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MASKANA.Vol. 9, Ed. 2, 9-16, 2018

https://doi.org/1= 0.18537/mskn.09.02.02=

Š Author(s) 2018. This work is distributed under the Creative Commons Attribu= tion 4.0 License.

=

 

Artículo de Investigación

 

Aplicación d= el modelo de Christaller para la distribución espa= cial de supermercados

= Iván F. Palacios Orejuela

= Carrera de Ingeniería Geográfica y del Medio Ambiente, Departamento de Ciencias de = la Tierra y la Construcción, Universidad de las Fuerzas Armadas (ESPE). Av. Gr= al. Rumińahui s/n, Sangolquí, Ecuador.

= Autor para correspondencia: ivan199632@hotmail.com

= Fecha de recepción: 17 de septiembre de 2018 - Fecha de aceptación: 16 de noviembre = de 2018

=  

RESUMEN

La distribución en un territorio de centros de actividad económica, como supermercados, obedecen a un área de influencia que abarca una población definida. Esta distribución puede explicarse mediante modelos espaciales geográficos que analizan su ubicación e interrelaciones entre núcleos económicos. Uno de estos modelos es la Teoría de Lugares Centrales (CPT), propuesta por Christaller en 1933. En Ecuador, = la principal empresa de servicio y comercialización de productos de primera necesidad es Corporación Favorita, la cual cuenta con supermercados Superma= xi y Megamaxi, ubicados en varias ciudades del país. Quito, Guayaquil y Cuenca, por su extensión e importancia para la economía = del país, fueron las ciudades escogidas para este estudio. Mediante un SIG se a= plicó la CPT con diferentes centros anidados de cobertura (rango 1, 2, 3, y 4), y= se ajustó el modelo a la ubicación de los supermercados. En Cuenca y Guayaquil= , el modelo explicó en forma correcta la distribución espacial de los supermerca= dos, mientras que en Quito el modelo demostró, en gran medida, la espacialización en el norte y sur de la ciudad, sin embargo, en el centro norte y en los valles de la ciudad no representó adecuadamente la dinámica espacial. La geografía económica, a través de la = CPT, explicó la distribución espacial de los supermercados, y presenta una herramienta técnica en la toma de decisiones para empresarios y al ordenami= ento territorial de una ciudad.

= Palabras clave: Modelos espaciales, Teoría de los Lugares Centrales, dinámica espacial, ordenamiento territorial, geografía económica.

 

ABSTRACT=

The distribution in a territory of centers of econ= omic activity, such as supermarkets, obey an area of influence that covers a def= ined population. This distribution can be explained by geographic spatial models that analyze their location and interrelations between economic cores. One = of these models is the Central Place Theory (CPT), proposed by Christaller in 1933. In Ecuador, the main company of service and commercialization of products of first necessity is Corporación Favorita, which has Supermaxi and Megamaxi supermarkets located in several cities= of the country. Quito, Guayaquil and Cuenca, for their extension and importance for the economy of the country were chosen for the study. Using a GIS, the = CPT was applied with different coverage centers (range 1, 2, 3, and 4), and the model was adjusted to the location of the supermarkets. In Cuenca and Guayaquil, the model correctly explained the spatial distribution of the supermarkets, while in Quito the model demonstrated to a large extent the spatialization in the north, south of the city, however, in the northern ce= nter and in the valleys of the city did not represent the spatial dynamics. The economic geography, through the CPT explained the spatial distribution of supermarkets, and presents a technical tool in the decision making for businessmen and the territorial ordering of a city.

Keywords: Spa= tial models, Central Place Theory, spatial dynamics, territorial ordering, econo= mic geography.

 

1.&n= bsp;          = INTRODUCCIÓN

Una de las más grandes empresas en el Ecuador (sino la más grande), en cuanto a servicios y comercio de alimentos y productos de primera necesidad, es Corporación Favorita C.A. Es una empresa ecuatoriana con más de 65 ańos en = el país, cuya historia comenzó en el ańo de 1952 con la inauguración de la “Bo= dega La Favorita” en el centro histórico de Quito, por parte de su dueńo fundado= r, el empresario Guillermo Wright (Corporación Favor= ita, 2018). Desde entonces, esta empresa ha crecido en todo aspecto, hasta convertirse en una de las empresas más importantes del país, a través de sus formatos de supermercados e hipermercados en casi todo el Ecuador, como son: Supermaxi, Megamaxi, Juguetón, Akí, Gran Akí, Super Akí= y Super Saldos; mismas que conforman las marcas propias de la empresa (Corporación Favorita, 2018).

