Efficient Frontier for Multi-Objective Stochastic Transportation Networks in International Market of Perishable Goods

Effective planning of a transportation network influences tactical and operational activities and has a great impact on business. Planning typically considers multiple aspects such as variable transportation costs, various levels of customer service offered, security of goods, and traveling time. These aspects often vary with time. Although the minimum cost flow problem is a widely seen approach to configure a transportation network, there is no much work considering variations on arcs; even more, the problem with varying nodes has hardly been addressed. In this work is developed a mathematical model for the multi-objective minimum cost flow problem, applied in networks with varying attributes on arcs. The model finds the set of non-dominated solutions for a multi-objective stochastic network having variations in attributes of its arcs and nodes, such as cost or transportation time. A modified version of the two-stage method was used to address the stochastic nature of the problem combined with the epsilon-constraint method, which is used for building the set of non-dominated solutions.This paper presents the main features of the model, the theoretical bases and a computational implementation. Experiments were applied in a transport network for the exportation market of ornamental flowers as perishable goods from Mexico to the United States, which considered variations in border crossing times.

ResumenUna planeación eficaz de una red de transporte tiene un gran impacto en las empresas, al considerar múltiples aspectos como costos de transporte, seguridad de las mercancías, tiempo de viaje y demás niveles de servicio ofrecidos. Atributos que frecuentemente varian con el tiempo. Aunque el problema de flujo a costo minimo (MCF) ha sido ampliamente visto para configurar redes de transporte, no hay muchos trabajos que consideren variaciones en los arcos. En este trabajo se desarrolla un modelo matemático para el problema MCF multi-objetivo, aplicado en redes con atributos variantes en los arcos. El modelo encuentra la Frontera Pareto para una red estocástica con variaciones en los atributos de costo o tiempo de transporte. Para enfrentar la naturaleza estocástica del problema se utiliza Descomposición de Benders para el problema estocástico de dos etapas, posteriormente se conjunta con el método ε-restricción, que es utilizado para la construcción del conjunto de soluciones no dominadas.Este articulo presenta las principales características del modelo, las bases teóricas y una implementación computacional. Los experimentos fueron aplicados en una red de transporte para el mercado de exportación de flores ornamentales como productos perecederos desde México a Estados Unidos, considerando las variaciones en los tiempos de cruce de fronteras.