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https://doi.org/10.37815/rte.v34n2.890

Artículos originales

 

Modelo de optimización para el problema de localización y ruteo vehicular en la distribución de ayuda humanitaria

A locatio= n-routing optimization model for distribution of humanitarian relief

 

Daniela Rivas Pastor1 <= /span>https://orcid.org/0000-0= 001-5525-5375,

Evelyn Olarte C= edeño1  = https://orcid.org/0000-0= 002-2137-9895, Erwin Delgado Bravo1, 2 https://orcid.org/0000-0= 001-5933-4839, Xavier Cabezas Garc= ía1 https://orcid.org/0000-0003-3128-001X= , Carlos Martín Barre= iro1 https://orcid.org/0000-0002-8797-681X=

 =

1Escuela Superior Politécnica del Litoral, Facultad= de Ciencias Naturales y Matemáticas, Guayaquil, Ecuador<= span style=3D'font-size:10.0pt;font-family:"Segoe UI",sans-serif;mso-ansi-langua= ge: ES-EC'>

drivas@espol.edu.ec, eolarte@espol.edu.ec, joxacabe@espol.edu.ec, cmmartin@espol.edu.ec 

 

2Escuela Superior Politécnica del Litoral, Centro Internacional del Pacífico para la Reducción del Riesgo de Desastres= , Guayaquil, Ecuador

edelgado@espol.edu.ec

 

Enviado:         2022/03/13

Aceptado:       2022/05/09

Publicado:      2022/06/30                         

Resumen

Sumario: Introducción, Descripción del problema, Revisión de literatura= , Modelo matemático para el problema de localización y ruteo de asistencia humanitaria, Aplicación en caso de estudio y Conclusiones.<= /span>

 <= /o:p>

Como citar:<= /span> Rivas, D., Olarte, E., Delgado, E., Cabezas, X. & Martín, = C. (2022). Modelo de optimización para el problema de localización y ruteo vehicu= lar en la distribución de ayuda humanitaria. Revista Tecnológica - Espo= l, 34(2), 166-180. http://www.rte.espol.e= du.ec/index.php/tecnologica/article/view/890


La respu= esta efectiva a las crisis humanitarias y emergencias originadas por desastres de diversa índole representa una tarea desafiante. Los aspectos logísticos inherentes a la planeación y ejecución de acciones de respuesta se orientan= a minimizar los costos y las pérdidas humanas de una forma eficaz.  En este estudio, se propone un modelo matemático que apoye la toma de decisiones de las organizaciones involucrad= as en brindar apoyo ante un evento emergente. Esa asistencia variada puede ir desde sugerir la ubicación de centros de transferencia temporales; la distribución de recursos a través de rutas secundarias desde los centros ha= cia las zonas afectadas por el desastre, y reducir el riesgo de que se entregue= n en forma tardía. El aspecto innovador de este trabajo es que se incorpora en la función objetivo una medida que cuantifica monetariamente el tiempo en que = una persona vulnerable se encuentra privada de un recurso, es decir, la diferen= cia de tiempo entre el momento en que la persona recibe la ayuda y el momento en que esta demanda es generada. Finalmente, se aplica el modelo propuesto en = una instancia derivada de los efectos causados por el terremoto en Ecuador en 2= 016.

 

= Pa= labras clave: = Localiz= ación, Ruteo Vehicular, Emergencia Humanitaria, Gestión de Riesgo.

 

Abstract

Responding effectively to humanitarian crises and emergencies caused by disasters of various kinds is a challenging task. The logistical aspects inherent to the planning and execution of response actio= ns are oriented to effectively minimize costs and human losses. This study proposes a mathematical model to support the decision-making of the organizations involved in providing support to an emergency event. Such var= ied assistance can include suggesting the location of temporary transfer center= s, distributing resources through secondary routes from the centers to the are= as affected by the disaster, and reducing the risk of late delivery. The innovative aspect of this work incorporates a measure that quantifies, in a monetary manner, the time in which a vulnerable person is deprived of a resource (time between the generation of aid demand and the aid reception). Finally, the proposed model is applied in an instance derived from the effe= cts caused by the earthquake in Ecuador in 2016.

 

Keywords: Location, Veh= icle Routing, Humanitarian Emergency, Risk Management.=

 

Introducción

A pesar de múltiples esfuerzos adoptados por diversos países para enfrentar situaciones de emergencias, los desastres naturales como terremotos, inundaciones, deslave= s, erupciones volcánicas, entre otros, siguen siendo un asunto de preocupación= por las posibles pérdidas humanas y económicas. Cada año, diversos eventos de emergencia ocurren en lugares e instantes inesperados, lo que sobrepasa en algunas ocasiones el pronóstico del impacto de estos sucesos.