Entre las marcas de La Favorita, se destacan sus supermercados Supermaxi y Megamaxi, los cuales se encuentran distribuidos en las principales ciudades del país como son: Ambato, Cuenca, Guayaquil, Ibarra, Latacunga, Loja, Machala, Manta, Portoviejo, Quito, Riobamba, Salinas y Santo Domingo (Corporación Favorita, 2018). Para abastecer la demanda de todo el país, la empresa cuen= ta con más de 6,000 proveedores, quienes entregan sus productos en el centro de distribución (CD) de La Favorita, ubicado en Amaguańa (cantón Rumińahui, Pichincha) (González, 2017). El CD fue construido en el 2001 y es reconocid= o en América Latina por su tecnología de punta en todas las fases del proceso de recepción, distribución y elaboración de sus productos, además, de sus 165 = mil metros cuadrados de infraestructura que albergan ocho bodegas (Fig. 1), de = las que despachan diariamente, más de 205,000 bultos a todos los locales del pa= ís (González, 2017).

 

Figura 1. Centro de Distribución de Corporación Favorita (Fuente: González, 2017).=

La distribución de los locales en el territorio, si bien es cierto, sigue un proceso de decisión gerencial y mercantilista, es posible también entender = la lógica de su ubicación desde el punto de vista de la geografía, cuya rama de estudio es la geografía económica. Dentro de esta ciencia existen los denominados modelos espaciales, que combinan la economía espacial y la geografía, entre los que se destacan los modelos de Vo= n Thünen (1876), Weber (1909), Christaller (1933), Lösch (1940), Isar= d (1956) y Krugman (1992) (Ramírez, 2001; Fu= jita & Krugman, 2004). El entendimiento de la dinámica espacial en economía sirve no solo para satisfacer las necesidades de los clientes, sino también, como instrumento para un ordenamiento territorial en las ciudades donde existen este tipo de focos de acumulación y circulación de bienes y servicios, que entran y salen del territorio.

La Teoría de Lugares Centrales o CPT (como será abreviado en el presente traba= jo), por sus siglas en inglés de Central Place Theory, es una herramienta utilizada para el análisis geográfico de las relaciones económicas (Sáenz, 2017). El mentalizador de la= CPT fue el geógrafo alemán Walter Christaller, quien planteó una organización jerárquica de ciudades, las cuales operan como lug= ares centrales que ofrecen bienes y servicios en un espacio isotrópico, es decir, homogéneo (Dennis, Marsland, & Cockett, 2002). La jerarquía de las ciudades está determinada por el umbral del lugar central. Se entiende por umbral, el rad= io a la redonda del lugar central que abarca la población mínima que una empresa requiere para alcanzar su punto de equilibrio en ventas (Garrocho, 2003). L= os lugares centrales de mayor rango son entonces aquellos que tienen el mayor umbral, además de ser los únicos que ofrecen bienes de tipo superior (Sáenz, 2017). Según Asuad (2014), este modelo requiere= los siguientes supuestos básicos:

o&nb= sp;  La superficie es isotrópica, es decir uniforme;

o&nb= sp;  El desplazamiento ocurre en todas direcciones, sin barreras físicas al movimiento;

o&nb= sp;  Existe un solo tipo de trasporte, y el costo de transporte está en función de la distancia;

o&nb= sp;  La población se distribuye a lo largo = de la superficie en forma homogénea;

o&nb= sp;  Los consumidores y productores poseen racionalidad;

o&nb= sp;  La población tiene los mismos recursos= ;

o   Las preferencias y demanda de los consumidores son homogéneas.

Al igual que el umbral, otro factor importante es el rango de mercado, correspondiente a la distancia máxima que los consumidores están dispuestos= a recorrer para la adquisición de un bien o servicio. La relación entre el um= bral y rango de mercado resulta en que el primero es menor o igual al segundo (Sáenz, 2017). Si se representa al rango y umbral como circunferencias se obtienen las áreas de mercado de la siguiente forma:

Figura 1: Estructura espaci= al de las áreas de mercado con círculos (Fuente: Asuad<= /span>, 2014).

Figura 2.<= /b> Configuración espacial de las áreas de merca= do con hexágonos (Fuente: Asuad, 2014).

Figura 3: Jerarquización de= las áreas de cobertura de los centros (Fuente: adaptado de Clark & Rushton, 1970).

