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Revisión literaria e histórica de medidas de complejidad de proyect= os y desempeño de proyectos

 =

Héctor Julio Polo Ábrego1,, Yarissa M. Palma2

1Estudiante de doctorado de la Unive= rsidad Tecnológica de Panamá (UTP), Dirección de Postgrado, Ingeniería de Proyectos

2Universidad Tecnología de Panamá, D= irección de Gestión y Transferencia del Conocimiento

&n= bsp;

*Autor = para correspondencia. Email: hjpoloa@gmail.= com

 

 

<= span class=3DMsoHyperlink>    Recibido: = 26 de septiembre de 2020 

<= span class=3DMsoHyperlink>Aceptado: 08 de octubre de 2020

­­­­­­­­___= _______________________________________________________________________

 =

Resumen

Esta revisión literaria es una indagación acerca de metodologías de medición del desempeño y complejidad de los proyectos, que evidencia la no existencia de una comparación entre ambas mediciones bajo la definición estándar de desempeño.  Se establece la diferencia entre las metodologías holísticas o cualitativas, y aquellas basadas en la teoría de grafos aplicada, y se exploran las variaciones y tendencias actuales de mediciones del desempeño y el éxito de los proyectos, llevándonos a reevalu= ar definiciones de los conceptos investigados y apreciar las ventajas que resu= ltan en utilizar los métodos basados en la teoría de grafos aplicada. Se concluye que los cronogramas de obra pueden, de estar bien realizados, ser utilizados como base para la medición de la complejidad de proyectos.

Palabras Clave: Complejidad de proyectos, v= alor ganado, índice de complejidad, índice de desempeño del cronograma

 

Abstract

This literary review seeks methodologies = to measure the performance and complexity of projects, and to demonstrate the non-existence of a comparison between both measurements under the standard definition of performance. The difference between qualitative and holistic methodologies and those based on applied graph theory is established, and current variations and trends in project performance and success measuremen= ts are explored, leading us to reevaluate the investigated concepts’ definitio= ns and appreciate the advantages that result from using methods based on appli= ed graph theory. It is concluded that work schedules can, done properly, be us= ed as a basis for measuring project complexity.

Keywords: Project complexity, earned = value, complexity index, schedule performance index.

 =

1.   Est= ado del Arte - Introducción

La intención de esta primera sección es la de explorar la literat= ura más reciente con tal de esclarecer los conceptos de: proyecto, complejidad,= la complejidad de un proyecto y el desempeño de un proyecto, valor agregado, y= el concepto del éxito de un proyecto también será explorado.

 

Seguido a la aclaración de estos conceptos, se abordan las dos gr= andes vertientes en el análisis de la complejidad de un proyecto, la que modela elementos de forma holística de un proyecto, y la que modela estrictamente = los elementos finitos de los cronogramas de proyectos.

 

De acuerdo con esta premisa, se establecerá una base teórica para adentrarnos en el método especifico utilizado en los cálculos de esta tesis= .

 

1.1.      =         Definiciones de Proyecto, Complejidad, Desempeño y Éxito

 

1.1.1.Proyecto

<= o:p> 

Un proyecto se define, según el PMBOK (Project Management Book of Knowledge o el Libro de Conocimientos de la Administración de Proyectos del Project Management Institute, PMI, el Instituto de Administración de Proyec= tos), como “el esfuerzo que se lleva a cabo para crear un producto, servicio o resultado único, y tiene la característica de ser temporal.  No es ni el producto, servicio o result= ado único por lo cual se hacen estos esfuerzos” [1]. pg. 5.  Esta es una definición ya aceptada por = la industria y será base de nuestra investigación.

 

 

1.1.2.      =   C= omplejidad

 

Existe un consenso de que la definición de “complejidad”, y la mi= sma aplicada a proyectos, ha sido difícil de determinar.  En esta sección llegaremos a explorar v= arias propuestas de autores que han abarcado el tema orientándolo a la administra= ción de proyectos.

 

 

1.1.2.1.      =          P= ropuesta de la definición de complejidad por Baccarini, 1996

 

Baccarini explora varios acercamientos al concepto de complejidad= por otros autores.  Inicia con el conce= pto de complejidad como una “dimensión del proyecto en sí” [2]. Continua con la definición de diccionario en la cual se define como aquello que consiste en muchas partes interrelacionadas [2]. De aquí deriva el concepto de la diferenciación de los elementos y la interconectividad de estos, comentando= que “esta interpretación de complejidad refleja la teoría de sistemas en la que= un sistema complejo es frecuentemente definido en términos de diferenciación y conectividad” [2]

 

 

 

 

 

Finalmente, su propuesta para la definición de la complejidad de = un proyecto es la siguiente:

=  

= “Se propone que la complejidad del proyecto ‘consta de muchas par= tes interrelacionadas y variadas' y que se pueda operacionalizar en términos de diferenciación e interdependencia.” [2]<= /o:p>

 

Esta definición es posteriormente aceptada por Wood, 2010 [3]

 

1.1.2.2.      =         L= as cuatro asociaciones de complejidad por Frame, 2002

 

J. Davidson Frame en el 2002 estudia el problema de los Proyectos complejos iniciando con el concepto de “complejidad”. No logra hacer una definición puntual, sin embargo, la asocia con 4 características: el tamaño= , la variedad, la dificultad y el cambio. De seguido abordaremos estos cuatro aspectos bajo la perspectiva de Frame.

 

 

a. La complejidad se asocia con el tamaño del objeto

 

Frame afirma que “generalmente, los objetos grandes con muchos componentes tienden a ser más complejos que aquellos más pequeños con menos componentes” pg.25. [4] Igualmente desarrolla la fórmula del máximo número = de relaciones entre estos elementos: “n(n-1) /2, o (n2-n) /2” pg.25[4], la cua= l veremos que será utilizada como base de la fórmula de complejidad de cronogramas desarrollado por Naga y Hageb.