 

El impacto de una emergencia se mitiga por la pronta entrega de apoyo humanitario para los afectados a través de una red primaria y secundaria de distribución, en la = cual se identifican, adicionalmente, puntos de aprovisionamiento y almacenaje. S= in embargo, a diferencia de otros sistemas de distribución, la gestión de la a= yuda humanitaria podría incluir la apertura temporal de centros de acopio o de transferencia de recursos cerca de las zonas afectadas por algún desastre p= ara atenderlos de una manera ágil, lo cual podría incidir en los costos del sistema. En efecto, el movimiento de recursos (humanos y materiales), puede alcanzar hasta el 80% de los costos de alguna operación de socorro <= !--[if supportFields]>ADDIN CSL_CITATION {"citationItems":[{"id":"ITEM-1","itemDa= ta":{"author":[{"dropping-particle":"",&= quot;family":"Clark","given":"Alistair",= "non-dropping-particle":"","parse-names":fals= e,"suffix":""},{"dropping-particle":"&qu= ot;,"family":"Culkin","given":"Bernadett= e","non-dropping-particle":"","parse-names&qu= ot;:false,"suffix":""}],"container-title":&qu= ot;International Journal of Computational Intelligence Systems","id":"IT= EM-1","issue":"1","issued":{"date-p= arts":[["2013"]]},"page":"233-257","= ;title":"A network transshipment model for planning humanitarian relief operations aft= er a natural disaster","type":"article-journal","volume&qu= ot;:"7"},"uris":["http://www.mendeley.com/document= s/?uuid=3D19f17540-9d7f-4814-a0ac-c66a9a9d54ba"]}],"mendeley"= ;:{"formattedCitation":"(Clark & Culkin, 2013)","plainTextFormattedCitation":"(Cla= rk & Culkin, 2013)","previouslyFormattedCitation":"(Cl= ark & Culkin, 2013)"},"properties":{"noteIndex":0},"schema&= quot;:"https://github.com/citation-style-language/schema/raw/master/cs= l-citation.json"}(Clark & C= ulkin, 2013), lo que se constituye en  un factor  vital a ser tomado en cuent= a por el tomador de decisiones.

 

Múltiples estudios dirigidos a proporcionar un marco de referencia, basados en modelos de optimización para la toma de decisiones, se han desarrollado para abordar el problema de distribución de ayuda humanitaria en situaciones de emergencias; cada una de ellas incluyendo diversas características operacionales propias= del evento, algunas se abordarán en el presente estudio.

 

El presente trabajo sig= ue la siguiente estructura: en la sección 2 se realiza una descripción del problema abordado, en la sección 3 se presenta una breve revisión de investigaciones relacionadas con el problema, en la sección 4 se explica el modelo propuesto para el problema descrito en la sección 2. En la sección 5= se muestra un ejemplo numérico de la implementación del modelo, considerando u= na instancia generada a partir de los efectos causados por el terremoto en Ecu= ador en abril del 2016. Finalmente, en la última sección,  se plantean las conclusiones, así como algunas futuras contribuciones.

 

Descripción del = problema

La estructura del siste= ma de distribución de ayuda humanitaria que se ha adoptado en este estudio sig= ue la línea de investigación propuesta por Khayal et al.,= ( 2015), la cual consiste en un conjunto de centros de aprovisionamiento (CA) desde donde se abastecen a todas las zonas afectadas= por una posible situación de emergencia que derive en algún desastre humanitari= o o económico (ZAD) a través de un conjunto de centros temporales de transferen= cia (CT) (Figura 1= ). Es precisamente en estos centros de transferencia, donde se realizan diversas actividades logísticas, por ejemplo,  recepción de carga, ordenamiento, empaquetamiento, etc.; por lo que, la selección y ubicación de estos deben cumplir ciertas condiciones que garanticen su operatividad como, por ejemplo, alta conectividad vial, accesibilidad de vehículos pesados, ac= ceso a servicios básicos, etc.

 

Generalmente, el movimi= ento de bienes entre los centros de aprovisionamiento y los centros temporales de transferencia toma un tiempo en ejecutarse debido al manejo de la carga, el traslado a través de la red vial, entre otras actividades logísticas. En es= te estudio, se ha adoptado que la logística de distribución de los recursos de= sde los CA hasta los CTs se ejecuta en un periodo de tiempo, es decir, recursos que se deciden enviar en un instante desde un ce= ntro de aprovisionamiento tardan un periodo en llegar a los centros de transferencia.

 

Figura = 1=

Estructura de una cadena de distr= ibución de ayuda humanitaria

 

Luego de que los centros temporales disponen de los recursos demandados por personas vulnerables en = las zonas afectadas, desde cada uno de estos centros empiezan y terminan divers= os circuitos, que son atendidos por un vehículo que pertenece a una flota homogénea.

