Construction of an Optimal Solution for a Real–World Routing–Scheduling–Loading Problem
Construcción de una Solución Óptima para un Problema de Asignación de Rutas, Horarios y Cargas del Mundo Real
Juan Javier González Barbosa, José Francisco Delgado Orta, Héctor Joaquín Fraire Huacuja, José Antonio Martínez Flores and María Lucila Morales Rodríguez
Instituto Tecnológico de Ciudad Madero, México, jjgonzalezbarbosa@gmail.com, francisco.delgado.orta@gmail.com, hfraire@prodigy.net.mx, jose.mtz@gmail.com, lmorales@gmail.com
]]> Article received on July 20, 2009.
Abstract
This work presents an exact method for the Routing–Loading–Scheduling Problem (RoSLoP). The objective of RoSLoP consists of optimizing the delivery process of bottled products in a company study case. RoSLoP, formulated through the well–known Vehicle Routing Problem (VRP), has been solved as a rich VRP variant through approximate methods. The exact method uses a linear transformation function, which allows the reduction of the complexity of the problem to an integer programming problem. The optimal solution to this method establishes metrics of performance for approximate methods, which reach an efficiency of 100% in distance traveled and 75% in vehicles used, objectives of VRP. The transformation function reduces the computation time from 55 to four seconds. These results demonstrate the advantages of the modeling mathematical to reduce the dimensionality of problems NP–hard, which permits to obtain an optimal solution of RoSLoP. This modeling can be applied to get optimal solutions for real–world problems.
Keywords: Optimization, Routing–Scheduling–Loading Problem (RoSLoP), Vehicle Routing Problem (VRP), rich VRP.
Resumen
Éste trabajo presenta un método exacto para el problema de Asignación de Rutas, Horarios y Cargas (RoSLoP). El objetivo de RoSLoP consiste en optimizar el proceso de entrega de productos embotellados en una compañía caso de estudio. El problema RoSLoP, formulado a través del conocido Problema de Enrutado de Vehículos (VRP), ha sido resuelto como una variable VRP enriquecida a través de métodos aproximados. El método exacto usa una función de transformación lineal, la cual permite la reducción de la complejidad del problema a un problema de programación entera. La solución óptima para éste método establece las métricas del desempeño para los métodos aproximados, los cuales alcanzan una eficiencia del 100% en distancia recorrida y 75% en vehículos utilizados, objetivos del VRP. La función de transformación reduce el tiempo del cálculo de 55 a cuatro segundos. Éstos resultados demuestran las ventajas del modelado matemático para reducir la dimensionalidad de problemas NP–Duros, lo cual permite la obtención de una solución óptima del problema RoSLoP. Éste modelado puede ser aplicado para obtener las soluciones óptimas para problemas del mundo real.
Palabras Clave: Optimización, Problema de Asignación de Rutas, Horarios y Cargas (RoSLoP), Problema de Enrutado de Vehículos (VRP), Problema VRP Enriquecido.
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