 

b. La complejidad se asocia con la variedad=

 

Se refiere a la cantidad de opciones existentes a la hora de toma= r todo tipo de decisiones.  “El dilema de = las opciones excesivas que un gerente de proyecto y su equipo se enfrentan es obvio” pg.27[4]. También menciona que las particularidades de un proyecto generalmente no se repiten con otro: “el hecho de que sus proyectos tienden= a ser únicos (a los gerentes de proyectos) los confunde porque las lecciones aprendidas de “sortear” por opciones de su proyecto anterior son frecuentem= ente irrelevantes en el [proyecto] actual” pg.27 [4].

 

c. La complejidad se asocia con la dificultad

 

“Cuando algo es difícil de realizar es generalmente visto como más complejo que algo que es fácil” pg. 28.  Aquí el autor hace comparaciones con el cálculo y la aritmética, sie= ndo la primera más compleja que la segunda.  Sin embargo, agrega que “la complejidad enraizada en la dificultad es generalmente manejada a través de la maestría,” que se traduce en “educació= n y experiencia” pg.28 [4]

 

d. La complejidad se asocia con el cambio

 

“La rapidez del cambio en el mundo de hoy contribuye hasta cierto= grado a la complejidad.  Una manera en qu= e lo hace es creando un blanco en movimiento”. pg. 30 [4] Bajo este concepto Fra= me incluye temas como cambios tecnológicos, aumento exponencial en la informac= ión disponible, en los cambios en los alcances y requerimientos de los proyecto= s, entre otros [4]

1.1.2.3.      =         El acercamiento dual de Vidal sobre el concepto de complejidad de <= /span>

proyectos, 2007

=  

Vidal, et. Al., tiene dos conceptos sobre complejidad.  Uno que desarrolla dentro de su metodol= ogía posterior, que es la complejidad de la administración misma del proyecto, y= la complejidad sistemática del mismo.

 

La primera la define como “la cadena de decisiones generales” tom= adas. [5]

 

La complejidad sistemática lo define analógicamente con un ejempl= o que parte de la intuición y no necesariamente proporcione algún resultado.

 

Vidal dice que esta complejidad sistemática “puede entenderse fácilmente a través de un ejemplo simple, el del nivel de detalle de la estructura de desglose del trabajo. Si la estructura de desglose del trabaj= o no es lo suficientemente extensa, el proyecto puede haberse descompuesto débilmente y los paquetes de trabajo no se han definido correctamente: como consecuencia, los paquetes de trabajo podrían descomponerse en subtareas qu= e no han sido definidas por el gerente del proyecto y es probable que la autoorg= anización resultante de esta ausencia de detalles afecte mal el desempeño del proyect= o. Por el contrario, si la estructura de desglose del trabajo es demasiado extensa, la descomposición puede ser demasiado compleja para usarse de mane= ra efectiva, ya que las interacciones y las interrelaciones entre los paquetes= de trabajo pueden ser demasiado numerosas para ser gestionadas adecuadamente.”= [5]

 

Vidal nos muestra una gráfica teórica de la relación entre la complejidad de un proyecto y el desempeño del mismo.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ilus= tración 1 - Curva de complejidad optima= [5]

 

 

 

En esta grafica se puede observar que, según la interpretación de Vidal, debe haber un nivel óptimo de complejidad que permita desarrollar el proyecto con buen desempeño.  Muy p= oca complejidad no permite alcanzar el máximo desempeño, y demasiada complejidad tampoco.

 

Esta teoría de Vidal está basada en un concepto de estructura de trabajo, que es en esencia, como mencionan Nassar y Hageb, la complejidad d= el cronograma y no necesariamente del proyecto en sí. [6]

 

Sin embargo, Vidal en un artículo posterior del 2011, menciona 4 aspectos que luego retomaremos en la exploración de la definición de la com= plejidad de proyectos. Estos 4 aspectos son: “1. el aspecto teleológico, 2. el aspecto funcional 3. el aspecto ontológico y 4. el aspecto genético” [7= ].

 

1.1.2.4.      =         T= eoría de la complejidad como fenómeno social de Weaver, 2009

=  

Weaver, considera que la teoría de complejidad tiene que ver con = las relaciones sociales dentro del proyecto, por encima de cualquier otro aspec= to: “La esencia de CRPR (“Complex Responsive Processes of Relating” o Procesos Receptivos Complejos del Relacionarse) y la teoría de redes sociales es que= el resultado final del proyecto, su éxito o fracaso, es creado por miles de decisiones individuales tomadas por los miembros del equipo del proyecto en= el curso de sus interacciones diarias entre sí, a través de conversaciones, incrustadas en sus relaciones. Es imposible que el Gerente de Proyecto esté= al tanto de cada conversación y decisión”. [8]

 

Donde CRPR se define como: “Los procesos de respuesta complejos (CRPR) ponen énfasis en la interacción entre las personas y la naturaleza esencialmente receptiva y participativa de los procesos humanos de organiza= ción y relación. La organización es una propiedad emergente de muchos seres huma= nos individuales que interactúan juntos a través de sus complejos procesos receptivos de relacionarse. (Stacey, Griffin, Shaw. 2000) Utilizan el lengu= aje en las conversaciones para transferir simultáneamente información e ideas, negociar el estatus social y desarrollar relaciones de poder (Cooke-Davies,= et al. 2007)”. [8]

 

Para Weaver, el tema de la complejidad se define bajo este concep= to de relaciones sociales, pero sigue siendo solo un elemento de las dimensiones a tomar en cuenta a la hora de planificar y controlar un proyecto utilizando = los cronogramas de obra.  Esto lo evide= ncia en sus 4 puntos describiendo las dimensiones de un proyecto:

 

