ABSTRACT We address the problem of expected cost minimization of meeting the uncertain fuel demand during a time planning horizon, where supply is provided by selecting discrete shipments with lead times. Due to uncertainty and the passage of time, corrective actions can be taken such as cancellation and postponement on supply of shipments with associated costs and delays. This problem is modeled as a stochastic multi-stage capacitated discrete lot-sizing problem with lead times. Computational experiments were performed on the resolution of various instances of the model for four information structures of uncertainty. The experimental optimal values and stochastic rating measures obtained show the validity and interest of the stochastic model, as well as the benefits that can be obtained with respect to a deterministic variant of the model that considers average demand.

In this paper we face a problem that considers the selection of several bus stops from many potential ones and the respective design of optimal routes for the bus transportation of personnel from the surroundings of their houses to the place in which they work. We propose an integer programming model for the mathematical formulation of the resulting location-routing problem. The proposed location-routing model is suitable to solve little and medium size instances of the problem. However, to face large size instances of the problem an alternative strategy is needed. For that purposes, we propose a hierarchical scheme by solving a set covering location model for the bus stops selection, followed of another one for the design of routes based on the previous bus stops selected. To solve the vehicle routing problem we also incorporate the heuristic of Holmes and Parkerfor the resolution of larger instances of the problem. The alternative strategy does not provide the global solution to the problem but it is easy to apply and essential to face larger instances of the problem.

En este artículo abordamos un problema que consiste en la selección de paraderos de detención y el respectivo diseño de rutas en los recorridos de buses que transportan personal desde el entorno de sus hogares al lugar en que laboran. Proponemos un modelo de programación entera de localización y ruteo como formulación matemática del problema en su conjunto. La formulación empleada permite alcanzar una solución óptima del problema al resolver diversas instancias de tamaño pequeño y mediano del mismo. Sin embargo, ante instancias de gran tamaño se hace necesario el empleo de alguna estrategia alternativa de resolución. Por ello se presenta igualmente un esquema jerárquico que resuelve el problema a través de un modelo de localización por cobertura para la selección de paraderos, seguido de otro diferente para el diseño de rutas, que asume como dada la ubicación de los puntos de detención. Este último considera igualmente el empleo de la heurística de Holmes y Parker en la resolución de las instancias de mayor tamaño. Los resultados exhibidos permiten apreciar la calidad de las soluciones entregadas por la estrategia alternativa respecto de la solución óptima del modelo propuesto y la necesidad de contar con alternativas de resolución en problemas de gran tamaño.