUMifx).

Estacionalidad por trimestres (Q1, Q2, Q3).

Tendencia.

𝑂𝑂𝐻13,𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 = 𝛽𝑜 + 𝛽1 ∗ 𝑂𝑂𝐻𝑡,𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 + 𝛽2 ∗ 𝑂𝑂𝐻𝑈𝑀𝑡,𝑎𝑡𝑣 + 𝛽3 ∗

𝑂𝑂𝐻𝑈𝑀𝑡,𝑖𝑓𝑥 + 𝛽4 ∗ 𝑄1 + 𝛽5 ∗ 𝑄2 + 𝛽6 ∗ 𝑄3 + 𝛽7 ∗ 𝑡𝑟𝑒𝑛𝑑 + 𝑒𝑡 (2)

El siguiente paso que hay que realizar es el procedimiento de selección de pasos inverso

(Backwards Stepwise Procedure), que consiste fundamentalmente en:

1. Empezar con el modelo que incluye todas las variables escogidas.

2. Eliminar variables individualmente y conservar el modelo si hay una mejora en

las medidas de precisión de la predicción.

3. Iterar hasta que no se encuentre ninguna mejora más.

La medida de precisión de la predicción utilizada es el Criterio de Información de Akaike

Corregido (AICc), que se define de la siguiente manera:

𝐴𝐼𝐶𝑐 = 𝐴𝐼𝐶 + 2(𝑘 + 2)(𝑘 + 3)

𝑁 − 𝑘 − 3 (3)

Siendo

𝐴𝐼𝐶 = 𝑁𝑙𝑜𝑔 (𝑆𝑆𝐸

𝑁) + 2(𝑘 + 2) (4)

Donde k es el número de variables en el modelo y N es el número de observaciones. SSE

es la suma de los errores estándares. El mejor modelo de predicción es aquél con el

mínimo AICc.

2.4 Resultados

Por un lado, para el cliente A se puede observar que, para la mayoría de las semanas, los

Pedidos en Mano del cliente y la variable ficticia estacional, o dummy, Q1 son las

variables más significativas, como se aprecia más adelante en la Tabla 3.



𝑂𝑂𝐻13 = 𝛽𝑜 + 𝛽1 ∗ 𝑂𝑂𝐻𝑡 + 𝛽2 ∗ 𝑄1 (5)

Por otro lado, el análisis del cliente B muestra que no hay un patrón estacional claro y

que, además de los Pedidos en Mano del propio cliente, la otra variable significativa son

los Pedidos en Mano + Ingresos de la división automovilística (ver tabla 4).

𝑂𝑂𝐻13 = 𝛽0 + 𝛽1 ∗ 𝑂𝑂𝐻𝑡 + 𝛽2 ∗ 𝑂𝑂𝐻𝑈𝑎𝑡𝑣,𝑡 (6)

En estas dos tablas, los valores en rojo poseen un t-valor inferior a 0.05, los verdes

inferiores a 0.001 y finalmente los azules tiene significancia prácticamente nula.

Para esos dos modelos finales, se repite el experimento de la regresión para obtener el

valor de las variables predictoras.











Ahora que se tienen los resultados finales, se procede con el análisis de los residuos con

el objetivo de comprobar si las suposiciones del modelo han sido o no satisfechas.

La primera suposición es la falta de autocorrelación, la cual se comprueba a través del

estadístico de Durbin-Watson. Se considerarán críticos aquellos valores del estadístico de

Durbin-Watson que sean inferiores a 1 o superiores a 3. El estadístico mencionado viene

definido por la siguiente fórmula:

𝑑 =∑ (𝑒𝑡 − 𝑒𝑡−1)²𝑇

𝑡=2

∑ 𝑒𝑡²𝑇𝑡=1

(7)

Donde et es el residuo de la observación t y T es el número total de observaciones.

En los gráficos mostrados a continuación se puede comprobar que los valores están

comprendidos en todo momento entre 1 y 3. Por lo que se puede concluir que se cumple

la suposición inicial de autocorrelación nula.

Figura 15. Distribución del estadístico Durbin-Watson para el cliente A

Figura 16. Distribución del estadístico Durbin-Watson para el cliente B

Para comprobar la normalidad de los residuos, se usa el test de Jarque-Bera (Hyndman &

Athanasopoulos, 2013), cuya fórmula matemática dice:

,000

1,000

2,000

3,000

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week

Durbin Watson Statistic

,000

1,000

2,000

3,000

4,000

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week




𝐽𝐵 =𝑛 − 𝑘

6(𝑆2 +

1

4(𝐶 − 3)2) (8)

Donde n es el número de observaciones y k el número de variables. S es la asimetría de

la muestra y C la curtosis de la muestra:

𝑆 =

1𝑛

∑ (𝑥𝑖 − �̅�)3𝑛𝑖=1

(1𝑛

∑ ((𝑥𝑖 − �̅�)²)3/2𝑛𝑖=1 )

(9)

𝐶 =

1𝑛

∑ (𝑥𝑖 − �̅�)4𝑛𝑖=1

(1𝑛

∑ ((𝑥𝑖 − �̅�)²)2𝑛𝑖=1 )

(10)

Figura 17. Jarque Bera test para el cliente A

Figura 18. Jarque Bera test para el cliente B

0,00

0,50

1,00

1,50

2,00

2,50

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week

Jarque Bera Test

0,00

2,00

4,00

6,00

8,00

10,00

12,00

14,00

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week

Jarque Bera Test



Examinando este estadístico a través de una distribución normal de alfa 5%, se concluye

que solo para las semanas 9 y 10 del cliente B, la condición de que los residuos están

distribuidos normalmente no se cumple. En consecuencia, la predicción basada en esas

dos semanas para ese específico cliente no es fiable sin un mayor y avanzado análisis.

Tras esto, el test final es el Coeficiente de Determinación Corregido, que mide el

porcentaje de los valores finales que son explicados por la función regresión. Viene

definido por la siguiente fórmula:

𝑅²̅̅ ̅ = 1 − (1 − 𝑅2)𝑛 − 1

𝑛 − 𝑝= 𝑅2 − (1 − 𝑅2)

𝑝 − 1

𝑛 − 𝑝

(11)

Donde p es el número total de variables independientes del modelo y n es el tamaño de la

muestra.

Para analizar esta medida, se debe saber que cuanto más cercano a 1 (100%), mayor será

el número de valores de la predicción explicados por la regresión. Como se observa en

las gráficas a continuación, las primeras 4 semanas para el cliente A, con estrategia de

demanda a corto plazo, tienen un valor del Coeficiente de Determinación Corregido. Sin

embargo, se puede apreciar que el cliente B, con estrategia de demanda a largo plazo,

obtiene un valor aceptable desde el principio.

Figura 19. Coeficiente de Determinación Corregido para el cliente A

000%

020%

040%

060%

080%

100%

120%

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week

Adjusted Coefficient of Determination



Figura 20. Coeficiente de Determinación Corregido para el cliente B

Se comparan ahora los dos clientes con los valores obtenidos para la división

automovilística, ATV, y se observa que se consigue un mejor valor del Coeficiente de

Determinación Corregido a nivel cliente.

Figura 21. Comparación del Coeficiente de Determinación Corregido

Como se explicó anteriormente, el Criterio de Información de Akaike Corregido (AICc)

indica la habilidad de predicción de un modelo. Sin embargo, para comparar el AICc a

nivel cliente, con solo 12 observaciones, y la división ATV, con 20 observaciones, se

define el AICc Medio, que viene determinado por el AICc para la semana t dividido por

el número de observaciones.

075%

080%

085%

090%

095%

100%

105%

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week


0,00

0,20

0,40

0,60

0,80

1,00

1,20

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week


Customer B Customer A ATV



Figura 22. Comparación del Criterio de Información de Akaike

En esta gráfica se puede ver que casi no existe diferencia en el AICc Medio, lo cual

significa que los tres modelos de regresión tienen similar precisión en la predicción.

En cuanto a los resultados más importantes de los modelos de regresión, los intervalos de

predicción, se da la siguiente definición:

�̂�𝑥0± 𝑡

𝑛−𝑘,1−𝛼2

∗ �̂�√1 + 𝑥0𝑇(𝑋𝑇𝑋)−1𝑥0

(12)

𝑌𝑥0 es el valor predicho, t es el estadístico-t con n-k grados de libertad y el valor dentro

de la raíz cuadrada es el error estándar de predicción.

Se muestra en la siguiente gráfica los intervalos de predicción de ambos clientes y de la

división automovilística.

0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

40,00

45,00

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week

Average AICc

Customer B Customer A ATV



Figura 23. Comparación de los intervalos de predicción 80% de confianza

2.5 Integración de los resultados en los Crawl Charts

La idea es que el Planificador de la Cadena de Suministro solo tenga que actualizar los

datos necesarios para definir los EDI Crawl Charts en el libro de Excel denominada la

“Herramienta de Predicción de EDI Crawl Charts”, que consiste en una interfaz fácil de

usar que realiza automáticamente los cálculos descritos a lo largo de este Trabajo,

aplicando las funciones de regresión que calculan el valor de predicción final. También,

calcula el error estándar de predicción para realizar los intervalos de predicción.

Figura 24. Ejemplo del resultado de la aplicación de la Herramienta de Predicción de EDI Crawl

Charts

0

20

40

60

80

100

120

140

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week

80% Confidence Prediction Intervals

Customer B Customer A Automotive Division

000

100.000.000

200.000.000

300.000.000

400.000.000

500.000.000

600.000.000

-26

-23

-20

-17

-14

-11 -8 -5 -2 2 5 8

11O

rde

rs o

n H

and

s at

th

e e

nd

of

the

Q

uar

ter

(pcs

)

Week

2016Q4

2016Q1

2016Q3

Low 80

High 80

Model Estimation



3. Conclusiones

El mayor desafío de este Trabajo fue la recopilación de datos. CEBIS, el servidor de datos

interno para los informes de Infineon, sólo ofrecía 4 observaciones a nivel cliente. 4

puntos no son suficientes para aplicar ninguna técnica de predicción y, por eso, se tenía

que considerar otro planteamiento en cuanto a los datos. Esta es la razón por la que no se

tuvo en cuenta los datos de CEBIS, si no los de EDI, que proporcionaba 12 observaciones.

Después de recorrer la literatura relacionada con el tema y los métodos aplicados en la

empresa, se decidió que los modelos de regresión eran la primera opción realista para

predecir con los Crawl Charts. Sin embargo, también se analizaron los modelos ARIMA,

con el objeto que cubrir la mayoría de las técnicas de predicción.