“1. Su tamaño inherente generalmente medido en términos de valor;= 2. El grado de dificultad técnica para crear la salida; 3. El grado de incertidum= bre involucrado en el proyecto; y 4. La complejidad de las relaciones ("pequeña p" política) tanto dentro del equipo del proyecto como = en torno al proyecto “. [8]

 

Interesantemente, para Weaver, recae en el “cronogramista”= o planificador la responsabilidad de atender sobre todo las dificultades técn= icas del cronograma y a su vez estar al tanto y trabajar en el punto de la complejidad “social” del proyecto, en conjunto con el gerente del proyecto.= [7]

 

 

 

 

 

1.1.2.5.      =         C= omplejidad de un proyecto por Luo, Lan et. Al., 2012

 

Luo presenta 3 claros acercamientos, los primeros dos para llegar= a la definición de complejidad, y luego el tercero para definir la complejidad d= e un proyecto.  Menciona que “la complejidad es definida al tener un numero grande de partes interactuando”<= /i> [9] y que “la ciencia de la complejidad es el estudio de estas interacciones.” [9]. Por ende, para Luo, la complejidad de un proyecto = es “considerada una de las más fundamentales propiedades de un proyecto y resulta de la interacción de sus diferentes partes con propiedades estructurales, dinámic= as e inciertas” [9]

 

 

1.2.      =        El concepto de desempeño de proyectos y su diferencia con el éxito del proyect= o.

 

1.2.1.      =   M= edición de desempeño utilizando el método de valor ganado.

 

El PMI le llama desempeño del proyecto al cociente resultante de dividir el valor ganado, entre el valor planificado, en algún momento del tiempo del proyecto.  A este result= ado le llama el índice de desempeño del cronograma.  Las variables son las siguientes:

 

“SPI (Schedule Perfomance Index o Índice de Dese= mpeño del Cronograma)

EV (Earned Value o Valor Ganado)

PV (Planned Value o Valor Planificado)

La fórmula sería:

SPI =3D EV/PV” [1] pg= . 183

 

Esta fórmula adoptada por el PMI fue desarrollada inicialmente por el cuerpo de defensa de los Estados Unidos [4, 10].  En sí, mide el avance económico permiti= endo observar desde el inicio problemas que pueden resultar a la larga en un proyecto impactado.  Su enfoque en = costos no quiere decir que no tome en cuenta el factor tiempo, ya que el mismo se = basa en utilizar las duraciones de las actividades del proyecto para crear el comportamiento base del plan del proyecto, y compararlo con las cifras real= es, tanto de valor, como de costos.

 

 

 

 

 

 

 

 

 

 

 

 

Ilus= tración 2 - Gráfica Ejemplo de Valor Ganado [11]

<= /span>

 

 

Lo que no se puede ver con una curva general de todo el proyecto,= se podría ver en análisis realizados a secciones de estos, de ser un proyecto = con mayor complejidad y tamaño.

 

1.2.2.      = Distinción del desempeño y el éxito de un proyecto=

 

Luo (2012), expresa la definición del desempeño del proyecto como aquello que “principalmente se enfoca en los indicadores de la ejecución del proyecto, mientras que el éxito del proyecto incluye el periodo posterior a= su terminación y su influencia” [9]  <= /span>

 

Luo menciona que la definición de éxito del proyecto “consistí= a en cumplir con el triángulo dorado de tiempo, costo y calidad” [9], pero considera esta definición como el “criterio original de medir el éxito d= e un proyecto, y que, aunque son importantes, no incluyen medidas de factores modernos del éxito de un proyecto.” [9]. Entre estos factores, menciona= el “tiempo, la calidad, la salud y seguridad, el rendimiento ambiental, la satisfacción= de los participantes, la satisfacción del usuario, y el valor comercial.” = [9]

 

1.3.      =        Complejidad de Proyectos – Vertiente holística

 

La palabra holística según la real academia de la lengua española= se define como:

 

“Que pertenece a… (ver holismo) una doctrina que propugna la conc= epción de cada realidad como un todo distinto de la suma de las partes que lo comp= onen.” [12]

 

La complejidad de proyectos ha sido observada de manera holística= , es decir, como aquel concepto que, al lograr discernirla de sus partes que la componen, nos puede proveer de una visión más clara de lo que representa.

 

Con una analogía sencilla, el ser humano es en sí la suma de toda= s sus partes: manos, piernas, cabeza, corazón, espíritu. Sin embargo, el ser huma= no no es sus manos, no es sus piernas, ni su corazón ni su espíritu.

 

La complejidad de proyectos ha sido observada de manera holística= en la mayor parte de la literatura disponible sobre la gestión de proyectos [3,5,7,8,13,14,15-21]. En esta manera holística/cualitativa de ver la complejidad de proyectos es preciso sopesar o ponderar los factores cualita= tivos para tratar de cuantificar elementos que, de otra manera, serían muy difíci= les de medir [7]. En estos casos, el investigador se ve en la difícil tarea de proponer un método estadístico que refleje el consenso y el aval de opinion= es de varios profesionales [7,15].

 

Para identificarlos dentro de esta categoría, he tomado los sigui= entes aspectos para determinar el criterio de clasificación:

 

1.&n= bsp;      En su mayoría los elementos = son cualitativos o difíciles de cuantificar, y deben pasar por un proceso de po= nderación para su cuantificación.

2.&n= bsp;      Contienen elementos fuera del proyecto en sí (véase sección 1.1.1. Proyecto de este artículo sobre= la definición de un proyecto).

3.&n= bsp;      Requieren de una revisión y aprobación posterior por parte de los participantes de los métodos propuest= os.

Dentro de estos elementos o factores se encuentran temas como: el análisis del cliente, estructura organizacional (roles, canales de comunicación, comunicación regular, la experiencia del equipo, la calidad d= e la toma de decisiones), resultado de arbitrajes, expectativas de los accionist= as o involucrados, el tamaño del proyecto, las interdependencias del proyecto co= n el ambiente, la interdependencia de los departamentos, la interdependencia de = los sistemas de información, el contexto cultural, y la complejidad tecnológica, entre otras [7,13].

