Un modelo para el diseño robusto de redes y análisis estadístico de su eficiencia

Abstract

The aim of this work is to design a robust distribution network under uncertainty in costs. These parameters can be modeled as points in a polyhedral set where the knowledge about dependence relations among them are represented. We will use the minmax regret paradigm that looks for a solution with an efficiency as close as possible to the optimum under each scenario of costs. These uncertain parameters will model the scenario under which the new network will be evaluated. First, we give an introduction motivating the purpose and usefulness of this problem in a globalized economy. Studies in different areas of the economy will show the need of mathematical models where the existing uncertainty in the different elements of the network is incorporated. Chapter 2 deals with the deterministic problem that solves a flow problem determining how to transport certain commodities from their origins to their destinations. We will analyse the design of a network with potential arcs under uncertain costs according to find a solution as close as possible to the best one under each scenario. Moreover, we will develop a Benders Decomposition algorithm to find numerically a robust design that solves this problem. In the last part of this work, different statistical studies have been carried out by using the software RStudio to compare the minmax regret network design with respect to the optimal design under the expected costs for a family of distributional conditions.