La regresión múltiple linear requiere recopilar las variables significativas para el modelo.

Se decidió usar variables que poseían un formato similar a los Crawl Charts, como los

Pedidos en Mano + Ingresos de la división automovilística, como también la

estacionalidad y la tendencia.

Tras haber elegido todas estas variables, se aplicó el procedimiento por pasos inverso para

eliminar aquellas variables no significativas y obtener así el mejor modelo posible. Para

cada semana de cada cliente, se consigue un modelo de regresión distinto. Sin embargo,

se decidió usar un solo modelo de regresión final para cada cliente, con el objetivo de

facilitar la incorporación de los resultados en la herramienta creada en Excel.

Una vez elegidos los dos modelos finales, se realiza un análisis de sensibilidad para

comprobar las suposiciones hechas para los modelos de predicción con regresión. Usando

el estadístico de Durbin-Watson, el test de Jarque-Bera, el Coeficiente de Determinación

Corregido y el Criterio de Información de Akaike Corregido se pudieron corroborar las

suposiciones mencionadas.

Después de haber validado los modelos, se pudo predecir el valor final de los pedidos

acumulados hechos en un trimestre para cada cliente desde la semana -26 hasta la semana

+11. Consecuentemente, es posible entonces el cálculo de los intervalos de predicción,

en este caso al 80% de confianza, y la integración en una herramienta para los

planificadores de la cadena de suministro.



4. Información sobre el Trabajo

4.1 Universidad de destino

La Universidad Técnica de Múnich, fundada en 1868, actualmente cuenta con unos

40.000 estudiantes de todo el mundo y es una de las universidades más importantes para

el desarrollo industrial del estado de Baviera. Personalidades como Carl von Linde o

Rudolf Diesel, así como también otros 13 premios Nobel, han pertenecido a esta

institución.

La “School of Management” está situada en el campus central de la universidad. Este

Trabajo fue realizado en el Departamento de Logística y Gestión de la Cadena de

Suministro. La tutora de este Trabajo fue Miray Öner-Közen.

4.2 Presupuesto

El sueldo de la tutora viene establecido por el estado de Baviera para los estudiantes de

PhD., el cual equivale a 30 horas de trabajo a 22,8€/h (Freistaat Bayern: Landesamt für

Finanzen.http://www.lff.bayern.de/download/bezuege/arbeitnehmer/entgelttabelle_tvl.p

df, 12.07.2015), dando un total de 684,00€.

El sueldo del autor es nulo. La licencia del software RStudio es gratuita y la de Microsoft

Office es de 79,00€. El coste total del trabajo es de 763,00€.

http://www.lff.bayern.de/download/bezuege/arbeitnehmer/entgelttabelle_tvl.pdf

http://www.lff.bayern.de/download/bezuege/arbeitnehmer/entgelttabelle_tvl.pdf



4.3 Planificación temporal





TRABAJO EN UNIVERSIDAD DE DESTINO

A continuación, se presenta el documento en inglés realizado en la Universidad Técnica

de Múnich. Este trabajo pertenece a la categoría de Bachelorarbeit reconocido con 12

ECTS.

Bachelor of Science an der Technischen Universität München

Forecasting Semiconductor Turnover for

Automotive Customers

Referent: Logistics and Supply Chain Management

Prof. Dr. Stefan Minner

Technische Universität München

Betreuer: Miray Öner-Közen, M.Sc.

Dr. Thomas Ponsignon from Infineon Technologies AG

Can Sun, M.Sc. from Infineon Technologies AG

Studiengang: Technologie- und Managementorientierte Betriebswirtschaftslehre

ERASMUS Exchange

Eingereicht von: Darío Khambatta Moreno

Connollystr. 3 , i12

80809 München

Matrikelnummer 03672591

Eingereicht am: 20.07.2016

ii

iii

Abstract

In this thesis the problem of forecasting at customer level with small amount of

data is addressed. It is the first forecasting analysis done at this granularity in

Infineon Technologies AG and its importance is critical because it provides new

results which are compared with the current forecasting methods applied in a

higher level, in this case divisions. The current “As-Is Status” of the forecasting

methodologies applied at the company is shown and, considering also new mod-

els, multiple linear regression is chosen as the forecasting technique to apply. The

shortage of relevant data at customer level was the most problematic issue for the

realization of this thesis, but the definition the so-called EDI Crawl Charts solved

it. A general procedure to forecast with linear regression for customers is ex-

plained and final regression models for each one are explained. Moreover, this

paper introduces the EDI Order Development Crawl Chart Tool, which is the

integration of the final forecasting models into Excel for the Supply Chain Plan-

ners.

iv

v

Table of Contents

Table of Contents ..................................................................................................... v

List of Figures ........................................................................................................ vii

List of Tables .......................................................................................................... ix

List of Abbreviations .............................................................................................. xi

1 Introduction........................................................................................................... 1

1.1 Forecasting in Supply Chain Management ........................................ 1

1.2 Semiconductor Industry ..................................................................... 3

1.3 Forecasting in the Semiconductor Industry ........................................ 8

2 Review of Literature and Research ..................................................................... 10

2.1 Forecasting Techniques .................................................................... 10

2.2 Forecasting Processes ....................................................................... 15

2.3 Forecasting Accuracy Measures ....................................................... 17

2.4 Demand Generation .......................................................................... 21

3 Methodology ....................................................................................................... 25

3.1 Data Representation ......................................................................... 25

3.2 Forecasting Technique Selection ..................................................... 29

3.3 Multiple Linear Regression .............................................................. 32

4 Results ................................................................................................................ 37

4.1 Integration of the Model into the Order Development Crawl Charts

............................................................................................................................ 48

5 Conclusion .......................................................................................................... 50

Bibliography .......................................................................................................... 53

Appendices ............................................................................................................ 57

Declaration of Authorship ..................................................................................... 61

vi

vii

List of Figures

Figure 1. Framework for Forecasting. Source: Vollmann 2008 .............................. 1

Figure 2. Moore's law for memory chips and microprocessors. Source:


................................................................................................................. 4

Figure 3. The Revenue in US billions and market growth rate of the global

semiconductor market. Source: The World Semiconductor Trade

Statistics (WSTS) for historical data: Infineon Intern (28.04.2010) ....... 4

Figure 4. Production flow by Infineon Technologies with Frontend (FE) and

Backend (BE). Source: Infineon Technologies Intern ............................. 5

Figure 5: Illustration of the Supply Chain Partners and their PCT. Source: Vaupel

2013 ......................................................................................................... 6

Figure 6. Supply Chain according to SCOR. Source: Infineon Technologies Intern

................................................................................................................. 7

Figure 7. New Forecast Map at Infineon Technologies .......................................... 8

Figure 8. CEBIS Crawl Charts. Source: Knezevic 2016 ....................................... 14

Figure 9. Infineon Granularities. Source: Ott et al. 2013 ...................................... 16

Figure 10. Granularity Total Accuracy Findings based on SMAPE3. Source: Ott

et al. 2013 .............................................................................................. 16

Figure 11. Orders from EDI for the Customer A................................................... 26

Figure 12. Orders from EDI for the Customer B ................................................... 26

Figure 13. EDI Crawl Charts for Customer A ....................................................... 27

Figure 14. EDI Crawl Charts for Customer B ....................................................... 27

Figure 15. Normalized CEBIS Crawl Charts for the Automotive Division. Source:

Knezevic 2016 ....................................................................................... 28

Figure 16. Normalized EDI Crawl Charts for Customers A and B ....................... 28

Figure 17. Forecast from ARIMA(1,1,0) with drift for Customer A .................... 31

Figure 18. Forecast from ARIMA(0,1,0) for Customer B ..................................... 31

Figure 19. Linear Regression Forecasting Procedure ............................................ 33

Figure 20. Durbin-Watson Statistic Distribution for Customer A ......................... 42

Figure 21. Figure 20. Durbin-Watson Statistic Distribution for Customer B ....... 43

Figure 22. Jarque Bera test for Customer A .......................................................... 43

Figure 23. Jarque Bera test for Customer B .......................................................... 44

Figure 24. Adjusted Coefficient of Determination for Customer A ...................... 45

Figure 25. Adjusted Coefficient of Determination for Customer B ...................... 45

viii

Figure 26. Comparison of the Adjusted Coefficients of Determination ................ 46

Figure 27. Average Akaike's Information Criterion Comparison ......................... 47

Figure 28. 80% Confidence Prediction Intervals Comparison .............................. 48

Figure 29. Forecasting Methods regarding demand history and time horizon ...... 49

Figure 30. Example of the result of the application of the EDI Order Development

Crawl Chart Excel Tool………………………………………………………….49

ix

List of Tables

Table 1. Europe semiconductors market value forecast: $ billion, 2014-19 ........... 5

Table 2. As-Is Status of the Forecasting methods at Infineon Technologies. ....... 10

Table 3. Results of the application of Multiple Linear Regression with Equation

30 for Customer A. ................................................................................ 38

Table 4. Results of the application of Multiple Linear Regression with Equation

30 for Customer B. ................................................................................ 40

x

xi

List of Abbreviations

AIC

AICc

ARIMA

ATV

BE

CCS

CEBIS

CT

EDI

FC

FO

GMRAE

IFX

MAPE

MPE

OOH

OOHUM

PCT

QoQ

R&D

RMSE

SCOR

SKU

SMAPE

SSPM

VRFC

Akaike’s Information Criterion

Corrected Akaike’s Information Criterion

Autoregressive Integrated Moving Average

Automotive Division

BackEnd

Chipcard & Security Division

Centrak Business Information System

Cycle Time

Electronic Data Interchange

Forecast

Firm Orders

Geometrical Mean Relative Absolute Error

Infineon Technologies AG

Mean Absolute Percentage Error

Mean Percentage Error

Orders on Hands

Orders on Hands + Revenue

Product Cycle Time

Quarter on Quarter

Research & Development

Root Mean Square Error

Supply Chain Operations Reference Model

Stock Keeping Unit

Symmetrical Mean Absolute Percentage Error

Seasonal Stable Pattern Model

Volume Rolling Forecasting

xii

1

1 Introduction

1.1 Forecasting in Supply Chain Management

In 1982, Arnold Kransdorff wrote an article in the Financial Times where he at-

tributed the term “Supply Chain” to Keith Oliver. As Oliver defined, Supply

Chain Management is “the process of planning, implementing, and controlling the

operations of the supply chain with the purpose to satisfy customer requirements

as efficiently as possible. Supply Chain Management spans all movement and

storage of raw materials, work-in-process inventory, and finished goods from

point-of-origin to point-of-consumption”. Within Supply Chain Management, we

can find the following subareas: Forecasting/Planning, Purchasing/Procurement,

Logistics, Operations, Inventory Management, Transport, Warehousing, Distribu-

tion and Customer Service (Heckmann, Shorten, & Engel, 2003).