 

El resultado de estos acercamientos son los diferentes métodos propuestos como lo son el método analítico por jerarquía [7] y la utilizaci= ón del método Delphi [14]. Otros acercamientos se limitan al modelado como una herramienta de análisis dentro de los procesos administrativos [13], o prop= onen una cuantificación de procesos meta-proyectuales (más allá del análisis de = un solo proyecto) [7,15].

 

En la siguiente sección se exploran las metodologías resultantes = debido a las conclusiones tomadas por varios autores dentro de esta clasificación holística de la complejidad de proyectos.

 

 

= 1.3.1.      =   C= omplejidad de Proyecto utilizando el método de descomposición funcional/dimensional, Sinha, 2006 [22]<= o:p>

 

Sinha propone utilizar el sistema de descomposición funcional para evaluar la complejidad de las actividades del proyecto.  Asume que “que la complejidad de una actividad de proyecto depende del número de sus dimensiones y los niveles de sus factores generadores de complejidad.” De este concepto desarrolla la siguiente formula:

 

 

 

 

En donde “Donde N es el número de dimensiones de una actividad de proyecto, CGFi es el número de factores generadores de complejidad en el ni= vel i y L es el número de nivel.” [22]

 

La razón por la cual se incluye dentro del grupo de definiciones holísticas de complejidad, yace en los factores que Sinha incluye dentro de= su descomposición funcional/dimensional.

 

Estos factores se pueden apreciar en su análisis ejemplo represen= tado por un modelo jerárquico de dimensiones recreada en la siguiente imagen:

 

<= /span>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ilus= tración 3 - Descomposición dimensional de una actividad de proyecto [22]

 

 

Estos elementos presentados requieren de una apreciación del gere= nte del proyecto.  Sinha menciona que p= ara esta evaluación “las actividades del proyecto fueron de un proyecto de construcción completado anteriormente y fueron administradas por un gerente= de proyecto con 30 años de experiencia.” [22] La tarea de realizar esta evalua= ción recae sobre el equipo administrativo, o como lo menciona Sinha, sobre el “gerente de proyecto” [22] agregando elementos cualitativos dentro del análisis.

 

 

 

= 1.3.2.      = Complejidad vista desde un punto de vista de model= ado de categorías, Vidal, 2007 [5]

 

 

Seguida tabla replicada de su categorización de las aristas o elemen= tos incluidos dentro de su modelado.  <= o:p>

 =

 =

Tabl= a 1 – Marco de referencia ALOE (Atributos, Enlaces (Links), Objetos, Evento= s) [5]

<= /span>

 

Ilus= tración 4 – De una falta de entendimiento global a ganancia en el entendimiento local [5]

El resultado buscado por Vidal es una representac= ión visual que ayuda a la comunicación de los involucrados en el manejo del proyecto.

 

 

 

 

 

Dentro del proceso del modelado existen elementos cualitativos que deben trabajarse:

 

“Donde a veces había cierta confusión y falta de acuerdo sobre la definición de todos los elementos que estaban involucrados en un proyecto, ahora hay un marco general y una estructura estandarizada que crea consenso dentro del equipo del proyecto.”

 

1.3.3.      = Complejidad vista desde un punto de vista de model= ado de categorías, Wood, 2010 [13]

 

Wood considera importante tomar en cuenta 16 temas principales pa= ra modelar la complejidad de un proyecto y de esta manera definirlo. [13]

 

Estos temas los subdivide en 5 categorías principales según la siguiente tabla:

 

 

Tabl= a 2- Temas de complejidad de proyectos [13]

 

La complejidad, incluso menciona las fórmulas previamente estable= cidas por Nassar and al. [6], pero no aclara cómo las usa en su metodología para modelar la complejidad del proyecto.

 

1.3.4.      = Complejidad de Proyecto utilizando el proceso jerárquico-analítico, Vidal, 2010 [7]

 

Similar al acercamiento por Wood [13] y Weaver [8], Ludvic prefie= re proponer un método que entra dentro de los métodos holísticos.

 

 

 

Ludvic utiliza, para su marco de evaluación, 18 factores esencial= es repartidas en 4 grandes categorías:

<= /span>

Tabl= a 3 – Marco refinado de la complejidad de proyectos [7]

<= /span>

 

Cabe destacar que Ludvic con= sidera este método una propuesta definitiva para solucionar la definición y medici= ón de la complejidad de un proyecto. Sin embargo, su éxito depende de la opini= ón de quienes participaron en el estudio mencionado.

 

Ludvic considera este método= :

 

“fiable, ya que los usuarios= finales confían en los resultados, medidas y escalas que se proponen. Durante el estudio    de caso, los participant= es del caso de estudio nunca impugnaron ningún resultado numérico”. [= 7]

=  =

No hay indicativo en el estu= dio de la cantidad de personas a las que se refería Ludvic ni existe un estudio estadístico que apoye esta afirmación.

 

 

1.3.5.      = Complejidad de Proyecto utilizando el método de factores por categorías,

Lan, 2016, [9]=

 

Lan considera que “se cree ampliamente que la complejidad está en gran medida relacionada con la subjetividad del observador”. Partiendo de este concepto, coincide, como mu= chos predecesores, de incluir en su método de medición, aspectos cualitativos en= su análisis.  La siguiente tabla demue= stra este acercamiento, con la cual procede a hacer su cálculo de correlación de= las respuestas obtenidas por las muestras de campo.  Su muestra se basa en 256 encuestados, cuyas respuestas fueron procesadas y categorizadas de la manera mostrada en la tabla sig= uiente.

