Resolución de un problema de rutas de vehículos con restricciones difusas
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Fecha
2018-06-28
Autores
Rodríguez Quintana, Pedro Leonardo
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Universidad Central “Marta Abreu” de Las Villas
Resumen
La Optimización Difusa es una de las áreas de la Optimización que resuelve problemas con parámetros imprecisos o inciertos. El objeto de estudio de la presente investigación es un problema de rutas de vehículos que considera la capacidad de los mismos como un conjunto difuso. En la modelación matemática, planteada desde el enfoque de la teoría de grafos, se conjugan ecuaciones del modelo clásico-determinista con una ecuación que incluye un número difuso. Para resolver el problema se propone un método que combina la técnica heurística del algoritmo de los ahorros o de Clarke & Wright, con el enfoque paramétrico del criterio de Verdegay que soluciona problemas de programación lineal difusa. Tras implementarse como una función en el RStudio, se resuelve un problema real para demostrar que el método obtiene soluciones adecuadas, ante la imposibilidad de emplear las técnicas clásicas de Optimización.
Fuzzy Optimization is a discipline of Optimization that solve problems with uncertain parameters. The goal of this paper is solving a vehicle routing problem with fuzzy constraints, particularly the capacity constraints has been represented with fuzzy number. The mathematical model was made as a network flows model that combine classic equations with fuzzy parameters. It is proposed a method based in Verdegay’s approach for solving fuzzy linear programming problems and Clarke and Wright Savings Algorithm, a classical heuristics. The proposed method is implemented as a function in RStudio software and a real problem is solved with it. The method obtained a good solution, however classic techniques cannot solve the problem.
Fuzzy Optimization is a discipline of Optimization that solve problems with uncertain parameters. The goal of this paper is solving a vehicle routing problem with fuzzy constraints, particularly the capacity constraints has been represented with fuzzy number. The mathematical model was made as a network flows model that combine classic equations with fuzzy parameters. It is proposed a method based in Verdegay’s approach for solving fuzzy linear programming problems and Clarke and Wright Savings Algorithm, a classical heuristics. The proposed method is implemented as a function in RStudio software and a real problem is solved with it. The method obtained a good solution, however classic techniques cannot solve the problem.
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Algoritmo de los Ahorros o de Clarke & Wright, Problema de Rutas de Vehículos con Restricciones Difusas, Programación Lineal Difusa, Clarke and Wright Savings Algorithm, Fuzzy Linear Programming, Vehicle Routing Problem With Fuzzy Constraints