For this thesis, we will focus on the first subarea, Forecasting/Planning. Forecast-

ing is the process of estimation in unknown future situations under risk and uncer-

tainty. Supply Chain Forecasting, in our case, informs different levels of decision

making, from Inventory Control at the individual Stock Keeping Unit (SKU) level

to a higher aggregate level, involving strategic decisions. Reconciliations of fore-

casts acquires great significance and importance in the Sales and Operations Plan-

ning processes (Figure 1) and therefore, in the Orders Management. However, the

compatibility between the forecast output and the time series which via extrapola-

tion form the input data, has not been an important matter when it comes to fore-

casting literature and consequently, the studies regarding this topic are limited.

(Syntetos, Babai, Boylan, Kolassa, & Nikolopoulos, 2016).

Figure 1. Framework for Forecasting. Source: Vollmann (2008)

Demand occurs when an End Customer orders a certain number of products at a

concrete point in time. There are three dimensions along which the supplier ag-

2

gregates the demand. These key dimensions are: products, time and locations. For

instance, customer A will demand product B next month, so the supplier has to

produce B before that date and locate and deliver it to the customer A. This means

that those three key dimensions are the basic information for the decision making

at the respective organizational level. Consequently, Planning and Forecasting are

based on the previous approach, as it is the extrapolation into different time hori-

zons.

As we observe on Figure 1 on the next page, depending on which granularity the

forecast will be applied to, we have different characteristics, such as forecast fre-

quency, length of forecast or cost of data processing and acquisition.

From historical data and through a concrete forecasting methodology, we are able

to predict future customers’ orders. The adequate production plan will be arranged

based on these predictions. Manufacturers will forecast in order to ensure that the

production get the sufficient level to satisfy their customer’s demand. It is worth

to highlight that the manufacturer should avoid producing an overcapacity and a

shortfall situation, as having too much inventory or not having enough to fulfill

the customer’ orders could both mean a financial catastrophe. This is called over-

and under-forecasting, respectively (Murray, 2016). These two issues will be ad-

dressed along the present thesis.

Forecasts give us also an intensive analysis of the customers’ behavior and this

information is crucially helpful in order to have a better control of the stock and

capacity. Accurate forecasts lead us to an efficient production, avoiding having

unused machinery or employees and making possible the products’ delivery to the

customer on time. It is also important the collaboration between supplier and cus-

tomer regarding forecasting in order to get more precise prediction intervals, as

the information is shared and therefore, the used data is not as limited as the one

of only one of both supply chain partners.

When this collaboration does not exist or is it not sufficient, we experience the so-

called “bullwhip effect”. The bullwhip effect refers to the tendency of orders to

increase in variability as it moves up the supply (Lee, Padmanabhan, & Whang,

1997). In the simplest situation, the customer demand leads to an order from the

retailer to fulfill its stock requirements, which at the same time reduces the stock

of the next step and this last orders to the next one, which could be for example

the manufacturer, and so until the chain is finished (Syntetos, Babai, Boylan,

Kolassa, & Nikolopoulos, 2016). The bullwhip effect has also been an object of

study regarding forecasting and that is the case of Najafi and Zanjirani Farahani

3

(2014), who analyzed the magnitude of the effect using different forecasting

methods.

To demonstrate the bullwhip effect the researchers use the “Beer Distribution

Game” (Sterman, 1989). As well as explaining graphically the significance of this

effect, researchers can get useful data out of the users to analyze topics like human

behaviors in complex systems, as C. Sun, T. Ponsignon and T. Rose (2015) stud-

ied in order to apply an agent-based modeling approach.

By observing historical data, we can also establish two new key components that

influent the forecasts. These two components are seasonality and trend. On one

hand, seasonality is a characteristic of a time series which states any predictable

change or pattern that recurs over the period of one year or less. On the other

hand, trends are noted by an upward or downward sloping line.

Different granularities need different forecast methods. First, for forecasting spe-

cific product quantities, machine capacities, workforce and production levels or

job assignments, we use a short-range forecast. The time span for the short-range

prediction is usually of a few weeks. Secondly, medium-term forecasts, done with

a horizon of months, target mainly items such as department capacities, product

groups, sales and production planning and budgeting. Finally, the long-range

forecasts that contemplate years’ horizon focus on product lines, factory capaci-

ties, capital expenditures, facility location and expansion or Research and Devel-

opment (R&D).

1.2 Semiconductor industry

The semiconductor industry is known to be one of the most dynamics industries in

the world. Due to this high market dynamics, the semiconductors devices have a

short life cycle, as Moore (1965) stated. Moore, cofounder of Intel, predicted that

the number of transistor per chip doubles each 18 to 24 months, giving that way

an ending date for semiconductor development. This is the so-called Moore’s law

and, as we can see in the graph below, it is an approximation to the actual data.

Hence, semiconductor manufacturers have to continuously innovate to come up

with more advanced and cheaper products.

4

Figure 2. Moore's law for memory chips and microprocessors. Source:


One of the main characteristics of the semiconductor industry is the high volatili-

ty. Although the long-term market grows constantly, except from the depressed

level of 2009 consequence of the financial world crisis, we can observe in the last

40 years high fluctuations on the demands from year to year that go from +70% to

-40%.

Figure 3. The Revenue in US billions and market growth rate of the global semiconductor

market. Source: The World Semiconductor Trade Statistics (WSTS) for historical data:

Infineon Intern (28.04.2010)

For 2015 the European semiconductor market revenue is expected to grow around

3%. And for the period 2015-2019, we can see clearly a positive tendency

(MarketLine, 2015).

5

Table 1. Europe semiconductors market value forecast: $ billion, 2014-19

We can also highlight from the semiconductor industry that its Research and De-

velopment-to-sales ratios and capital-to-sales ratios are higher and grow faster

than other industries (Liu, Leat, Moizer, & Megicks, 2013).

As mentioned before, the semiconductors have a relatively short product life cycle

and therefore, inventory control, Just in Time production and Make-to-Order sys-

tems are essential to avoid obsolescence and to keep up with the high innovation

rate (Liu, Leat, Moizer, & Megicks, 2013).

Moreover, there is a notable interdependency between innovation and demand.

There is a drop on the pricing of existing products due to innovation and the pro-

duction of new products, providing for them a distinguished space for their pric-

ing (Chen, Rangan, & Rock, 2011).

Another important characteristic of the semiconductor industry are the Cycle

Times variations. While for the Front-End (FE) the Cycle Time (CT) ranges from

40 to 100 days, the Back-End (BE) goes from 5 to 20 days. That makes a total CT

of 4 months which, in compare to the 1 week cycle time of the silicon suppliers or

the 2 to 6 hours of the end customers, is much higher (Swaminathan, 2000).

Figure 4. Production flow by Infineon Technologies with Frontend (FE) and Backend (BE).

Source: Infineon Technologies Intern

6

Finally, one last characteristic is that the semiconductor industry is very suscepti-

ble to demand fluctuations because of the high bargaining power of customers and

the high bargaining power of suppliers. This bargaining power from the upstream

and downstream industries is caused by the fast reactions these industries have to

demand changes in compare to the semiconductor industry (Vaupel, 2013).

On the example of automotive products, the automobile manufacturers, because of

their production cycle time (PCT) of just a few hours, can readjust their produc-

tion plan almost instantly. However, the semiconductor supplier needs a range of

a few months to produce and therefore, it is impossible to provide the manufactur-

er the products with the enough lead time to follow the market changes.

Figure 5: Illustration of the Supply Chain Partners and their PCT. Source: Vaupel 2013

There are two possible solutions to the above mentioned problem. The first one is

to increase the stock inventory, so that the semiconductor industry can always

provide to its customers. This approach has several disadvantages. The most im-

portant one is that because of the short product life cycles, the semiconductor

products become obsolete quickly and the losses can be high. Furthermore, the

stock is an idle capital and its cost is not contemplated nowadays as accorded to

the Just in Time or the Kaizen philosophy.

The second and most feasible option is to produce based on the customer forecast.

In Infineon this is made through the Electronic Data Interchange Forecast (EDI

Forecast), which is an interface where the customer can reserve demand capacity

but without actually triggering the product order. Later on, this EDI Forecast

would turn into an order with a certain “Wish Date” of deliver, also in the same

interface. This last update is made on weekly basis.

However, if the EDI Forecast from the customer is not accurate enough, it could

lead to wrong production decision because of useless supply reservation

(Knoblich, 2012).

7

1.2.1 Infineon Technologies AG

This company is engaged in designing, developing, manufacturing and marketing

semiconductors and complete system solutions (MarketLine, 2015). Infineon op-

erates within five business segments: chip card and security, power management

and multi-market, automotive, industrial power control and other operating sys-

tems.

All the data used and the obtained results from this thesis are a matter of applica-

tion just in the automotive division (ATV). Infineon’s automotive segment focus-

es on power semiconductors, sensors, microcontrollers and discrete semiconduc-

tors. Those products can be used in several applications such as keyless entry,

safety management, power windows or comfort locking.

As for 2014, Infineon recorded revenues of $5,760M with an increase of almost

the 13% compared to the previous fiscal year, making it one of the big semicon-

ductors companies competing with Intel Corporation, Samsung Electronics and

STMicroelectronics. (MarketLine, 2015).

Infineon Technologies’ Supply Chain structure is based on the Supply-Chain Op-

erations Reference Model (SCOR®), which is a process referenced model created

by the APICS Supply-Chain Council. The SCOR® model divides the supply chain

into five sections: Plan, Source, Make, Deliver and Return, as we can see in Fig-

ure 6.

Figure 6. Supply Chain according to SCOR. Source: Infineon Technologies Intern

This thesis will be focused on the Plan section. The Plan section regards the Order

Management, the Demand Planning, the Capacity Planning and the Production

Management. The main aim of the thesis is to take the historical data from the

8

customers’ orders and provide a forecast of the total amount of products at the end

of each quarter. This forecast value can be used by both the financial department

as a measure of the total quarter turnover and by the Supply Chain Planners who

can take care of the production planning taking into account the approximated

given value. Consequently, the forecasting models presented in this paper will

affect the 4 different parts if the Plan section of the SCOR® model.