 

Tabl= a 4 - Factores de complejidad potenciales y medidas de éxito de proyectos complejos de construcción

<= /span>

 

 

<= o:p> 

1.3.6.      = Conclusiones sobre las metodologías de la vertiente holística<= o:p>

 

La vertiente holística/cuali= tativa sopesa o pondera los factores cualitativos para tratar de cuantificar eleme= ntos que, de otra manera, serían muy difíciles de medir.  En estos casos, el proponente, se ve en= la difícil tarea de formular un método que a todas luces tiene aspectos subjetivos, porque las ponderaciones se hacen en base a la experiencia u opinión del autor, o que está avalada por la opinión de un grupo de persona= s de manera más o menos democrática.

 

Una cantidad muy pequeña de = la literatura relacionada con esta temática abarca métodos cuantificables para= la obtención de un método de medición de la complejidad de proyectos.  Estos métodos se basan normalmente en la teoría de grafos aplicada, y la mayoría de las veces participan los nodos, arcos, métodos gráficos de simplificación y, en algunos casos, una combinac= ión de los factores mencionados. Algunos métodos incluyen recursos, duraciones = de las actividades y otros elementos que no son información de fácil acceso en todos los proyectos, y por ende de estos no se puede realizar una generalización aplicable.

 

 

La literatura más reciente c= ontinúa inclinándose por un enfoque holístico, dejando para la década pasada aquell= as investigaciones relacionadas al modelado del cronograma, siendo esta última vertiente la que produce figuras de índices de complejidad más intuitivas y sencillas que prometen su facilidad de uso, en la profesión de gestión de proyectos.  Sin embargo, carecen de= una explicación convincente de su utilidad basándose en los conceptos de cronogramas de proyectos y cuáles son sus funciones dentro de un proyecto.<= o:p>

 

Reafirmamos que es posible s= eguir por la vertiente del modelado de cronogramas propuesto para mostrar que una teoría de grafos ayuda en cierta medida, pero no completamente, a la medici= ón de la complejidad del proyecto en sí, tratando de seguir algunos métodos po= r su sencillez de uso, sin dejar de ser cuantificable.

 

 

1.4.      =        Complejidad de proyectos – vertiente del modelado de cronogramas

 

Una cantidad muy pequeña de = la literatura relacionada con esta temática se centra en la obtención de un mé= todo de medición de la complejidad de proyectos [6,23,24,25] basándose en modelo= s de los proyectos con información “concreta”.  Estos métodos se basan generalmente en la teoría de grafos aplicada,= y participan la mayoría de las veces los nodos y arcos de la red del cronogra= ma de proyectos, con métodos que incluyen la simplificación de la red, y algun= os de ellos, una combinación de lo anterior. Algunos métodos incluyen recursos, duraciones de las actividades y otros elementos que no son información de f= ácil acceso en todos los proyectos, y por ende de estos no se puede realizar una generalización aplicable [6].

 

La discusión que produce est= e método resulta en dos formas de definición de complejidad.  Nassar y Hegab definen su método como <= i>“la medición de la complejidad del cronograma del proyecto” [23], o sea la medición de complejidad de un aspecto del total de la complejidad de un proyecto, mientras que Vidal et al. definen este método como “las medici= ones del modelo de la estructura del proyecto representada como un grafo” [7= ,26].  Ninguno percibe este acercamiento como = algo que logre definir la complejidad de un proyecto en su totalidad.=

 

Aquí es donde la definición = de un proyecto y de complejidad deben ayudar a definir justamente el alcance de e= stos métodos y mediciones.  Al no haber = un consenso de este, se presenta la siguiente síntesis para obtener una defini= ción base de esta investigación:

 

1.      = Un proyecto se define, según= el PMBOK, como el esfuerzo que se lleva a cabo para crear un producto, servici= o o resultado único, y tiene la característica de ser temporal.  No es ni el producto, servicio o result= ado único por lo cual se hacen estos esfuerzos [1].

 

2.      = “Un sistema es un objeto, qu= e, en un ambiente dado, intenta alcanzar un objetivo (aspecto teleológico) al realiz= ar una actividad (aspecto funcional) mientras su estructura interna (aspecto ontológico) evoluciona con el tiempo (aspecto genético) sin perder su identidad” [7].

 

3.      = Y que “la complejidad de un = proyecto es la propiedad de un proyecto que hace difícil comprender, prever y manten= er en control su comportamiento general, aun cuando se haya dado información razonablemente completa sobre el sistema del proyecto” [7].

 

Tomando en cuenta estos 3 conceptos, se aprecia la utilidad del modelado de un cronograma de obra que abarque los siguientes elementos:

 

1.      = Se establece la estructura del proyecto (aspecto ontológico)

 

2.      = Se establece el objetivo final, incluso objetivos parciales (aspecto teleológico)

 

3.      = Se modela los esfuerzos por medio de actividades (aspecto funcional)

 

4.      = Se modela su evolución con el tiempo (= aspecto genético)

 

5.      = Sus elementos están interrelacionados = para tener secuencia, unidad, e identidad.

 

6.      = Contiene, si está bien realizado, la p= rincipal y mayor cantidad de información necesaria para poder administrar un proyect= o.

 

De lo anterior, se considera que medir la complejidad de un cronogr= ama es lo más cercano a medir, por definición, la complejidad de un proyecto.

 

Otros elementos externos serian meta-proyectuales o multi-proyectua= les (más de un proyecto), y aunque son útiles, no serán fundamento de esta investigación.

 

 

1.4.1.      =   M= etodologías de análisis de complejidad de proyectos por la vertiente del modelado de cronogramas

 

Las fórmulas propuestas que están relacionadas con el tema de la complejidad de proyectos calculado en base a los cronogramas de obras se presentan aquí de forma cronológica según la fecha de los artículos de referencia.