 

A pesar de cubrir, en gran parte, el área de influencia del mercado, existen ciertas zonas que no son atendidas (Fig. 2), por lo que Christaller propuso representar el umbral y rango mediante hexágonos, y así cubrir todas las áreas de influencia (Fig. 3). Una de las principales propiedades de la = CPT es que, el sistema está conformado de una jerarquía espacial de centro (hexágono mediano) anidados a otros centros de bajo orden (hexágonos más pequeńos), dentro de las áreas de orden mayor (hexágono más grande) (Clark & Rushton, 1970), esto se explica mejor en = la Fig. 4.

El modelo de Christaller fue establecido de forma cualitativa (Asuad, 2014), sin embargo, algunos trabajos han realizado aproximaciones geométricas de la CPT (Sonis, 2005), semejante a las teorías de combinación poliédrica de Weyl (1935). Por su parte, Beckmann & McPherson (1970) propusieron una versión cuantitativa, que se muestra a continuación.

Cada ciudad (centro) de espacio j, posee una población Pj que es una fracción constante c de = ese espacio.

Pj =3D cPj

(1)

 

donde: 0<c<1, la jerarquía de las ciudades de ese espacio es tal que= p1 es la población de m= enor orden jerárquico y r la poblaci= ón rural dependiente de ella, por lo que la población del área servida por la ciudad de mayor rango, P1<= /sub>, es función de la población de menor rango p1 y de r, denotado como:

P =3D p1 + r

(2)

 

Si la ecuación (2) se reemplaza en (1), la población de mayor rango es igual a= la partición de esa ciudad en el espacio j, Cp1, agregada su población rural r, que es igual a la fracción de la población c por la población ru= ral entre el total de la población de las ciudades, representada como 1–c:

P1 =3D Cp1, &, P1 = =3D p1 + r

(3)=

P1 = =3D Cp1 + r

 

P1 = =3D Cr / (1 – c)

(4)=

 

Por lo que, la población de la ciudad de orden 1 es igual al número de veces que represente la población d= e la ciudad de menor orden, incluyendo su población rural respecto a las ciudade= s en su conjunto de ese espacio. Además, las ciudades de una región, servidas por una ciudad de mayor orden (Pn), se obtienen de la población de menor orden Pn-1 que controla (1 + = s), donde s son los centros satélites de servicio y, al considerar que la población de la ciudad n, Pn permanece, y se tiene:

Pn =3D Pn-1 (1 + s) – Pn-1 + Pn

(5)

 

Al incluir la constante c:

Pn =3D Pn-1 (1 + s) – cPn-1 + cPn

(6)

Pn =3D Pn-1 (1 + s – c) + cPn

 

Pn =3D [(1 + s= – c) / (1 – c)] Pn-1

(7)

 

Debido a que en la CPT s y c son constantes a través de las jerarquías, se asume relación constante entr= e el tamańo de las ciudades de menor orden y de la población, con un comportamie= nto descendente.

Pn =3D [(1 + s – c) / (1 – c)]n-1 P1

(8)

Al sustituir el valor de P1 (Ec. 4) y simplificar la expresión (Ec. 8) resulta:<= o:p>

Pn =3D [(1 + s – c) / (1 – c)]n-1 Cr/(1– c)<= /o:p>

 

Pn =3D [(1 + s – c) / (1 – c)]n  rc / (1 + s – c)

(9)

 <= /o:p>

&= nbsp;

Esto indica que, si se conocen l= os asentamientos de la población rural r, se puede determinar el tamańo del área de mercado y la población de sus cen= tros en cualquier orden.

La diferencia entre los modelos de la nueva geografía económica (NGE) y los mo= delos de la CPT, se debe a que estos últimos intentan una aproximación más realis= ta y aplicable, a través de una amplia gama de actividades humanas relacionadas = en sus análisis, bajo la mecánica de que estas actividades están incrustadas e= n el espacio (Mulligan & Ca= rruther, 2012). Lo anterior hace posible que el modelo CPT tenga implicaciones práct= icas de política y planeación urbana (Sáenz, 2017). Sin embargo, también existen críticas al modelo propuesto por Christaller, principalmente en el supuesto de espacio estático, esto es, no contempla los cambios en el estatus socioeconómico de las personas (= Lal & Kumar, 2011) y, además, no considera el papel que juegan los oligopolistas y las externalidades en los procesos de aglomeración (Martin & Sunley, 1996).