In the Figure 7, we can observe that the Customer Revenue Forecast, through the

Customer Demand Forecast, is located in a financial level and not in a production

level, but it takes the data from the Orders done by the customers. As mentioned

before, although it is located in the financial level, it can be also used by the Sup-

ply Chain planners for the production planning.

It is worth highlighting that the horizon considered for the Customer Demand

Forecast and for the Division Demand Forecast is from 1 to 42 weeks, which can

be considered as short-term forecasting.

Figure 7. New Forecast Map at Infineon Technologies

1.3 Forecasting in the semiconductor industry

The semiconductor industry is a high tech industry and needs to keep up with the

most innovative trends, reduce the Product Cycle Time and face with the strong

upcoming Asian competition. While fulfilling those challenges, Infineon has also

to satisfy the flexible customer demand, as well as giving high service level

through shorter lead times.

9

At the same time, Infineon should try to grow its profit and reduce its costs in or-

der to stay competitive. This is the main reason why Infineon’s Supply Chain

needs a good information exchange. The main information needed for the demand

planning is the forecast. This forecast is both the demand forecast done by the

customer and the one done by the company itself. With the data from those two,

the Supply Chain Management could be done more accurately (Knoblich, 2012).

As Seitz (2014) exposed, long production times can be balanced improving the

forecasting accuracy. Furthermore, inaccurate forecasts could be the cause of sev-

eral problems such as wrong product mix or wrong BackEnd and FrontEnd capac-

ities.

Consequently, an accurate forecast could minimize some critical issues such as

high production costs, long lead times and high market volatility (Ott, Heilmayer,

& Sin Yee, 2013).

The target of this thesis is the demand forecast done by Infineon. Although there

is currently a forecast at a division level, this thesis will address for the first time

in Infineon forecasting at a customer level, in order to find out if the analysis at

that granularity leads to more accurate forecast and to a better understanding of

the customer order behavior.

Out of the different divisions in which Infineon is divided, the biggest one in

terms of revenue and also the most stable is the Automotive division. Consequent-

ly, we can assure that the creation for a forecasting model for the automotive cus-

tomers could be really significant and representative when it comes to analyzing

of decisive customers. Moreover, this stability makes the forecasting more feasi-

ble. That is because if we try to forecast a division which has high fluctuation on

its demand, when we go down to the customer level, those fluctuations could be

even higher and the accuracy of the forecasting model will not be valuable at all.

10

2 Review of Literature and Research

Before starting the forecasting methodology, we will state the forecasting methods

which have been used in Infineon until the date. This will make easier the deci-

sion of what technique to apply later. If this technique chosen is one of the already

applied ones at Infineon, its integration will not be that complex.

However, we will also analyze more techniques that are important enough to be

considered such as the Autoregressive Integrated Moving Average (ARIMA)

models.

We can classify the forecasting methods into four different groups: techniques,

processes, accuracy measurements and demand generation. For the aim of this

thesis we will especially focus on the forecasting techniques, which are the mod-

els that return the final forecasting value we are looking for. However, we will

also give a brief overview of the processes, accuracy measurements and demand

generation used at Infineon.

Table 2. As-Is Status of the Forecasting methods at Infineon Technologies.

2.1 Forecasting Techniques

First, we will explain the forecasting techniques. These techniques are mathemat-

ical formulas that out of historical data of previous orders return a forecast for a

future time point. The following techniques are the ones that have been used or

are currently in use at Infineon Technologies:

11

2.1.1 Firm Orders Scheme

The forecasts are the firm orders from that same week:

( 1 )

where FC(t) is the forecast for time t and FO are the firm orders for t (Habla,

Drießel, Mönch, Ponsignon, & Ehm, 2007).

2.1.2 Book-to-Bill Scheme

Considering the fact that both, the ratio of the demand quantity of period t and

period t-1 and the ratio of the current firm orders, from period t, and from the pre-

vious period, t-1, we can formulate the following method:

( 2 )

In the case that FO(t-1) := 0, FC(t) := FO(t). This is the current methodology at

Infineon. Contrary to the Firm Orders Scheme, the Book-to-Bill Scheme also

takes into account the information from the previous period, t-1 (Habla et al.,

2007).

2.1.3 Parameter-driven Scheme

Forecast should depend on historical demand data as well as on historical firm

orders. To formulate a model based on this approach, we use an exponential

smoothing technique:

( 3 )

where β is the smoothing parameter and it’s ranged between 0 and 1, 0 ≤ β≤ 1,

and the initial demand is FC0 ≥ 0. The number of periods with historical data is

notated by k. That way, we incorporate the influence of more recent data.

Therefore, the Parameter-driven scheme is given by:

( 4 )

12

where the importance of the historical data and current firm orders are reflected by

the parameters a and b. For this scheme, a≥0, b≥0 and a+b≤1.

In order to choose the right parameters (a,b, β, FC0) for the forecast calculation,

we use a nonlinear optimization model:

with the following constraints:

Consequently, the chosen parameter will cause the minimal sum of absolute fore-

cast errors (Habla et al., 2007).

2.1.4 Random Walk or Naïve Forecast

With this model, all forecast for the future are equal to the last observed value of

the periods. Therefore, the only observation considered is the last one and the

forecast for all the future periods will remain constant.

However, there is a more advanced method, known as Naïve2, which is adjusted

form seasonality:

indexseansonaltheisSS

OO

OofvalueadjustedseasonallytheisO

SOFNaive

j

j

t

t

t

jtt

,

)(2

*

*

*

1

( 5 )

where F is the forecast and O the actual orders.

13

2.1.5 Simple Moving Average

N

OOOOF ntttt

t

...321

( 6 )

The simple average of the observed data equals the future forecasts, assuming that

all the observations are of same importance. When a new forecast is generated, the

demand in the oldest period is replaced by the newest one and that is why it is

called “moving average”.

2.1.6 Exponential Smoothing

10,

1,)1( 11

01

andfactorsmoothingtheis

tFOF

OF

ttt

( 7 )

If we continue this series into the past, we will get in the end, the following for-

mula:

...))1()1()1(( 4

3

3

2

21 ttttt OOOOF ( 8 )

With this new approach, the weights decrease exponentially as the observations

are older. Hence, the oldest observations have the smallest weights. To find an α

with low error, we use large amounts of historical data.

2.1.7 Quarter-on-Quarter Approach

The CEBIS Order Development Crawl Chart is a graph reflecting the business

development by showing the quarterly cumulative revenue of the past and the

outlook of the most probable revenue based on revenue, orders on hand and cus-

tomer forecast. Its range is from week -26 (26 weeks before the quarter starts) till

week 14, which means the end of the quarter. The week 0 symbolizes the start of

the quarter and with it the Orders on Hand begin to transform also into revenue, so

within the quarter we have a mix of orders and revenue.

14

Figure 8. CEBIS Crawl Charts. Source: Knezevic 2016

Currently, the forecast method used at the automotive division is called “Quarter-

on-Quarter analysis”. This approach states that the percentage change of the or-

ders in compare to the previous quarter will be the same change at the final reve-

nue. For instance, if for week -13 the amount of orders is 20% higher than the

previous quarter, the expected revenue for the end of the quarter, week 14, will be

also 20% higher than the revenue from the last quarter.

Mathematically, the Quarter-on-Quarter (QoQ) approach is:

( 9 )

where R is the final revenue of the quarter, is the one of the previous

quarter and OOH means Orders On Hands for the week t. Therefore, week by

week we can get a forecast for the ending revenue.

The application of this method gives us completely different results for the diverse

divisions. While for the Chip Card & Security (CCS) division for week -21 we

have an average absolute deviation of 50%, for ATV it is around 5%.

15

2.1.8 Linear Regression

Finally, Knezevic (2016) applied linear regression for the Crawl Charts at the di-

vision model. He compared two different regression models: the simple linear

regression and a multiple linear regression which included one seasonality varia-

ble and also one variable to model the slopes found at the Crawl Charts, the “Er-

weitertes Modell”:

( 10 )

Where U are the final revenues of the quarter q, AB are the Orders on Hands +

Revenue from the division for the week t, Q1 is a dummy variable to define the

seasonality of that fiscal year quarter, ST is the variable calculate to represent the

change on the slope on the CEBIS Crawl Charts and e are the residuals.

Knezevic concluded that for some divisions the simple linear regression is better

and for the others, the “Erweitertes Modell”. For the application of this thesis, it is

worth highlighting that for the automotive division the best model to apply is the

“Erweitertes Modell”. Therefore, further comparisons will be made between the

customer forecasting technique and the “Erweitertes Modell” applied at the auto-

motive division.

2.2 Forecasting Processes

After having explained the most important forecasting techniques applied at In-

fineon Technologies, we will continue with the forecasting processes.

Infineon uses different product granularities for forecasting sales, operational de-

mand and for the Volume Rolling Forecast (VRFC). VRFC is a process of pro-

duction volume planning, which aligns demand and capacities for a 12 months

horizon.

It involves Sales, Marketing, Supply Chain Management, Frontends and

Backends. VRFC spans from the Biz Scenario to the Production Program. The

volume of production is calculated with the forecast on a rolling horizon. Then,

the previous forecasts are updated and the next forecast is added to this horizon,

which is 12 months. Therefore, the market uncertainties caused by the planning

numbers are reduced. For this last one, which is monthly based, Ott, Heilmayer

16

and Sin Yee (2013) study the impact of forecast accuracy on its accuracy on time

over the entire planning.

For each product at Infineon, there are four main levels (or tiers), which are the

granularities that could be divided into: package family, package class, package

group and package name, as we can see in the illustration.

Figure 9. Infineon Granularities. Source: Ott et al. 2013

Ott et al. concluded that there is a direct relation between granularity and accura-

cy, as the higher the granularity, the higher the accuracy. The biggest gap is be-

tween the “basic type” and the “package name”, as we can see in the figure below.

Figure 10. Granularity Total Accuracy Findings based on SMAPE3. Source: Ott et al. 2013

All of the above was calculated based on SMAPE3, which will be explained later,

because this error measurement is not affected by low data values that could cause

distortion. That way, we could identify any potential under- or over-forecasting.