 

Bajo este escenario, en cada uno de los  period= os que pertenecen a un horizonte de planificación  se tie= ne que la demanda de las ZADs, y la cantidad de recursos disponibles en los CAs son conocidos, pero su número podría variar en el tiempo debido al reabastecimi= ento de los recursos en cada periodo y en cada CA. Por otra parte, en un periodo dado podría suceder que la demanda de recursos = es mayor a la oferta disponible, por lo que, se requiere atender la demanda no satisfecha en periodos posteriores, incurriendo con ello en un costo de penalización (dependiente del tiempo en que se entrega el faltante) por pri= var de asistencia humanitaria a personas vulnerables ante un desastre.

 

En el contexto de asistencia humanitaria emergente, los requerimient= os de recursos pueden variar en el tiempo, por lo tanto, la apertura de un cen= tro de transferencia será dinámico para responder rápidamente ante estos cambio= s. Asimismo, debería permitir el almacenamiento temporal de recursos para aten= der futuras entregas, considerando la capacidad de estos.

 

Revisión de literatura

A lo largo de la literatura se observa que diversas estrategias han = sido adoptadas para mitigar los efectos que un eventual desastre pudiere causar = en una población. Algunas de estas estrategias están enfocadas en la formulaci= ón de modelos matemáticos para diversos problemas generados en las etapas de p= reparación (antes), por ejemplo, localización de centros de atención inmediata y model= os de evacuación; o en la etapa de respuesta (después) del evento de emergencia tales como localización de centros temporales de transferencia de ayuda humanitaria, distribución de ayuda a personas vulnerables o transferencia de heridos (Hezam & Nayeem, 2021)<= !--[if supportFields]>. Esta sección = se enfoca en la revisión de trabajos previos enfocados en atender una emergencia de f= orma reactiva, debido a la naturaleza del problema previamente descrito.

 

Luego de un desastre, uno de los problemas a enfrentar inmediatament= e es la entrega de asistencia humanitaria (kits alimenticios) a las personas en estado de vulnerabilidad. Diversas decisiones deben ser adoptadas por el en= te gubernamental que gestiona la dotación de estos recursos, así, por ejemplo: dónde localizar los puntos de abastecimiento o de transferencia de los recursos, cómo se entregarán los bienes requeridos y cuándo se deberá hacer dicha entrega. En lo referente a la localización de instalaciones que apoya= n el proceso logístico de entrega de la asistencia humanitaria, se aplican los clásicos enfoques para resolver este problema de optimización: modelos de máxima cobertura, p-median o el problema de cubrimientos de conjuntos (Hezam & Nayeem, 2021)<= !--[if supportFields]>.

 

Múltiples autores utilizan diversos enfoques para apoyar la toma de decisiones en el proceso de distribución de los recursos, algunos de ellos = con el objetivo de minimizar los costos logísticos de  esta acción (Horner & Downs, 2010; Rabta et al., 2018), u optimizar l= os tiempos de respuesta por la emergencia (Campbell et al., 2008). Otros autores abordan la distribución de recursos enfocada en minimizar la cantidad de demanda no satisfecha (Afshar & Haghani, 2012; Al Theeb & Murr= ay, 2017; Yi & Kumar, 2007), incorporando = en la función objetivo un costo de penalización por demanda insatisfecha. Al Theeb & Murray, (2017) define este c= osto de penalización como fijo para cada tipo de recurso a ser entregado. Sin em= bargo, en logística humanitaria el costo de penalización por la privación de algún recurso, definido como el valor económico del sufrimiento humano por la fal= ta de acceso de un bien o servicio (Holguín-Veras et al., 2013),  es dependiente de la diferencia de tiem= po entre el momento en que la demanda del recurso es requerida y el momento en= que la demanda es satisfecha, así como la edad, género y otras condiciones socioeconómicas del destinatario de la ayuda (Holguín-Veras et al., 2013).

 

Khayal et al. (2015) incorpora implícitamente estos costos de penalización en la función objetivo por dema= nda no satisfecha en un modelo de optimización, el cual está enfocado en locali= zar un conjunto de centros temporales de transferencia de recursos y de asignac= ión de los recursos desde el centro de transferencia, sin considerar el ruteo vehicular desde el centro de transferencia a las zonas afectadas por un eventual desastre. Por otro lado, Wang et al.(2014) aborda el problema de localización de instalaciones y ruteo de vehículos de manera integral en un modelo de optimización multiobjetivo que evalúa tiempos de recorrido, confiabilidad de las rutas y costos logísticos sin incorporar penalización por demanda no satisfecha. Finalmente, Afshar & Haghani (2012<= !--[if supportFields]>) integran los problemas de localización y distribución pretendiendo minimizar la demanda = no satisfecha, ponderando de acuerdo con la necesidad del bien, siendo este parámetro definido de antemano, no garantizando el cumplimiento de toda la demanda requerida en el horizonte de planificación.