Dentro de sus aplicaciones, existen diversos trabajos que emplean este modelo para= su explicación, por ejemplo: para explicar el acceso a espacios públicos (Smith & Floyd, 2013); en el entretenimiento de las funciones de ubicación y l= os resultados económicos derivados de alojar un evento deportivo (Daniels, 200= 7); en aproximaciones de microeconomía (Becerra, 2013); en el crecimiento de po= los regionales (Parr, 1973; Ru= shton, 2010); en arqueología (Smith, 1979); y para la planeación de la ubicación espacial de centros comerciales (West, Von Hohenbalken, & Krone, 1985; Clark, 1982; Garrocho, 2003), entre otros.

Este último es el enfoque del presente estudio, el cual tuvo por objetivo aplica= r la Teoría de Lugares Centrales de Christaller, para representar la distribución de los locales Supermaxi y Megmaxi en las ciudades de Quito, Guayaquil y Cuenca, con el fin de explicar la ubicación espacial de sus centros y subcentros de cobertura en dichas ciuda= des.

 

= 2.      =      = MATERIALES Y MÉTODOS

La información requerida para este estudio fue recogida del portal web de la empresa, en cuanto a la ubicación de los locales Supermaxi y Megamaxi en las tres ciudades analizadas, además de c= ontar con la ubicación del CD de La Favorita. Para su especialización su utilizó = un SIG, con el cual se realizó el modelo CPT con las áreas de influencia y sus respectivos rangos.

 

2.1.        Descripción del área de estudio

El área de estudio comprendió las tres ciudades más importantes del Ecuador: Quito, Guayaquil, Cuenca, las cuales se encuentran ubicadas en los cantones= que llevan sus mismos nombres (Fig. 5). La ciudad de Quito, capital ecuatoriana, cuenta con 2’239,191 habitantes (INEC, 2010) y es la capital política administrativa del país. Se encuentra ubicada sobre la hoya de Guayllabamba= , en el lado oriental del volcán Pichincha; está subdividida en nueve administraciones zonales, que a su vez se fraccionan en 32 parroquias urban= as y 33 rurales y subrurales (DMQ, 2018). Se incluyó= a la ciudad de Sangolquí, debido a la cercanía con Quito y a la presencia de dos locales de Supermaxi en su territorio.

“La perla del pacífico”, como se conoce a la ciudad de Guayaquil, es la capital económica del Ecuador, gracias a la presencia del Puerto de Guayaquil, el c= ual es el punto más importante de ingreso y salida del comercio en el país, con= un 83% de todas las importaciones y el 70% del total de las exportaciones (Ecuavisa, 2016). Posee una población de 2’350,915 habitantes (INEC, 2010).= Su división política comprende 16 parroquias urbanas y 5 rurales (GAD Guayaqui= l, 2018).

La ciudad de Cuenca, capital de la provincia de Azuay, se encuentra en la sier= ra sur del país y posee una población de 505,585 habitantes, según las cifras oficiales del último censo poblacional (INEC, 2010). A esta ciudad se la considera como un foco de desarrollo muy importante para el Ecuador, por su organización territorial, política y económica, lo que ha llevado a convert= irse en la sede de la Superintendencia de Ordenamiento Territorial (SOT), organi= smo encargado del ordenamiento territorial de país.

Figura 5.= Mapa de ubicación de los cantones Quito, Guayaquil y Cuenca en el Ecuador.

=  

(a)

(b)

(c)

Figura 6:= Distribución espacial de los locales Superma= xi y Megamaxi en las ciudades de Quito (a), Guayaq= uil (b) y Cuenca (c).

=  

2.2.        Distribución espacial

Como se mencionó anteriormente, el entendimiento de la ubicación espacial de los locales Supermaxi y Megamaxi, en este caso de estudio, permite analizar sus interacciones, su área en la cobertura de servicios y contribuir a la toma de decisiones para el ordenamiento territo= rial de una ciudad. En la Figura 6, se aprecia la ubicación de los distintos loc= ales Supermaxi y Megamaxi en las ciudades bajo estud= io.

A continuación, mediante herramientas SIG, se procedió a realizar el modelo d= e la CPT. Se usó el software ArcGis 10.2 para la generación de los hexágonos en las tres ciudades (Fig. 7). Se aplicaron cua= tro valores para definir el rango de mercado, los cuales fueron jerarquizados d= e la siguiente manera: hexágono de rango 4 (27.8 km), hexágono de rango 3 (9.3 k= m), hexágono de rango 2 (4.5 km) y hexágono de rango 1 (3 km), según el criterio cualitativo del modelo. Estos valores fueron establecidos mediante la experimentación y optimización de las áreas de influencia en las ciudades b= ajo estudio, para garantizar una cobertura total del servicio según las categor= ías asignadas.