Ilus= tración 5 - Red de actividades en arcos o flechas – Fuente – recreación de ilustración encontrada en https://knowledge4civil.= wordpress.com/2017/04/09/uses-of-cpm-and-pert-in-construction-management/

Antes de continuar, la historia de estos métodos está directamente relacionada a la evolución que = hubo en el desarrollo del método de creación de redes de cronogramas de proyectos.  En un inicio se basaban= mucho en las redes en donde las actividades eran representadas en los arcos o fle= chas de las redes (ver ilustración 5). Posteriormente se adoptó el método de representar las actividades en los nodos (ver ilustración 6).

Ilus= tración 6 - Red de actividades en nodos – fuente: simplificación de ilustración encontrada en https://www.tomfanelli.c= om/how-to-visualize-your-infographic-part-3/

 

1.4.2.      = Pascoe, 1966, Red de Actividad en Flecha

 

La fórmula de Pascoe resulta en índice simple, en la cual solo se toman, sin modificaciones o análisis previos, el número de actividades y el número de arcos de un cronograma.  =

 

En donde “C” es el índice de complejidad de proyectos, “a” el númer= o de relaciones o arcos, y “n” el número de nodos o actividades. [6]<= /span>

 

1.4.3.      = Davies, 1974, AOA

 

Davies, ya utilizando teoría de grafos, reconoce que existe un lími= te máximo y un límite mínimo de relaciones posibles por número de nodos (actividades) en una red. A esto le da un factor de 2x de forma arbitraria = para ayudar al cálculo del análisis.

 

En donde “C” es el índice de complejidad de proyectos, “a” el númer= o de relaciones o arcos, y “n” el número de nodos o actividades. [6]<= /span>

 

1.4.4.      = Kaiman, 1974, redes AOA

 

Kaiman resuelve su fórmula de manera similar a Pascoe, solo agregán= dole un factor al cuadrado al número de arcos/relaciones.

 

=

 

 

En donde “C” es el índice de complejidad de proyectos, “a” el númer= o de relaciones o arcos, y “n” el número de nodos o actividades. [6]<= /span>

 

1.4.5.      = Kaiman, 1974, redes AON (pero no toma en cuenta los nodos).<= o:p>

 =

Con esta fórmula, Kaiman ignora los arcos y contempla solo las actividades, utilizando el número de actividades precedentes para establecer una proporcionalidad con el número de actividades totales.

 

 

=

 

En donde “ ” es = el número de actividades precedentes y “ ” el = número de actividades [6], enfocándose más en las situaciones de embudo que pueden suceder en la consecución de actividades en un cronograma.

 

 

1.4.6.      = Badiru citado por Nassar et al., junio 2006=

 

Badiru presenta una fórmula del índice de complejidad de proyectos tomando en cuenta más variables que solo actividades y relaciones de una red del cronograma.  La fórmula es la siguiente:

 =

“Donde L=3D número de actividades en l= a red; ti=3Dduración esperada de la actividad i; R =3D número de tipos de recursos= ; xij =3Dunidades de los recursos tipo j requeridas por la actividad i; Zj =3D nú= mero máximo del tipo de recursos j disponibles; p =3D máximo número de predeceso= res inmediatos en la red; y d=3D la duración PERT del proyecto sin restriccione= s de recursos.” . [6]

 

Esta es una fórmula orientada a medir la complejidad de una sola actividad, y tendría que hacerse interacciones de esta por cada actividad p= ara poder evaluar la complejidad de un proyecto completo.  Tiene la dificultad de que no muchos cronogramas incluyen en todas sus actividades recursos específicos a la tar= ea. Por lo cual en algunos proyectos el índice total del proyecto resulta parci= almente incorrecto.

 

 

 

 

 

 

 

 

1.4.7.      = Medida de complejidad para cronogramas de proyecto= s, Khaled M. Nassar1 and Mohamed Y. Hegab, Junio 2006, AON [6]

 

 =

repre= senta los arcos y  los nodos o actividades.  Esta fórmula no se asegura que los dígr= afos no sean mínimos, pero si contempla los límites como aquellos que tengan arc= os de redundancia.  También utiliza dí= grafos que tengan un número máximo de arcos como base para una banda superior de m= edición. [6] Cabe mencionar que dentro de estos análisis no se contemplan proyectos = en que las últimas actividades no estén relacionadas entre sí, tema que se aba= rca dentro de la propuesta al proponer un hito final como un estándar de desarr= ollo de cronogramas.

 

 =

1.4.8.      = Índice de Complejidad de Proyectos basado en la Topología, Boushaala, 2010 [25]

 =

 

Boushala propone aumentar el detalle de los factores a variables a utilizar a la hora de realizar la métrica de la complejidad del proyecto, a= gregando las rutas críticas a las variables de número de actividades y relaciones, ya establecidas.

 

Dónde:

 

 =3D número de rutas críticas en la red

 =3D número de actividades críticas en la= red

 =3D número de actividades en la red=

 



 

 

1.4.9.      = Basado en la centralidad y centralidad de rutas. K= han, 2010 = [27]

 

Para Khan, los índices propuestos anteriormente no representan una complejidad del proyecto o cronograma, sino una medición de la calidad de e= sta [27].  Critica los métodos anterior= es por no incluir suficientes factores de medición, como la duración de las actividades. Afirma que solo funcionan para comparar un proyecto con otra instancia de sí misma, y que la definición de complejidad está limitada a la relación entre número de arcos y actividades [27].

 

Sin embargo, Khan no llega a medir complejidad, si no la estabilidad misma del cronograma, definiendo su índice de centralidad como la medición = de la buena calidad de un cronograma que a su vez sucede cuando los valores de= la ruta crítica son estables y no es seriamente afectada por cambios menores e= n la duración de una actividad [27]

 

Khan presenta la siguiente formula:

 

 =

= =

 

 =

=

 

 

Aquí  denota el número de nodos en el grupo  y  es la duración de la ruta de abismo (sink path) a través del nodo “n”.  Estas definiciones fueron inspiradas por el análisis de redes en donde el concept= o de centralidad fue utilizado para identificar los actores más importantes (Bataglj, 1996, Brandes, 2001).  Kh= an interpreta la medida de calidad de forma similar, definiendo cantidad como:=

 

 

 

 

1.4.10.M= étodo para la eliminación de redundancias en una red, H.A. Bashir, Julio 2010 [24= ]

 =

Este método se presenta aquí como un elemento importante, tal como = su creador indica, como soporte al método de Nassar, presentado en el punto 1.2.7.  Este método provee la maner= a de reducir los arcos de una red a un mínimo.