Using a change factor of granularity we can determine the effects of the granulari-

ty change, resulting that as the change factor decreases, so does the change of ac-

17

curacy. Consequently, the highest factor of change has the biggest impact to accu-

racy level.

Finally, the authors also demonstrated that when the VRFC timeframe comes

closer to the final demand date, the forecast accuracies of the granularities in-

crease.

Out of some interviews with experts on the planning field in Infineon, the three

more possible causes for inaccuracy where: “positive thinking” bias, management

contradiction and economic planning.

The first one is caused by the overestimation of the volume of production due to

emotions. When these expected orders don’t realize, the human presumptions lead

to a “negative thinking” bias.

Secondly, management expects both high turnovers and accuracy, which cannot

be fulfilled at the same time, causing this contradiction.

Last but not least, the economic planning, concerning time constraints and effort

limitations, make the work be done only on the representative products, reducing

the other products’ accuracy and therefore, the overall one.

2.3 Forecasting Accuracy Measures

Regarding the forecasting accuracy measures, Jing (2011) gathered the different

measures applied at Infineon, which are the following ones:

2.3.1 RMSE (Root Mean Square Error)

n

t

tt FOn

RMSE1

2)(1

( 11 )

where O are the orders received, F the forecast demand and n the number of

SKUs.

This approach has several drawbacks. The main one is that without knowing the

scale of the data, we cannot conclude if the forecast is accurate. Moreover, errors

of large scale data can affect considerably the results of the RMSE.

However, it is helpful for decision making, as it can be directly related to cost of

extra inventory or loss of sales.

18

2.3.2 MPE (Mean Percentage Error)

n

t t

tt

O

OF

nMPE

1

1

( 12 )

There are two big disadvantages when it comes to the application of this measure.

The first one is that, as it is an average percentage error, the positive and negative

errors will cancel out each other, leading to a small error, which does not reflect

the reality. The other drawback is that it can be skewed by outliers. A series of

outliers with high forecast can dominate the overall forecasting, overweighting the

small forecast and order numbers. It is worth highlighting that MAPE, SMAPE1

and SMAPE2 have also the same problem.

2.3.3 MAPE (Mean Absolute Percentage Error)

n

t t

tt

O

FO

nMAPE

1

1

( 13 )

This approach does not cancel out the errors, as it is absolute, but it adds another

problem, as if the orders are zero, the result will be undefined.

2.3.4 SMAPE (Symmetric Mean Absolute Percentage Error)

%2/)(

11

1

n

t tt

tt

FO

FO

nSMAPE

( 14 )

This way, there is no possibility that the denominator becomes zero. However, it

ranges from 0% to 200%, which makes complex the interpretation of the result. It

also favors more forecasts that are higher than the actual demand than those which

are lower than the actual order.

%1

21

n

t tt

tt

FO

FO

nSMAPE

( 15 )

The difference with the SMAPE1 is that the range is from 0% to 100%, but the

main problems remain unsolved.

19

[%]

)(

3

1

1

n

t

tt

n

t

tt

FO

FO

SMAPE

( 16 )

This is the used measure at Infineon, because it is relatively protected from the

forecast bias and from the outliers. Although it cannot eliminate totally the up-

ward bias, it is known that it mitigates the problem.

2.3.5 GMRAE (Geometric Mean Relative Absolute Error)

n

n

t ttrw

ttm

OF

OFGMRAE

1

( 17 )

This measure calculates the geometric mean of the ratios between the absolute

errors of the random walk forecasts and the forecasts made by the company.

We will have a valuable result only if both the nominator and the denominator

are not equal to zero. On the one hand, if the GMRAE is greater than 1, the

random walk forecast is better than the one of the company. On the other

hand, if it is lower than one, it will mean the opposite.

2.3.6 Percent Better

{1

0

1 100

tWhere

n

j

BetterPercent

jttrwttm OFOFif

otherwise

n

t

t

( 18 )

Percent Better calculates the number of SKUs for which our own forecast is closer

to the actual demand, comparing to the random walk forecast.

2.3.7 Accuracy at Infineon Technologies

As Armstrong and Colloply (1992) proposed, the following factors will be the

ones to use to compare the different forecast error measures: reliability, construct

validity, outlier protection, bias protection, sensitivity and relationship to decision

20

making. Applying those, Jing (2011) concluded that SMAPE3 was the best fore-

cast accuracy measure to apply at Infineon Technologies.

As SMAPE3 measures the forecast error, the forecast accuracy at Infineon Tech-

nologies (IFX) can be measured by:

[%]

)(

1

31@

1

1

n

t

tt

n

t

tt

FO

FO

SMAPEIFXAccuracy

( 19 )

However, the SMAPE3 can be also calculated taking into account the effects of

the forecast accuracy and planning efficiency on forecast stability. That way, the

calculation of SMAPE3 for Basic Type and Process Group will be:

a. Determination of Over- and Under-forecasting:

if

( 20 )

if

( 21 )

b. Relation to the sum of forecasts and orders:

( 22 )

( 23 )

c. Final formula for SMAPE3:

( 24 )

21

There is a tendency to underforecast approximately by 3%, due to the fact that the

automotive division, with the aim of a full loading, asks for non-used capacities

from the rest of the divisions. Thus, this was not included in the original forecast,

as initially, it was not owned by the automotive division.

Disney and Towill (2003), Bray and Mendelson (2012) and Chen and Lee (2012)

concluded that the aggregation of granularities smoothens slightly the internal

Bullwhip Effect. In addition, it is possible to reduce uncertainties applying an ag-

gregated time level forecast.

There is still a big discrepancy between theoretical and practical perspectives re-

garding the fact whether a forecast is better on a higher or a lower aggregated lev-

el (Boylan, 2011).

2.4 Demand generation

Finally, the last part to consider of the forecasting methods at Infineon is the de-

mand generation, which was basically researched by the University of Hagen

(Mönch & Ewen, 2013). Demand generation consists of creating new feasible

data that can be used in the different simulation processes. There are two main

approaches for the demand generation:

2.4.1 Heath and Jackson’s approach

It yields normally distributed data for the final demand and forecast with respect

to a given correlation scenario.

The predictions made at time s for the quantity demanded at time t are D(s,t),s < t.

D(s,t),s < t is a vector whose length is equal to the number of products taken into

account. The information update is described by the following formula:

( 25 )

where ε(s,t), as just mentioned above, is the information update from s-1 to s, re-

garding the demand at time t.

To continue with this approach, the authors made the following assumptions:

22

1. For k,s,t ≥ 0, k≠s, ε(s,s+t) and ε(k,k+t) are identically and independent

distributed with normal distribution of variance σ²t and mean 0, be-

cause εs is uncorrelated with all εu for u ≤s-1 and E[εs]=0, εs is a sta-

tionary process and εs is normal. Here, ε(t) is the random variable and

ε(s,s+t) is the realization of ε(t) in period s.

2. For all periods t, with t > s, the information for demand forecasting

generation is also available in period s. Therefore, forecast accuracy

will increase, as D(s,j) is more accurate than D(s -1,j), with j≥s.

Let us consider the state Xs of our system in period s with n products and forecast

horizon H.

where D(i, j)k is the prediction made in period i for the demanded quantity of

product k in period j and µk is the mean for the respective product k.

Now, the update vector should be:

with ε(j)k update for the predicted demand of product k made j periods ahead.

Then, we consider the covariance matrix

of the update vectors with

in order to generate correlated data, normally distributed random variables with

mean 0.

Let C = (cij) be a lower triangular matrix with Σ = CCT, then

Now we are able to generate Xk, the state of our system in period k, from Xk-1 and

the k-th realization of our update vector. We obtain:

23

( 26 )

Certainly, the components

Are built of normally distributed random variables

with mean µi and variance

2.4.2 A Two-stage Approach for the Generation of Non-normal Distributed

Demand

However, none of the products from ATV, CCS, IPC and PPM analyzed by

Mönch and Ewen (2013) are normally distributed or correlated significantly,

which means that this generation demand approach is not suitable. Hence, Mönch

et al. proposed a Two-Stage approach for non-normal distributed demand. As

proposed by Croston (1972), Willemain et al. (1994) and Johnston and Boylan

(1996), the number of periods without positive demand and the amount of demand

are considered separately.

We consider an update vector with size equal to the forecast horizon and the l + 1-

th component of the update vector uv[l +1] stores the empirical distribution of

independent of k ≥ 1. We calculate the empirical distribution

for every component of the update vector for each product through the minimum

order quantity.

Then, we determine the empirical distributions of the number of periods without

demand and for the amount of final demand for each product.

Therefore, the procedure to generate demand is separated into two stages. First,

we generate the final demand. Consequently, using empirical distribution we can

24

determine the number of periods without demand. When we reach a period with

positive final demand, the empirical distribution gives the multiples of the mini-

mum ordering quantity of the final demand.

Secondly, the update vector is used to generate the forecast from the final de-

mand, because:

( 27 )

25

3 Methodology

3.1 Data Representation

The Crawl Charts are based on the data from Infineon’s Internal Reporting Data

(CEBIS), which show the data from previous, actual and next quarters on the form

of Orders on Hands + Revenue (OOHUM). As we explained before, the value for

week 14 in the Crawl Charts is the vale for the final Revenue, which gives us high

valuable information.

However, at customer level, the CEBIS just saves the information for the last

year, which in the end means 4 points of data for each week. Consequently, to

make a trustable forecasting model, more data should be gathered. For that, we

use the EDI (Electronic Data Interchange).

The EDI is an electronic interface for exchanging information between two differ-

ent companies, which regarding our case are Infineon and the customer. There, the

customer makes purchase orders, gives an estimated forecast and receives confir-

mation and shipping notices. From the EDI, the data from the orders made by a

customer since 2013Q3, quarters in fiscal year, is available in terms of units of

products. Due to the high amount of data to get out that information, the EDI had

to be transferred first from the used software into a plain text file and from there

into different excel workbooks, 5 for each year of data, because of Excel’s pro-

cessing memory limitation. The parameters used to get the final information were:

Customer Name, Orders in pieces, Due Week (Delivery Week) and Difference

Load Due Week.

Arrange was made through the use of Pivot Table, where we filter the customer

through the Customer Name and define the Delivery Week as the columns and the

Difference Load Due Week as rows, making the values the sum of the orders. We

can observe the result in the next graphs:

26

Figure 11. Orders from EDI for the Customer A

Figure 12. Orders from EDI for the Customer B

These charts show the difference between the ordering behavior of Customer A

and Customer B, while the first customer reaches the a high number of orders in

week -6, approximately, the second one reaches it much earlier, in week -12, if we

consider the last year’s behavior, which it is the one that seems more stable. This

remarks that Customer A follows a shorter term behavior in comparison to Cus-

tomer B, because they order the most when the quarter is about to start, unlike

Customer B, whose orders are pretty significant even a quarter ahead.