 

Modelo matemático para el problema de localización y ruteo de asistencia humanitar= ia

Para definir el modelo de optimización para el problema descrito en = la sección 3, en la Tabla 1<= /span> se detallan lo= s parámetros y las variables de decisión considerados en la formulación del modelo:=

 

Tabla 1=

Notación, parámetros y variables consider= ados en el modelo de optimización

Índices

 

Centros de aprovisionamiento de recursos.

Zonas afectadas por el evento de desastre.

Centros de transferen= cia de recursos.

Centros de transferen= cia o zonas afectadas por el evento de desastre.

Tipos de recursos.

Periodos.<= /span>

 

 

Conjuntos

 

Conjunto de centros d= e aprovisionamientos.

Conjuntos de zonas afectadas<= span lang=3DPT style=3D'font-size:10.0pt;mso-fareast-font-family:Calibri;mso-a= nsi-language: PT;mso-fareast-language:EN-US'> por el evento de desastre.

Conjunto de potencial= es centros temporales de transferencia de recursos.=

Conjunto de zonas afectadas centros temporales.

Conjunto de recursos<= o:p>

Conjunto de periodos = en el horizonte de planificación

 

 

Parámetros

 

Capacidad de los vehículos disponibles en los potenciales centros de transferencia.

 

 

Espacio requerido para almacenar una unidad del recurso

 

 

Abastecimiento del recurso k<= span lang=3Des-419 style=3D'font-size:10.0pt;font-family:"Cambria Math",seri= f; mso-fareast-font-family:Calibri;mso-ansi-language:#580A;mso-fareast-lan= guage: EN-US'>∈K  en el centro de aprovisionamiento o  en el periodo t

 

 

Demanda del recurso <= /span>  en la zona afectada  inmediatamente luego del = evento del desastre

 

 

Capacidad máxima del potencial centro de transferencia .

 

 

Costo fijo por la operación temporal del centro de transferencia .

 

 

Costo de penalización por privar a la zona afectada por el desastre <= /span>  de poseer una unidad del recurso  en el periodo t  y que es satisfecha en el periodo .

=

 

=

 

 

 

 

 

 

Variables

 

Variable binaria que = toma el valor de 1 cuando el centro temporal de transferencia  está operando en el perio= do , 0 en caso contrario.

 

 

Variable binaria que = toma el valor de 1 cuando la zona afectada por el desastre  es asignado al centro temporal de transferencia  en el periodo , 0 en caso contrario.

 

 

 y  pertenece a una ruta generada en el ce= ntro temporal de transferencia  en el periodo  en la solución óptima, 0 = en caso contrario.

 

 

Cantidad por enviar d= el recurso k<= span lang=3Des-419 style=3D'font-size:10.0pt;font-family:"Cambria Math",seri= f; mso-fareast-font-family:Calibri;mso-ansi-language:#580A;mso-fareast-lan= guage: EN-US'>∈K  en el periodo  desde el centro de aprovisionamiento <= /span>  hasta el centro de transferencia .

 

 

Nivel de inventario d= el recurso k<= span lang=3Des-419 style=3D'font-size:10.0pt;font-family:"Cambria Math",seri= f; mso-fareast-font-family:Calibri;mso-ansi-language:#580A;mso-fareast-lan= guage: EN-US'>∈K  a inicios del periodo  en el centro de aprovisionamiento .

 

 

 al final del periodo  en el centro de transferencia <= /span> .

 

 

 en el periodo  desde el centro de transferencia  hasta la zona afectada po= r el desastre <= !--[if gte msEquation 12]>i<= /span>I .

 

 

Cantidad por enviar d= el recurso k<= span lang=3Des-419 style=3D'font-size:10.0pt;font-family:"Cambria Math",seri= f; mso-fareast-font-family:Calibri;mso-ansi-language:#580A;mso-fareast-lan= guage: EN-US'>∈K  en el periodo  desde el centro de transferencia  hasta la zona afectada po= r el desastre <= !--[if gte msEquation 12]>i<= /span>I  para satisfacer demanda no satisfecha en el periodo .

 

 

 del recurso  en el periodo

 

 

 hasta la zona afectada po= r el desastre <= !--[if gte msEquation 12]>i<= /span>I  en el periodo ..

 

 

 en el periodo  en la ruta generada en el centro de transferencia .