 

 

 

 

 

 

 

 

 

 

Ilus= tración 7 - Red de actividades en nodos del proyecto hipotético [24]=

 

 
1.4.10.1.          Basándose en una matriz de = red de actividades como la red y la matriz ejemplificada arriba, el método cons= iste en los siguientes pasos:

 

1.      = Construcción de la matriz de predeceso= res inmediatos, MIP (Matrix of Inmediate Predecessors);

 

 

 

 

 

 

 

 

 

 

Tabl= a 5 – Matriz de predecesores inmediatos del proyecto hipotético [24]

 

2.&n= bsp;      La transformación del MI= P a una matriz de formato de menor nivel de formato triangular, o LTF (Lower Triangular Format Matrix);

 

 

 

 

 

 

 

 

Tabl= a 6 – Matriz triangular inferior del proyecto hipotético [24]

3.       Transformación del LTF en una matriz de mínimos arcos adyacentes;

4.       La construcción del dígr= afo de mínimos arcos.

 

1.4.10.2.          El método para transformar = una LTF en una Matriz de mínimos arcos es la siguiente:

 

1.      = Reemplazar todas las entradas diagonal= es por “0”.

2.      = Después de transformar todas las entra= das diagonales de la LTF de “1” “a “0” s, cada columna es consultada en secuenc= ia, desde la columna 1 a la columna 5, para identificar las entradas de “1”.

3.      = La búsqueda nos debe mostrar que la pr= imera entrada que tiene valor de “1” es la entrada e21 (la entrada en la columna = 2 y fila 1).

4.      = Se procede a buscar en la fila 2 por c= eldas que contengan “1” que estén en las columnas mayores de 2, y las entradas correspondientes en la fila 1, e31, e41, e51, son restringidas a 0, siempre= y cuando la fila 2 tenga el valor de “1” en esas columnas.<= /p>

5.      = Continuar el proceso anterior resulta = en la matriz de mínimos arcos adyacentes, mostrada en la Tabla =

 

 

 

 

 

 

 

 

 

 

 

 

Tabl= a 7 – Matriz de mínimos arcos adyacentes del proyecto hipotético [24]<= /o:p>

 

 

 

 

 

 

 

 

 

 

 

 

 

Ilus= tración 8 - Red de mínimos arcos del proyecto hipotético [24]=

 

1.5      =          Complejidad vs Desempeño <= o:p>

 

No hay un estudio comparativo que haga una correlación entre los índices de complejidad desarrollados por el método de modelado de grafos y = el desempeño de los proyectos. Por ende, es difícil (con la documentación actu= al), evaluar si la complejidad definida en estos métodos realmente describe la c= omplejidad de proyectos como un factor determinante en la ejecución de un proyecto, au= nque todos están de acuerdo en que sí.  = La literatura actual se dedica a encontrar un método utilizable mas no hace la comparación de estos métodos o índices propuestos con el desempeño de proye= ctos para así tener una estadística que permita observar esta relación.  Por ende, parte de esta investigación es proveer tal estadística.

 

Sin embargo, dos autores han hecho la correlación entre la compleji= dad utilizando el método holístico y el desempeño o éxito de un proyecto.  Lan [9] y Yang [28] resuelven hacer el estudio de la relación tomando en cuenta el éxito de un proyecto, no el des= empeño del mismo. Lan, comprende el desempeño del proyecto como un factor incluido dentro del concepto de éxito, o sea como uno de los factores a tomar en cue= nta dentro de todas sus categorías. Yang, por su parte, no toma en cuenta el desempeño como índice métrico, sino como parte de su estudio comparativo en= tre el buen liderazgo y el éxito del proyecto.

Parte del valor de esta investigación es poder realizar la correlac= ión entre dos índices razonables de conseguir e intuitivos y observar si puede = ser aplicado de forma regular al análisis de proyectos a futuro. 

 

1.6      =          Conclusiones

 

Durante la revisión de estos métodos se ha observado que algunos de ellos han dejado de ser de mayor utilidad.  Todos los métodos que basan sus redes de cronograma en actividades e= n arcos son obsoletos debido a que hoy todos los cronogramas se basan en redes en d= onde las actividades se representan por nodos.

Otros métodos incluyen elementos como recursos o duraciones de las actividades para definir complejidad.  Los recursos en un cronograma no siempre pueden utilizarse para la evaluación de un cronograma porque no siempre las actividades están cargadas con recursos, incluso en algunos casos no es práctico utilizar recursos en = un cronograma, aunque sea lo ideal o deseable.

 

Las duraciones de las actividades podrían ser un elemento a tomar en cuenta, sin embargo, los métodos propuestos, como en el propuesto por Kahn = [27] o Boushala [25], usan como base el concepto de que a medida que un proyecto= se atrasa, empieza a incrementar la cantidad de rutas casi-críticas, por ende aumenta la cantidad de actividades concurrentes que deben realizarse, y más actividades en la cual la gestión de proyectos debe enfocarse de forma concurrente.

 

Este concepto igual va de la mano con el concepto de redes y arcos,= sin necesidad de un análisis de la criticalidad misma, ya que la criticalidad n= o es en sí un factor de complejidad. Una red lineal tiene todas sus actividades críticas.  Lo que hace más complejo= un proyecto parece ser la cantidad de actividades a la cual el gerente debe po= ner atención al mismo tiempo.  Un análi= sis estrictamente de arcos y nodos se acerca más a este paralelismo y por ende funciona como índice de análisis de la complejidad de proyectos.  Se debe crear un índice de paralelismo = del cronograma en adición a la proporcionalidad de arcos y nodos, lo cual será = tema de futuras investigaciones.