Out of these data, an approximation to the CEBIS’ Crawl Charts could be done,

obtaining a cumulative curve in which each which represents the value of the sum

of the orders of the previous weeks and the current one. This modified Crawl

27

Charts, from now on EDI Crawl Charts, at the end of the quarter returns the value

of the total amount of orders done by a customer of that quarter.

Figure 13. EDI Crawl Charts for Customer A

Figure 14. EDI Crawl Charts for Customer B

Here we can observe the change on the amount of orders between the historical

data. It is worth highlighting that the spread between the different quarters is

higher for Customer A than for Customer B, confirming the statement that Cus-

tomer B has more stability than Customer A regarding the order behavior. This

could also indicate certain seasonality in which some quarters follow a repetitive

pattern. This matter would be analyzed later.

28

The main differences between this own Crawl Charts and the ones made by CE-

BIS are that we do not consider the cancelations nor the orders coming from

weeks earlier than week minus 26. Without cancelations, the Crawl Charts out of

EDI do not suffer a change in the slope, making the orders go down when the

quarter starts and the customers decide whether or not to continue with the

planned orders or to cancel. We can appreciate this behavior in the normalized

charts, like the following ones:

Figure 15. Normalized CEBIS Crawl Charts for the Automotive Division. Source: Knezevic

2016

Figure 16. Normalized EDI Crawl Charts for Customers A and B

From these normalized Crawl Charts we can spot one more differential fact: the

initial offset. While the CEBIS Crawl Charts show an initial offset (Figure 15),

consequence of the orders from weeks earlier than week -26, the absence on the

EDI for that data, makes the EDI Crawl Charts start almost from zero (Figure 16).

Moreover, we can appreciate once again the difference between Customer A and

Customer B regarding the order behavior. The curves of Customer B in the nor-

malized EDI Crawl Chart almost resemble a linear function and the different quar-

ters seem to overlap more than the ones from Customer A.

Customer A Customer B

29

However, we can also conclude that both customers, out of the EDI data, reach

the 50% of the total amount of orders of the quarter in between week -8 and week

-6. The introduction of an initial offset just like the one at CEBIS Crawl Charts

could slightly vary this percentage, as we know from the last year CEBIS data that

the initial offset of Customer B is higher than the Customer A’s one. Therefore,

the calculation of this offset depends on the obtaining of the orders from weeks

earlier than week -26, which in the future could make the EDI Crawl Charts more

accurate and closer to the CEBIS Crawl Charts.

Regarding this future data gathering, we must state again that the use of EDI

Crawl Charts is just an approximation to the CEBIS Crawl Charts and that if in

the future is it possible to have the data at customer level for CEBIS for more than

one year, the EDI Crawl Charts would be discarded and the forecasting would be

done with the real accurate data, not with an approximation.

The EDI Crawl Chart does not include the week cero and it finishes at week +12.

This is because we consider the quarter starting from week 1 and finishing at

week 13, so there are no orders from the customer for week 13. Thus, the week 0

for the CEBIS Crawl Charts is the week 1 for the EDI Crawl Charts and the week

13 for the CEBIS Crawl Charts is the week 12 for the EDI Crawl Charts.

3.2 Forecasting Technique Selection

When it comes to the forecasting technique selection, the two main choices are the

Autoregressive Integrated Moving Average (ARIMA) models and the Seasonal

Stable Pattern Models (SSPM). The reason why only these two will be considered

is that they are both an aggregation of some of the different models explained be-

fore.

ARIMA is a combination of differencing with autoregression and moving average

models based on time series, whose formula is:

( 28 )

y’t differenced series; c constant; et white noise; φ autoregressive parameter; θ

moving average parameter.

30

Non-seasonal ARIMA models depend on three different parameters, p,d and q,

where p is the order of the autoregressive part, d is the degree of first differenced

involved and q is the order of the moving average part.

ARIMA models cover the most forecasting models for time series. These series

must be stationary or made stationary by differencing. Stationary means that the

series has no trend and that it varies around its mean with a constant amplitude

and therefore, its autocorrelations remain constant too (Nau, 2016).

Fulfilling those requirements, we get the different models with the values of p, d

and q. Thus, the simplest model ARIMA(0,0,0) would be just White Noise and

ARIMA(0,1,0) Random Walk. Models of the type ARIMA(p,0,0) would be Auto-

regressions and ARIMA(0,0,q) Moving Averages.

The statistical software R simplifies significantly the selection and calculation of

an appropriate ARIMA model regarding our data. Considering the value of the

amount of orders from the customer at the final week of the quarter for the last 12

quarters, we get a time series with 12 observations.

The auto.arima() function included in the “forecast” package minimizes the Cor-

rected Akaike’s Information Criterion (AICc), which we will explain in the next

section, and the Maximum Likelihood Estimation to obtain the best possible

ARIMA model. The smaller the value of those two measurements, the better the

ARIMA model is.

The function follows the Hyndman-Khandakar algorithm which consist of model-

ling the number of differences d through Kwiatkowski–Phillips–Schmidt–Shin

(KPSS) tests and the values of p and q using a stepwise procedure to get the min-

imum AICc (Hyndman & Athanasopoulos, 2013).

Applying this function the chosen customers, Customer A and Customer B, we

get for the first one ARIMA(1,1,0) with drift, which is a differenced first-order

autoregressive model. We can appreciate the 80% and 90% prediction intervals in

the following graph.

31

Figure 17. Forecast from ARIMA(1,1,0) with drift for Customer A

Regarding Customer B, auto.arima() returns the model ARIMA(0,1,0), which is

the Random Walk forecasting model

Figure 18. Forecast from ARIMA(0,1,0) for Customer B

However, Alba and Mendoza (2001), showed that while ARIMA models need

more than 50 observations, 100 for some authors, to be applicable with accuracy,

SSPM could work with smaller samples. As we have 12 observation, SSPM is the

method that has to be selected.

32

“All SSPMs are based on the observation that the sales that occur during a given

period of a quarter typically conform to a regular pattern involving the end-of-

quarter total” (Yelland, 2006, S. 799).

Thus, we have to check the assumption of having this regular pattern each quarter.

For that, we observe the week in which the 50% of the orders are reached for each

quarter. If we check again Figure 16 we can see that for both customers for the all

the quarters, this value is reached approximately on week -5.

Yelland (2006) chose 7 candidate SSPMs to test their performance. The selected

models were:

The “dummy” SSPM, which returns the same value of the previous quarter

forecast in each week.

A binomial seasonal distribution, as the first models of Chen and Fomby

(1999) and Oliver (1987).

Alba and Medonza’s (2001) inverse Pareto model.

The simple normal SSPM.

The logistic normal SSPM.

The second model of Chen and Fomby (1999).

Linear regression of quarterly totals against cumulative weekly bookings,

which is a Bayesian version of the frequentist models in Guerrero and Eli-

zondo (1997).

Yelland (2006) proved that between those different SSPM models, linear regres-

sion was the one with the best performance, as it was the model that covered more

of the actual quarterly total 80% of the time on prediction intervals of 80% confi-

dence and the one with the best GMRAE.

3.3 Multiple Linear Regression

“Regression analysis is the art and science of fitting straight lines to patterns of

data” (Nau, 2016). With the use of a linear equation the dependent variable is

predicted from other independent ones.

( 29 )

The linear regression model assumes the following points:

33

1. The expected value of Y is a linear function of the X variables.

2. The unexplained variations of Y are independent random variables.

3. Homoscedasticity, which means that all the variables have the variance.

4. They are all normally distributed.

The error is a deviation from the straight line calculated by the regression. We

assume that these errors:

1. Have mean zero.

2. Are not autocorrelated.

3. Are not related to the predictor variable.

Nau (2016) considered that a suitable regression model must have the following

requirements:

1. Collect useful and trustable reliable data.

2. Spot quality issues regarding the data.

3. Transform the data in case there is no linearity or normality.

4. Refine and compare models.

5. Test the assumptions and check whether they are satisfied.

6. Through the accuracy measurements, choose the most appropriate model.

The main objective is to have one regression model for each customer. Same var-

iables will be considered for the different weeks, in order to avoid having high

complexity. The forecasting calculation will follow the next flow chart:

Figure 19. Linear Regression Forecasting Procedure

34

The first two steps contemplate the data gathering from EDI and the calculation of

the adapted Crawl Charts, the so-called EDI Crawl Charts, which has to be done

for each customer. Then, comes the selection of all the variables or predictors that

can be introduced in the regression model. This selection is done just once and the

outcome is the following one:

Orders on Hands from the customer in pieces (OOH).

Orders on Hands + Revenue of the Automotive division in pieces:

(OOHUMatv).

Orders on Hands + Revenue of Infineon Technologies in pieces:

(OOHUMifx).

Seasonality by quarters (Q1, Q2, Q3).

Trend.

( 30 )

Thus, 7 variables in total, taken into account the 3 ones from the seasonality, are

integrated in our model. The Orders on Hands from the Customer are the orders

done via EDI for the last 12 quarters, which we have explained before. On the

contrary, the Orders on Hands + Revenue from the automotive division and the

entire Infineon (Automotive, Chipcard & Security, Industrial Power Control and

Power Management & Multimarket division) are taken from CEBIS also for the

last 12 quarters. The decision of including these two variables is based on the idea

of testing the correlation between a specific customer behavior and the entire divi-

sion or company’s behavior, as we are forecasting the orders of a customer that is

highly relevant in revenues for the automotive division and for Infineon itself and

another one whose impact on the total revenue is not that much significant.

Furthermore, we introduce a seasonality pattern in the regression model through

dummy variables. Consequently, q1 will take the value “1” when we consider the

first quarter of each year and “0” when is one of the other quarters and the same

for the variables q2 and q3. The variable q4 is not included as it would be a re-

dundant one: the last quarter of the fiscal year is determined by the variables q1,

q2 and q3 because it is specified when these dummy variables are all set to zero.

35

Finally, a linear trend is considered by including the predictor xt = t in order to

observe whether there is or not an upwards or downwards trend regarding the cus-

tomer orders.