 

Con base en la notaci= ón descrita, un modelo de optimización para el problema abordado en la sección= 3 es como sigue:

 

La ecuación (1) representa la función objetivo a minimizar, la cual comprende los costos logísticos de distribución de la ayuda humanitaria (primera y segunda componente de la ecuación), los costos de penalización por la privación de = los recursos a las personas vulnerables ante la emergencia (tercera componente)= y los costos derivados por la instalación de los centros temporales de transferencia (cuarta componente).

 

 

(1)

El siguiente conjunto= de restricciones permite asignar una zona con personas vulnerables con algún centro de transferencia que aporte en satisfacer su demanda, siempre que es= te centro esté operativo.

(2)

 

Las siguientes restricciones garantizan la conservación de los flujos de cada tipo de recu= rso a ser entregado a las personas vulnerables, tanto en los centros de aprovisionamiento (3) como en los potenciales centros de transferencia (4).= En efecto, la primer componente de la parte izquierda de la ecuación (3) representa el nivel de inventario a inicio de un periodo, mientras que la segunda componente representa el abastecimiento al centro del recurso analizado, por lo que, la suma de estas componentes representa la cantidad total disponible a inicios de un periodo, y este valor debe ser igual a la = suma de la cantidad a entregar a todos los potenciales centros de transferencia (primera componente de la parte derecha de la ecuación (3)) y el inventario inicial en el periodo consecutivo (segunda componente).

 

Asimismo, la parte izquierda de la ecuación (4) representa la cantidad disponible de un recurs= o en algún periodo. A diferencia de la ecuación (3), el abastecimiento de los centros de transferencia proviene de los centros de aprovisionamiento que envían los recursos en el periodo anterior. La cantidad total a la izquierd= a de la ecuación (4) es igual a la suma de los recursos entregados a tiempo (pri= mera componente a la derecha de la ecuación (4)) y los recursos que satisfacen demandas no cumplidas en periodos anteriores (segunda componente) a las zon= as afectadas por el desastre, así como lo que queda en almacenamiento al final= del periodo analizado (tercera componente).

 

(3)

 

 

(4)

 

El siguiente conjunto= de restricciones garantiza que la capacidad de cada centro de transferencia no supere la capacidad del centro de transferencia. La inclusión de la variable binaria  permite además que, si el centro de transferencia no opera en un periodo dado ( ), nada se envíe desde el centro de aprovisionamiento en el periodo anterior (= ) y que el inventario al final del periodo sea nulo ( ).

 

(5)

 

Las siguientes restricciones permiten el envío de recursos a una zona afectada desde un ce= ntro de aprovisionamiento solo cuando la asignación entre ellas es admitida en a= lgún periodo ( = xijt =3D1), siendo <= /span>  un número grande que haga que la relació= n sea redundante cuando esto ocurra.

 

(6)

 

Las siguientes relaciones posibilitan, en primer lugar, calcular la demanda y el instante a partir del cual puede ser entregado el segundo kit = de asistencia humanitaria (7), mientras que la ecuación (8) garantiza el cumplimiento en la entrega de la demanda de recursos.

(7)

 

 

(8)

 

El conjunto de restricciones, presentado a continuación, garantiza que, si en un periodo d= ado no se encuentra operativo un centro de transferencia, entonces el inventari= o al final del periodo anterior de ese centro de transferencia debe ser cero.

 

(9)

 

La ecuación (10) calc= ula, en cada periodo, la cantidad de recursos asignado desde cada centro de tran= sferencia a cada zona afectada por algún desastre.

 

(10)

 

Las siguientes ecuaci= ones garantizan que, si una zona afectada por el desastre no está asignada, en u= n periodo, a un centro de transferencia ( ), entonces aqu= ella zona no pertenecerá a alguna ruta generada desde el centro de transferencia= .

 

(11)

 

(12)

 

Los conjuntos de restricciones (13) y (14) <= span lang=3Des-419 style=3D'mso-fareast-font-family:Georgia;color:black;mso-ansi= -language: #580A;mso-fareast-language:EN-US;mso-bidi-font-weight:bold'>facultan relaci= onar las variables de carga transportada en los vehículos entre dos zonas afecta= das por algún desastre. En efecto, suponiendo que , es decir, la sección de la ruta generada en el centro de transferencia  se ejecuta entre las  zonas consecutivas  y  en el periodo , entonces la cantidad la parte derecha de la restricción (13) se reduce a   lo que indica que la carga al salir de l= a zona  debe ser obligatoriamente al menos el va= lor de  En caso contrario ( 0), la restricc= ión (13) es redundante (siempre que  sea lo suficientemente grande).