 

1.7   Referencias

 

[1] Project Management Body of Knowledge (PMBOK Guide), Proje= ct Management Institute. Newtown Square, Pa., 2008, 4th Ed.<= /p>

[2] Baccarini, David. “The concept of project complexity-a review,” International Journal of Project Management, Vol. 14, No. 4, pp.201-204, (1= 996).

[3] Wood, H= annah Louise, Ashton, Philip. “The Factors of Project Complexity,” 18th CIB World Building Congress. Salford, UK., 2010

 

[4] Frame, J. Davidson. The New Project Management, Tools for an = Age of Rapid Change, Complexity, and other Business Realities, Jossey-Bass A Wiley Company, San Francisco, Ca., 2nd Ed. 2002

[5] Vidal, Ludovic-Alexandre, Marle, Franck, Bocquet, Jean-Claude.  “Modelling Project Complexity,” ICED’07/515, 2007.

 

[6] Nassar,= Khaled M., Hegab, Mohamed Y. “Developing a Complexity Measure for Project Schedule= s,” Journal of Construction Engineering and Management, Vol. 132, No. 6, June 2= 006.

 

[7] Vidal, Ludovic-Alexandre, Marle, Franck, Bocquet, Jean-Claude. <= /span>“Measuring = Project Complexity using the Analytic Hierarchy Process,” International Journal of Project Management 29 pp.718–727, 2011

[8] Weaver, Patrick. “Scheduling in the Age of Complexity,” PMI College of Scheduling Annual Conference 17 - 20 May 2009

 

[9] Luo, Lan, et. al. “Investigating the Relationship between Project Complexity and Success in Complex Construction Projects,” Journal of Manage= ment in Engineering, July 2016

[10] Fostel, C. (2011). The value of earned value management. Paper presented at PMI® Global Congress 2011—North America, Dallas, TX. Newtown Square, PA: Project Management Institute.” [Online]. Available: https://www.pmi.org/learning/library/value-earned-value-management-62= 32

 

[11] Reichel, C.= W. (2006). Earned value management systems (EVMS): "you too can do earned value management" Paper presented at PMI® Global Congress 2006—North America, Seattle, WA. Newtown Square, PA: Project Management Institute [Online]. Available: pmi.org/learning/library/earned-value-management-systems-analysis-802= 6

 =

[12] Real A= cademia Española [Online].  Available: dle.rae.es/holismo?m=3Dform; dle.rae= .es/hol%C3%ADstico=

 =

[13] Wood, = Hannah Louise, Ashton, Philip. “Modelling Project Complexity,” Procs 26th Annual A= RCOM Conference, pp.1111-1120, September 2010

 =

[14] Xia, B= o & Chan, Albert. “Measuring Complexity for Building Projects—A Delphi Study,” Engineering, Construction and Architectural Management Vol. 19 No. 1, pp. 7= -24, 2012

 =

 =

[15] Akiles= awaran, V, Hazez, G.B., Morin, T.L. “Complexity of the Project Sequencing Problem,” Operations Research · August 1983

 =

[16] Castejón-Limas, Manuel, Ordieres-Meré, Joaquín, González-Marcos, Ana, González-Castro, Víctor. “Effort estimates through project complexity,” Springer Science+Business Media, LLC [Online]. Available: www.researchgate.net/publication/220461783_Effort_estimates_through_p= roject_complexity [Jul. 16, = 2010].

 =

[17] Henrik= sen, JO “Taming the Complexity Dragon,” Winter Simulation Conference – Titans of Simulation, 2006.

 =

[18] Svetla= na Cicmil, Terry Cooke-Davies, Lynn Crawford, and Kurt Richardson. Exploring the Complexity of Projects. Project Management Institute. Newtown Squar= e, Pa, Kindle Edition, 2009.

 =

[19] Obolen= sky, Nick. Leading Complex Projects. ICCPM. Kindle Ed., 2013.<= /span>

 =

[20] Terry, Cooke-Davies. Aspects of Complexity: Managing Projects in a Complex Worl= d. Project Management Institute. Newtown Square, Pa. Kindle Ed., 2011

 =

[21] Cavana= gh, Michael. Project Complexity Assessment. ICCPM. Kindle Ed., 2013.

 =

[22] Sinha, Sanjeev. “An Innovative Technique to Measure Complexity Of A Construction Project Activity,” Architectural Engineering and Design Management · January 2006

 =

[23] Nassar, Khaled. “Schedule Network complexity vs Project complexity,” Proceedings of= the International Conference on Computing in Civil and Building Engineering (20= 10).

 =

[24] Bashir= , H. A. “Removal of Redundant Relationships in an AON Project Network for Evaluating Schedule Complexity,” Journal of Construction Engineering and Management © = ASCE pp.787 -793, July 2010.

 =

[25] Bousha= ala, Amer A. “Project Complexity Indices based on Topology Features,” World Acad= emy of Science, Engineering and Technology 69, pp. 49-54, 2010.

 =

[26] Trudea= u, Richard J. Introduction to Graph Theory. Dover Publications Inc., New York, 1993 2ed.

 =

[27] Khan, = Muhammad Ali. “Quantitative quality assessment of network-based schedules” Proceedin= gs of the International Conference on Computing in Civil and Building Engineer= ing, 2010.

 =

[28] Yang, = Li-Ren et al. “The association among project manager´s leadership style, teamwork = and project success” International Journal of Project Management, 2011

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Invest. Pens. Crit. (ISSN 1812-3864; eISSN 2644-4119)

DOI: 

Vol. 9, No. 1, Enero – Abril 2021 =  

pp. 112 - 135

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