The next step to be done is the Stepwise Procedure, which is a strategy to limit the

number of models to be considered. In this case, we apply backwards stepwise

regression, which is basically the following approach:

1. Start with the model that includes all the chosen variables.

2. Remove one variable at a time and keep the model if there is an improve-

ment on the forecasting accuracy measure.

3. Iterate until no further improvement is found.

Even though the backwards stepwise regression does not necessarily leads to the

best possible model, it can guarantee a good one.

This Stepwise Procedure can be done either manually or automatically. Knezevic

(2016), who studied the regression models at the division level for Infineon Tech-

nologies, applied this methodology using Excel and iterating manually until find-

ing a good value for the forecasting accuracy measure. On the contrary, we ap-

plied the statistical software “R”, through the function “stepwise()” included on

the package “Rcmdr”, which selects the model with the lowest Corrected

Akaike’s Information Criterion (AICc), which we will now explain, among the

other important forecasting accuracy measures for the regression models compari-

son.

Akaike’s Information Criterion is defined by the following formula:

( 31 )

where k is the number of variables or predictors in the model and N is the number

of observations. SSE is the Sum of the Standard Errors. The best forecasting mod-

el is the one with the minimum AIC’s value.

However, when the sample considered is small, the AIC is biased as it selects too

many variables. That is why there is a bias-corrected formula, the Corrected

Akaike’s Information Criterion:

36

( 32 )

For this measure, the minimum value is the best one, as with the AIC (Hyndman

& Athanasopoulos, 2013).

If we apply this procedure for all the weeks, we will get one regression for each

one, as we can observe on the tables below. There we can also test the signifi-

cance of the variables of each regression. As our main objective is to stablish one

regression for each customer, we must decide which variables to include based on

the statistical t-test significance.

37

4 Results

On the one hand, for the customer Customer A we can see that for the majority of

the weeks, the Orders on Hand from Customer A and the seasonal dummy varia-

ble Q1 are the most significant ones, as we can see in the table below. Therefore,

those are the two final variables that will define Customer A’s regression (see

Table 3).

( 33 )

On the other hand, the analysis for Customer B showed that there is no clear sea-

sonality pattern and that apart from the Orders on Hand of the customer itself, the

other significant variable are the Orders on Hand + Revenue of the ATV division

(see Table 4).

( 34 )

In those two tables, the values in red have a t-value significance less than 0,05, the

green ones less than 0,001 and finally, the blue values have a significance of 0,

approximately.

For those two final models, we run again the regression experiment to get the val-

ue of the intercepts and the different predictors.

38

39

40

41

42

Now that we have the final results, we proceed with the residual diagnostics in

order to check whether the assumptions of the model have been satisfied or not.

The first assumption we will check is the lack of autocorrelation. For that we will

use the Durbin-Watson statistic. The Durbin-Watson statistic it is used to detect if

the hypothesis that there is no autocorrelation in the residuals, which can take val-

ues from 0 to 4. A distribution around 2 symmetrically means that autocorrelation

does not exist in our regression. We will consider critical those values which are

lower than 1 or higher than 3. The Durbin-Watson statistic is defined by the fol-

lowing formula:

( 35 )

Where et is the residual for the observation t and T is the total number of observa-

tions.

In the graphs below we can check that all the Durbin-Watson statistic values are

ranged between 1 and 3. Therefore, we can conclude that the initial assumption of

no autocorrelation is fulfilled.

0,00

0,50

1,00

1,50

2,00

2,50

3,00

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week


Figure 20. Durbin-Watson Statistic Distribution for Customer A

43

0,00

1,00

2,00

3,00

4,00

-26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 1 3 5 7 9 11

Week


Figure 21. Durbin-Watson Statistic Distribution for Customer B

To test the normality of the residual we use the Jarque-Bera test (Hyndman &

Athanasopoulos, 2013), whose mathematical formula is the following one:

( 36 )

where n is the number of observations and k the number of variables. S is the

sample skewness, C is the sample kurtosis:

( 37 )

( 38 )

Figure 22. Jarque Bera test for Customer A

https://en.wikipedia.org/wiki/Skewness

https://en.wikipedia.org/wiki/Kurtosis

44

Figure 23. Jarque Bera test for Customer B

Testing this statistic through a normal distribution of alpha 5%, we conclude that

only for weeks 9 and 10 of the Customer B, the condition of residuals normally

distributed is not achieved. Consequently, forecast out of those two weeks for that

specific customer should not be trusted without a further and advanced check.

However, this is not a big issue because the forecasts at that time are not as useful

as the earlier ones. At weeks 9 and 10, all the production has been planned and the

final number of orders will not change significantly in comparison with week 12,

which indicated the end of the quarter.

Then, final test is the Adjusted Coefficient of Determination, which measures the

percentage of final values that are explained by the regression function. It is de-

fined by the following formula:

( 39 )

where p is the total number of explanatory variables in the model (not including

the constant term) and n is the sample size. We use the Adjusted Coefficient of

Determination instead of the Coefficient of Determination, R², because it is not as

biased as this last one. The Coefficient of Determation tends to have a higher

value when we introduce more variables to the regression. The Adjusted

Coefficient of Determination tries to correct this issue.

In order to analyze this measure, we must know that the closer to 1 (100%), more

forecast values are explained by the regression. As we can observe in the figures

below, the first 4 weeks for the Customer A, with short-term demand strategy,

have a low value for the Adjusted Coefficient of Determination. However, we can

45

appreciate that the Customer B, with long-term demand strategy, we get an

acceptable value from the beginning.

Figure 24. Adjusted Coefficient of Determination for Customer A

Figure 25. Adjusted Coefficient of Determination for Customer B

We compare now the two customers with the values obtained for the automotive

division, ATV, and we observe that we get a better value of the Adjusted Coeffi-

cient of Determination at customer level.

46

Figure 26. Comparison of the Adjusted Coefficients of Determination

The regression done for the Automotive Division starts at week -21, because M.

Knezevic (2016) found out that the data from week -26 till week -22 gave a wrong

result. However, for our regressions at customer level, data points from -26 and

forward are all usable. That is the reason why all the measures can only be actual-

ly compared from week -21 and on.

The adjusted coefficient of determination is the proportion of variation in the

forecast variable that is explained with by the regression model (Hyndman &

Athanasopoulos, 2013). Although validating the forecasting model through the

out-of-sample performance is better than using this coefficient, it is also helpful to

know this goodness-of-fit. This does not mean that the forecasting model of Cus-

tomer B is better than the one of Customer A, but it is useful to check whether the

variables or predictors we chose for our models lead to a good forecast.

As we have explained before, the Corrected Akaike’s Information Criterion

(AICc) indicates the predictivity ability of a model. However, to compare the

AICc at customer level, with 12 observations, and the division ATV, with 20 ob-

servations, we created an Average AICc, which is defined by the AICc for week t

divided by the number of observations.

47

Figure 27. Average Akaike's Information Criterion Comparison

In the graph we can see that there is almost no difference for the Average AICc.

This indicates that the three regression models are similar in terms of predictivity

accuracy.

Regarding the most important result of the regression models, the prediction in-

tervals, we can define them by:

( 40 )

is the predicted or fitted value, t is the t-statistic with n-k degrees of freedom

and the value inside the square root is the standard error of the prediction.

In the graph we can see the comparison between Customer B, Customer A and the

Automotive Division of the percentage prediction intervals for each week. There

is no significant difference between the prediction intervals from week -26 until

week -5. From week -5 we can observe that the prediction interval for ATV is

much narrower than the customer ones, especially than Customer A.

48

Figure 28. 80% Confidence Prediction Intervals Comparison

This last result was expected as Customer B has a more stable demand and that

leads to less variation in the forecasted final value and therefore, to prediction

intervals not that wide. However, it is worth highlighting that even though we are

forecasting at a customer level, the maximum prediction intervals are ±20% and

only at some certain weeks for Customer A. This means that, although the overall

forecasting is a bit less accurate that the one for the entire division, we can obtain

an applicable forecast that shows us more about the customer demand behavior

and that can be an extra aid for the Supply Chain Planner when deciding.

The implementation of these models makes them the first statistical forecasts

made at customer level in Infineon Technologies. Moreover, it sets a general pro-

cedure to follow for the rest of the customers’ forecasts.

4.1 Integration of the Model into the Order Development

Crawl Charts

The Supply Chain Planner at Infineon uses the Order Development Crawl Charts

frequently in order to analyze the demand, as we have seen before. An accurate

forecast could be critically helpful for the Supply Chain Planner. However, the

previous results are done with a specific statistical software and therefore, it

should be integrated in an user-friendly, in this case the user is Supply Chain

Planner, interface: the Crawl Chart Forecasting Tool. That is the reason why we

decided to integrate the multiple regression models into Excel. As we can see in

the figure below, the Supply Chain Planner will be able to analyze and forecast

the customer demand behavior at a short-term horizon based on our statistical

49

forecasting method, but it will still be needed a judgmental forecasting based on

the Supply Chain Planner’s experience to model the production for a longer fore-

casting horizon.

Figure 29. Forecasting Methods regarding demand history and time horizon

The idea is that the Supply Chain Planner just needs to introduce into the EDI

Crawl Chart Forecasting Tool the updated values for the data points, which are the

Orders on Hands of the customer. With those data points and through the use of

the value of the different variables already calculated, we apply the regression

formula that calculates the forecast final values. We also calculate the Standard

Error of the Prediction in order to be able to calculate the prediction intervals, as

explained before.

Figure 30. Example of the result of the application of the EDI Order Development Crawl Chart Excel

Tool

50

5 Conclusion

The main challenge of this thesis was the data gathering. CEBIS, Infineon’s inter-

nal data server for the reports, only provided 4 observations at the customer level.

4 points were not enough to apply any forecasting technique and therefore, anoth-

er approach for the data had to be considered. That is the reason why we took into

account not the CEBIS data, but the data coming from the EDI.

After going through the literature research and the methods applied at Infineon,

we decided that the regression models were the first realistic and good choice for

forecasting with Crawl Charts. However, we analyzed the ARIMA models too, so

we spanned the majority of the common forecasting techniques.

The multiple linear regression models required gathering possible significant vari-

ables for the model. We decided to choose variables that have the similar Order

Development Crawl Chart format, such as the Orders on Hands + Revenues from

the automotive division and from the entire Infineon, as well as variables that de-

fined the seasonality and the trend. The slope used in the “Erweiteres Modell” was

discarded for our models as the EDI Crawl Charts have no cancelations and there-

fore, no change in the slope in terms of increasing or decreasing.