 

(13)

 

 

(14)

 

La restricción (15) garantiza que la capacidad de los vehículos no sea excedida.

 

(15)

 

Finalmente, el domini= o de las variables de decisión se establece a partir del siguiente conjunto de restricciones:

(16)

(17)

 

Aplicación en caso de estudio

Por la naturaleza reactiva del problema abordad= o, uno de los supuestos adoptados en la formulación del modelo propuesto es qu= e el impacto del desastre natural (deslave, inundación, sequía entre otros) es conocido de antemano. La magnitud del impacto del desastre sin duda depende= de la naturaleza de este, ya sea en la accesibilidad a las zonas afectadas o el número de personas a asistir debido al evento emergente. Por ello, el enfoq= ue propuesto en esta investigación para la distribución eficiente de recursos puede ser aplicado en diversos escenarios donde se requiera asistir con ayu= da humanitaria, a personas en estado de vulnerabilidad por la ocurrencia de al= gún desastre natural sin importar la naturaleza de este.

 

 Uno de estos, cuyos efectos se ha documentado y es objeto de aplicación del modelo presentado, es el terremoto= que sacudió Ecuador el 16 de abril de 2016 que provocó cuantiosas pérdidas huma= nas, así como destrucción en infraestructura vial y edificaciones, especialmente= , en cabeceras cantonales ubicadas en la  Costa norte y centro de Ecuador (Instituto Geofísico de la Escuela Politécnica Nacional, 2022) En la Figura 2= se muestran algunas de las cabeceras cantonales (representadas por un círculo azul) con mayor índice de afectaci= ón en infraestructura, medido como la razón entre el número de edificaciones destruidas y el número de edificaciones registradas. Como se puede observar, Pedernales y Jama fueron las cabeceras cantonales con mayor índice de perju= icio en comparación con las zonas restantes, en estas cabeceras cantonales algun= as manzanas fueron destruidas casi en su totalidad como, por ejemplo, en Pedernales (Figura 3= ).

=  

Fuente Metadatos: http://www.geoportaligm.gob= .ec/portal/index.php/sismo-2016/

 

F= igura

Cabeceras cantonales con mayor incidencia de afectación por terremoto en Pedern= ales

&nb= sp;

 

= Fuente Metadatos: http://www.geoportaligm.gob.ec/portal/index.php/sismo-2016= /

 =

F= igura

Porcentaje de edificios destruidos por manzanas en Pedernales por terremoto.

 =

 

Una revisión del número de edificaciones destruidas por el terremoto muestra que Jama tuvo una mayor afectación en comparación con las otras cabeceras cantonales (Figura 4= ). Bajo el supu= esto que cada edificación sirve de hogar para un grupo familiar y tomando como referencia 3.78 el tamaño promedio de cada hogar en Ecuador en el periodo 2011-2012 (INEC, 2012) se tiene que, aproximadamente, 19000 personas estuvieron en situación de vulnerabilidad p= or el evento sísmico en las regiones analizadas.

 

Figura 4=

Número de edificaciones destruidas en cabeceras cantonales

Fuen= te Metadatos: http://www.geoportaligm.gob.ec/portal/index.php/sismo-2016/

 

Ante la magnitud del evento sísmico, múltiples entidades públicas y privadas se activaron con el objeto de brindar asistencia humanitaria a los damnificados. El Gobierno Nacional, a través de la anterior Secretaría Naci= onal de Gestión de Riesgo (ahora Servicio Nacional de Gestión de Riesgo y Emergencias), emitió una guía para la distribución de ayuda humanitaria (Secretaría Nacional de Gestión de Riesgo, 2011)= , la cual   consistió en la entrega quincenal de m= áximo dos kits alimenticios a un grupo familiar de 4 personas; además, kits de limpieza, hogar y cocina para albergues con capacidad de 50 personas.<= /o:p>

 

A pesar de que la normativa establece 15 días como la diferencia en tiempo de las entregas de cada kit alimenticios a cada familia, en el prese= nte estudio se ha considerado que la diferencia en tiempo de las entregas de ca= da kit alimenticios a cada familia es 7, para que la ejecución del modelo sea = manejable en tiempos computacionales, pues esta investigación no abarca el análisis de centros temporales de acogida,  sin= o  la distribución de  los kits alimenticios a familias de cada edificación destruida. Adicionalmente, en la guía se establecen especificac= iones en cuanto al ancho y largo de los kits, siendo estos 60 cm y 80 cm, cada un= o de ellos con un peso de aproximadamente 22 kg. En este análisis se ha asumido = una altura de 20 cm, por lo que almacenar un kit alimenticio consume 0.096 metr= os cúbicos de espacio físico.