Figura 7: Construcción de los hexágonos según la jerarquía del área de influencia.

 

= 3.      RESULTADOS Y DISCUSIONES

Una vez aplicado el modelo de Christaller a la distribución espacial de los supermercados Megamaxi y Supermaxi en las tres ciudades, se tuvo como resultado lo mostrado en las Figuras 8, 9, 10:

 

Figura 8:= Modelo de Christaller para la ciudad de Guayaquil.

Figura 9<= /span>: Modelo de Christaller<= /span> para la ciudad de Quito.

Figura 10: Modelo d= e Christaller para la ciudad de Cuenca.

 

En el caso de la ciudad de Guayaquil, la CPT se ajusta de manera coherente con= la distribución espacial en la que se encuentran ubicados los locales Supermax= i y Megamaxi en dicha ciudad, lo que garantiza un área de cobertura bien aprovechada y, además, sin competencia entre estos. Se puede observar de mejor manera el ajuste del modelo en la parte céntrica de la ur= be, debido a la correspondencia de un único local por hexágono de rango 1 (ver = Fig. 11). También se puede apreciar que, al menos hay un supermercado en cada hexágono de rango 3 (ver Fig. 8).

Figura 11: Distribución apropiada de locales según el modelo de Christaller en Guayaquil.

 

En la ciudad de Quito, se obtuvo un buen modelo de distribución espacial en las zonas norte y sur de la ciudad, así como en Sangolquí, mientras que, en el centro norte y valles de la capital (Cumbayá y Tumbaco), la CPT no se ajust= ó a la ubicación de los locales Supermaxi y Megamaxi (Fig. 12), lo cual sugiere dos posibles razones: (i) una mala distribución geográfica de los locales en la ciudad, o (ii) = el modelo de Christaller no explica el comportamie= nto de la distribución en esta zona. Sin embargo, esto último sería menos probable= , ya que el modelo explica favorablemente la especialización en el resto de la ciudad. También es importante notar que el hexágono de rango 4 (área total = de cobertura), no engloba a todos los locales de la ciudad, esto significa que= el modelo no se ajusta completamente a su distribución del área de cobertura. = Finalmente, para la ciudad de Cuenca, el modelo de Christaller se ajusta de forma excelente para explicar la distribución de los supermercado= s en la ciudad, como se demuestra en la Figura 10, sin competir entre ellos y con una cobertura total de la ciudad.

(a)

 

(b)<= span style=3D'mso-bidi-font-style:italic'>

Figura 12: Mala distribución de los locales segú= n el modelo de Christaller en la zona centro norte= (a) y valles (b) de Quito.<= /b>

 

= 4.      CONCLUSIONES

La Teoría de Lugares Centrales de Christaller demo= stró en casi todos los casos, que la distribución espacial de los locales Superm= axi y Megamaxi, se ajustan de forma correcta al mod= elo de hexágonos propuesto por Chirstaller, por lo que, gracias a la geografía económica, es factible un análisis técnico para comprender y mejorar la ubicación en el territorio de este tipo de negocios= .

El modelo de Christaller, es una herramienta que a= yuda no solo al entendimiento de la dinámica de la economía espacial, sino tambi= én a la toma de decisiones, por parte de los gerentes o dueńos de las empresas, = para la ubicación de nuevos supermercados, y para el mejoramiento del ordenamien= to territorial de una ciudad.

A través del uso de la CPT, se determinó que las ciudades de Guayaquil y Cuen= ca se ajustan correctamente al modelo propuesto; por su parte, en Quito, la CP= T no explicó totalmente el comportamiento de la distribución espacial en sus locales, sobre todo para la parte centro norte y valles de la ciudad.<= /o:p>

A pesar de los resultados, que en su mayoría fueron satisfactorios, se observó ciertas limitaciones del modelo, en cuanto al nivel de detalle que permite conocer la cobertura de las áreas de servicio a escalas más grandes (por ba= rrio o manzana), además de la falta de información respecto a la ubicación exact= a de los proveedores dentro de cada hexágono, con lo cual se podrían definir de mejor forma los rangos de cobertura en cada hexágono y así obtener un ajuste completo del modelo sin dejar por fuera a ciertos locales, como fue el caso= de Quito.

El presente estudio entrega una propuesta técnica para la explicación de la geografía económica en cuanto a la distribución, ubicación e interrelación = de una red de supermercados, como son Supermaxi y Megamax= i en las ciudades analizadas, que podría ayudar, a diversas escalas, en posteriores trabajos relacionados a la temática expuesta.=

 

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