After taking all these variables, we applied the stepwise procedure in order to re-

move variables that are not significant for our models and to get the best possible

model. For each week of each customer we got a different regression model.

However, there it was simple to decide which would be the final regression model

for each customer. Two variables, apart from the intercept, where chosen. For

both customers the Orders on Hands of themselves where included in the respec-

tive models, which is the fact that allows the integration of the forecasting model

into the EDI Crawl Charts.

The second variable was different for Customer B and for Customer A. For the

first one, the Orders on Hands + Revenues from the automotive division influ-

ences the forecasted value of the final amount of orders of that customer. Regard-

ing the second one, Customer A, neither the behavior of the automotive division

nor the behavior of the entire Infineon were considered. However, the results con-

cluded that there is certain seasonality at a quarter level that had to be included in

the model.

51

Once the two final models were decided, we ran a sensitivity analysis in order to

check the assumptions made for the regression forecasting model. Using the Dur-

bin-Watson statistic, the Jarque-Bera Test, the Adjusted Coefficient of Determina-

tion and the Corrected Akaike’s Information Criterion we were able to corroborate

the mentioned assumptions.

After validating the models, we could forecast the final number of cumulative

orders done in one quarter for each customer from week -26 until week +11. Con-

sequently, it is possible then the calculation of the prediction intervals, in our case

of 80% confidence, and the integration into a tool manageable for the Supply

Chain Planners.

5.1 Further improvements

The final results presented in this thesis must be considered as an approximation

of the actual forecasted revenue because of the input data, as explained before.

Therefore, the Central Business Information System (CEBIS) Data, which con-

tains the real revenues should be used, as soon as the data at customer level is

available, following the procedure shown in this paper. The use of CEBIS Data

enables the full automation of the Order Development Crawl Chart Tool, because

the input data can be download directly from the database and avoids the manual

introduction.

Finally, the next main step could be the application of this methodology to all the

customers inside the automotive division in order to get the full vision of the fore-

casting at customer level and its comparison to the forecast done at division level.

52

53

Bibliography

Akaike, H. (1974). A New Look at the Statistical Model Identification. Automatic Control,

IEEE transactions on, 19(6), 716-723.

Álvarez Luque, M. (2015). Modelling and Evaluation of Stock Target Setting Approaches

in a Semiconductor Supply Chain using Agent-Based Simulation. Neubiberg:

Infineon Technologies AG.

Armstrong, J. S., & Collopy, F. (1992). Error Measures for Generalizing about Forecasting

Methods: Empirical Comparisons. International Journal of Forecasting 8, 69-80.

Boylan, J. (2011). A 'Softer' Approach to the Measurement of Forecast Accuracy. The

International Journal of Applied Forecasting, 23, 16-20.

Bray, R., & Mendelson, H. (2012). Information transmission and the bullwhip effect: An

empirical investigation. Management Science, 58 (5), 860-875.

Chen, H., Rangan, S., & Rock, S. (2011). Inventory Write-downs in the Semiconductor

Industry. Colorado: Leeds School of Business, University of Colorado at Boulder.

Chen, L., & Lee, H. (2012). Bullwhip effect measurement and its implications. Operations

Research, 60 (4), 771-784.

Chen, R., & Fomby, T. (1999). Forecasting with Stable Seasonal Pattern Models with an

Application to Hawaiian Tourism Data. Journal of Business and Economic

Statistics, 17(4), 497–504.

Croson, R., & Donohue, K. (2003). Impact of POS Data Sharing on Supply Chain

Management: an Experimental Study. Production and Operations Management

12(1), 1-11.

De Alba, E., & Mendoza, M. (2001). Forecasting an Accumulated Series Based on Partial

Accumulation: A Bayesian Method forShort Series with Seasonal Patterns.

Journal of Business & Economic Statistics, Vol. 19, No. 1, 95-102.

De Alba, E., & Mendoza, M. (2006). Forecasting an Accumulated Series based on Partial

Accumulation II: A new Bayesian Method for Short Series with Stable Seasonal

Patterns. International Journal of Forecasting, 22(4), 781-798.

54

De Alba, E., & Mendoza, M. (2007). Bayesian Forecasting Methods for Short Time Series.

The International Journal of Applied Forecasting, (9), 41-44.

Disney, S. M., & Towill, D. R. (2003). “On the bullwhip and inventory variance produced

by an ordering policy. Omega, 31 (3), 157-167.

Guerrero, V. M., & Elizondo, J. A. (1997). Forecasting a Cumulative Variable Using its

Partially Accumulated Data. Management Science 43, 879– 889.

Habla, C., Drießel, R., Mönch, L., Ponsignon, T., & Ehm, H. (2007). A Short-Term Forecast

Method for Demand Quantities in Seminconductor Manufacturing. IEEE

Conference on Automation and Engineering.

Heckmann, P., Shorten, D., & Engel, H. (2003). Supply Chain Management at 21: The

Hard Road to Adulthood. Booz Allen Hamilton Inc.

Hyndman, R. J., & Athanasopoulos, G. (2013). Forecasting: Principles and Practice.

Monash University: OTexts.

Jing, Z. (2011). SMAPE: Symmetrical Mean Absolute Percentage Error. Neubiberg,

Munich: Infineon Technologies.

Knoblich, K. (2012). Mastering Demand Challenges via Collaboration and Information

Sharing Excellence on the Example of Infineon Technologies. Focus:

Measurement and Evaluation of EDI Forecast and Process for Improvement.

Munich.

Königer, J. (2016). A generic approach of Agent-based Modeling in the Semiconductor

Supply Chain on the Example of the Supply Chain Planner. Neubiberg: Infineon

Technologies AG.

Lee, H. L., Padmanabhan, V., & Whang, S. (1997). The Bullwhip Effect in Supply Chains.

Sloan Management Review 38(3), 93-102.

Liu, S., Leat, M., Moizer, J., & Megicks, P. a. (2013). A Decision-focused Knowledge

Management Framework To Support Collaborative Decision Making For Lean

Supply Chain Management. International Journal of Production Research, 51 (7),

2123-2137.

MarketLine. (2015). Industry Profile: European Semiconductors. Washington DC:

MarketLine.

55

Möller, K., Federmann, F., Pieper, S., & Knezevic, M. (2016). Predictive Analytics zur

kurzfris-tigen Umsatzprognose – Entwicklung eines Prognosemodells auf Basis

von Auftragseingängen bei der Infineon Technologies AG. Infineon Technologies

AG Neubiberg: Controlling, 28. Jg., H. 8-9.

Mönch, L., & Ewen, H. (2013). Refinement and Extensions of a Simulation-based

Framework to Support the Design of Infineon’s Supply Chain II (RESC II). Fakultät

für Mathematik und Informatik, Lehrgebiet Unternehmensweite

Softwaresysteme.

Murray, M. (2016). Forecasting in the Supply Chain. Retrieved from

http://logistics.about.com/od/strategicsupplychain/a/Forecasting.htm

Nafaji, M., & Z, F. R. (2014). New Forecasting Insights on the Bullwhip Effect in a Supply

Chain. IMA Journal of Management Mathematics 25, 259-286.

Nau, R. (2016, May 1). Statistical Forecasting: Notes on Regression and Time Series

Analysis. Retrieved from people.duke.edu/~rnau/411home.htm

Oliver, K. (1982, June 4). (A. Kransdorff, Interviewer)

Oliver, R. M. (1987). Bayesian forecasting with stable seasonal patterns. Journal of

Business and Economic Statistics, 5(1), 77-85.

Ott, H. C., Heilmayer, S., & Sin Yee, C. S. (2013). Granularity Dependency of Forecast

Accuracy in Semiconductor Industry. Poznan: Poznan University of Technology.

Sterman, J. D. (1989). Modeling Managerial Behavior: Misperception of Feedback in a

Dymanic Decision-Making Experiment. Management Science 35(3), 321-339.

Subbaiah, V. (2014). Fundamental Settings for an Agent-based Simulation of the

Semiconductor Supply Chain Plan Process at Infineon Technologies. Neubiberg:

Infineon Technologies AG.

Sun, C., Ponsignon, T., Rose, T., & Narayanan, A. (2015). Complexity Analysis Through

the Modeling of Human Behavior in a Complex Supply Chain Planning

Environment. Winter Simulation Conference.

Swaminathan, J. M. (2000). Tool Capacity Planning For Semiconductor Fabrication

Facilities Under Demand Uncertainty. European Journal of Operational Research,

120 (3), 545 – 558.

56

Syntetos, A. A., Babai, Z., Boylan, J. E., Kolassa, S., & Nikolopoulos, K. (2016). Supply

Chain Forecasting: Theory, Practice, Their Gap and the Future. European Journal

of Operational Research 252, 1-26.

Vaupel, K. (2013). Effects of Forecast Accuracy and Planning Efficiency on Forecast

Stability. Neubiberg: Infineon Technologies Supply Chain Innovation.

Vollmann, T. E. (2008). Manufacturing planning and control systems for supply chain

management. New York: McGraw-Hill.

Yelland, P. M. (2006). Stable Seasonal Pattern Models for Forecast Revision: A

Comparative Study. International Journal of Forecasting 22, 799-818.

57

58

59

60

61

Ehrenwörtliche Erklärung

Ich erkläre hiermit ehrenwörtlich, dass ich die vorliegende Arbeit selbständig

angefertigt habe. Die aus fremden Quellen direkt und indirekt übernommenen

Gedanken sind als solche kenntlich gemacht.

Ich weiß, dass die Arbeit in digitalisierter Form daraufhin überprüft werden kann,

ob unerlaubte Hilfsmittel verwendet wurden und ob es sich – insgesamt oder in

Teilen – um ein Plagiat handelt. Zum Vergleich meiner Arbeit mit existierenden

Quellen darf sie in eine Datenbank eingestellt werden und nach der Überprüfung

zum Vergleich mit künftig eingehenden Arbeiten dort verbleiben. Weitere

Vervielfältigungs- und Verwertungsrechte werden dadurch nicht eingeräumt.

Die Arbeit wurde weder einer anderen Prüfungsbehörde vorgelegt noch

veröffentlicht.

München, den 20.07.2016

Darío Khambatta Moreno

Documents

PREDICCIÓN DE LA DEMANDA DE SEMICONDUCTORES PARA …oa.upm.es/46890/1/TFG_DARIO_KHAMBATTA_MORENO.pdf · aplicados a un nivel superior, en este caso departamentos. Se muestran las