 

Por otra parte, dada la naturaleza del recurso a ser suministrado a = las personas en estado de vulnerabilidad, se define como función de costos de penalización a = , siendo = el tiempo de desfase desde el momento en que la demanda es requerida y el mome= nto en que es entregada, la cual fue adoptada por Holguín-Veras et al. (2013<= !--[if supportFields]>) para cuantificar el valor monetario que las personas están dispuestas a pagar por obtener agua. En lo referente a la flota de vehículos que se encargarían de transportar los kits desde los centros temporales de transferencias hasta las zonas afectadas po= r el evento sísmico, se ha considerado que la misma es homogénea con un peso máx= imo de carga de 22 toneladas, lo que permitirá transportar un máximo de 1000 ki= ts en cada uno de los vehículos.

 

En lo referente a los centros de aprovisionamiento, se ha selecciona= do las ciudades de Quito y Guayaquil (cuadrados rojos en la Figura 5= ) por su alta conectividad hacia diversas regiones del país con diferentes modos de transporte, así como por la concentración en estas regiones de múltiples actividades económicas. Generalmente, los entes encargados de la distribuci= ón de asistencia humanitaria poseen en inventario un número de kits que les permite atender a personas en condición de vulnerabilidad a la brevedad posible. Sin embargo, si el inventario disponible es menor a lo demandado, = se requiere que estos centros se reabastezcan. Bajo este escenario, se ha adop= tado que cada centro de aprovisionamiento se reabastezca de forma dinámica confo= rme la Figura 6= . Por otra part= e, para el presente estudio se han escogido como potenciales instalaciones temporales de transferencias las ciudades de Pedernales, Chone y Portoviejo= (rombo turquesa en la = Figura 5= ).

 

Figura 5=

Localización de Centros de Aprovisionamiento y Potenciales Centros de Transferencias

Figura 6=

Suministro temporal de kits alimenticios en los centros de aprovisionamiento

Finalmente, para esta investigación se requiere el cálculo de la distancia recorrida por los vehículos entre los centros de aprovisionamient= o y las instalaciones temporales de transferencia, a través de la red vial nacional. Por ello, a partir de la red de carreteras de Ecuador, se aplicó = el algoritmo de la distancia más corta entre un par de puntos, el cual se encuentra implementado en el paquete de Análisis de Redes del QGIS3.

 

El modelo propuesto en la sección 4 fue implementado en GAMS 24.0.2 y ejecutado con la instancia derivada del terremoto en el año 2016, utilizando CPLEX en una PC Intel Core i7-9700 CPU 3 GHz con 8 procesadores definiendo = el valor de 12 horas como el tiempo máximo de ejecución del algoritmo. Los resultados muestran, con un GAP=3D6.4%, que en las tres ciudades (Portoviej= o, Chone y Pedernales) se deberá instalar un centro de transferencia de kits alimenticios durante los días (periodos) que se muestran en la Figura 7= . Por ejemplo, = en Pedernales se deberá ubicar un centro sólo en los periodos 2 y 9. Asimismo,= en el periodo 2, deberían operar los tres centros temporales de transferencia.=

 

Figura 7=

Periodos de operación de centros temporales de transferencia de kits alimenticios

 

La Figura 8= muestra la planificación de la distribución del primer kit alimenticio que se entregar= á a las personas con vulnerabilidad, domiciliados en las zonas afectadas. Aquí = se muestra también que, en todas las ciudades, con excepción de Jama y Portovi= ejo, se entrega la demanda requerida en solo una visita, mientras que en ciudades como Portoviejo se tendrá que realizar la entrega en dos envíos, siendo el porcentaje de entrega en el primer envío mucho menor que el realizado en la segunda entrega. Como se puede observar, durante el primer periodo es impos= ible realizar entrega a las zonas afectadas, ya que el tiempo de aprovisionamien= to desde los centros de aprovisionamiento hasta los centros de transferencias = es de 1 día, por lo que el recurso requerido se encuentra en camino durante el primer periodo (día).

 

 Figura 8=

Planificación de la distribución del primer kit alimenticio a = ser entregado en las zonas afectadas

 <= /span>

 

En relación con la distribución de los kits alimenticios, en cada periodo, la planificación de las rutas no solo depende de la demanda requer= ida por las zonas afectadas, sino también de la ubicación de los centros tempor= ales de transferencia. Así, en el periodo 2 (segundo día de entrega de los recursos), el día anterior se despachan los recursos desde Quito hasta los centros de transferencia ubicado en Chone y Pedernales, y desde Guayaquil a Portoviejo y Chone, es decir ambos centros de aprovisionamiento abastecen al centro temporal ubicado en Chone.

 

Posteriormente, desde el centro de trasferencia ubicado en Pedernale= s se distribuyen los recursos a Jama, Pedernales y Muisne en ese orden de visita (línea violeta en la Figura 9= ), desde Chone a las zonas Jama, Canoa, Bahía de Caráquez y San Vicente (línea naranja en la= Figura 9= ),  mientras que desde Portoviejo se distri= buyen los kits alimenticios a las poblados de Jaramijó, Manta, Montecristi y Portoviejo (línea azul en la Figura 9= ). En contraste= , en el periodo 4 (cuarto día de entrega de los recursos), se generan dos rutas:= la primera partiendo desde Chone hasta Jama y la segunda desde Portoviejo para abastecimiento de la misma región. (Figura 10).

 

F= igura

Rutas de distribución de kits alimenticios en el segundo periodo (día)<= span lang=3DES-US style=3D'mso-fareast-font-family:Calibri;mso-fareast-lan= guage: EN-US;mso-no-proof:yes'>

F= igura

Ruta de distribución de kits alimenticios en el cuarto periodo (día)

= &= nbsp;

Conclusiones

En este trabajo, se propone un modelo de optimización para tomar decisiones sobre la ubicación dinámica de centros de trasferencia de ayuda humanitaria y la forma en que los recursos son entreg= ados a personas vulnerables ante una emergencia. La flexibilidad en su formulaci= ón, específicamente en los parámetros determinísticos incorporados, permite adoptarlo en diversos tipos de desastres naturales (deslaves, inundaciones, terremotos entre otros). Sin embargo, la naturaleza del evento emergente pu= ede incidir en la confiabilidad de la red de transporte o en la caracterización= de la demanda.

 

Adicionalmente, con base en el análisis d= el caso de estudio, se pone en evidencia que la ubicación temporal de los cent= ros es vital en problemas referentes a ayuda humanitaria por la dinámica de la demanda requerida. No obstante, los tiempos de repuesta podrían mejorarse s= i el enfoque de asistencia humanitaria es proactivo y no reactivo, mediante la evaluación de la posibilidad de instalar centros de transferencia permanent= es en zonas propensas a ser afectadas por un eventual desastre. Bajo estos escenarios, se hace viable extender el estudio del problema abordado a mode= los de optimización robustos o estocásticos que tome en cuenta lo expuesto anteriormente.

Un aspecto por destacar en la formulación= del objetivo del modelo propuesto es que la misma integra costos logísticos en = la distribución de recursos (componentes 1,2 y 4 de la función objetivo) y cos= tos sociales por la no entrega de recursos en la cantidad requerida y el momento adecuado (componente 3 de la función objetivo). Estos últimos costos representan la valoración monetaria por la privación de recursos vitales a = las personas vulnerables. Una incorrecta calibración de los parámetros que defi= nen esta función de costo podría sesgar los resultados obtenidos, priorizando la disminución de los costos logísticos. Por ello, futuros estudios enfocados = en un modelo biobjetivo pueden ser una estrategia vál= ida en el abordaje del problema planteado. Finalmente, se ha incorporado costos de penalización por la entrega tardía de algún recurso a la población vulnerab= le. Bajo este contexto, otras dimensiones podrían ser analizadas en futuros trabajos que incluyan alguna componente de prioridad, a través de ponderaci= ones adecuadas, por edad o grado de afectación.

 

Referencias

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Campbell, A. M., Vandenbussche, D., & Hermann, W. (2008). Routing for relief efforts. Transportation Science, 42(2), 127–145. https://doi.org/10.1287/TRSC.1070.0209 =

Clark, A., & Culkin,= B. (2013). A network transshipment model for planning humanitarian relief operations after a natural disaster. International Journal of Computatio= nal Intelligence Systems, 7(1), 233–257.

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Instituto Geofísico de la Escu= ela Politécnica del Litoral. (2022). Informes y Noticias. Disponible en: https://www.igepn.edu.ec/eq20160416-informes-noticias

Khayal, D., Pradhananga,= R., Pokharel, S., & Mutlu, F. (2015). A model for planning locations of temporary distribution facilities for emergency response. Socio-Economic Planning Sciences, 52, 22–30. https://doi.org/10.1016/J.SEPS.2015.09.002

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6

Daniela Rivas, Evelyn Olarte, Erwin Delgado, Xavier Cabezas, Carlos Martín

5

Modelo de optimización pa= ra el problema de localización y ruteo vehicular en la distribución de ayu= da humanitaria

 

E= scuela Superior Politécnica del Litoral, ESPOL

<= /p>

 

R= evista Tecnológica Espol – RTE Vol. 34, N° 2 (Junio, 2022)

<= /p>

 

R= evista Tecnológica Espol – RTE Vol. 34, N° 2 (Junio, 2022)

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