Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Column Generation for Bi-Objective Vehicle Routing Problems with a Min-Max Objective

International audienceColumn generation has been very useful in solving single objective vehicle routing problems (VRPs). Its role in a branch-and-price algorithm is to compute a lower bound which is then used in a branch-and-bound framework to guide the search for integer solutions. In spite of the success of the method, only a few papers treat its application to multi-objective problems and this paper seeks to contribute in this respect. We study how good lower bounds for bi-objective VRPs in which one objective is a min-max function can be computed by column generation. A way to model these problems as well as a strategy to effectively search for columns are presented. We apply the ideas to two VRPs and our results show that strong lower bounds for this class of problems can be obtained in "reasonable" times if columns are intelligently managed. Moreover, the quality of the bounds obtained from the proposed model are significantly better than those obtained from the corresponding "standard" approach

Localización y ruteo de vehículos capacitado multi-objetivo con consideraciones de sostenibilidad

En la actualidad las empresas, entidades gubernamentales, la comunidad academica y cientifi ca, enfocan su atención en el desarrollo sostenible. Uno de los sectores de mayor interés en este enfoque es la logística, especificamente el area de transporte. La inclusión de consideraciones de desarrollo sostenible implica cambiar la planeación, diseño y operación de sus procesos lo que impacta directamente en la e ficiencia y competitividad..

Localización y ruteo de vehículos capacitado multi-objetivo con consideraciones de sostenibilidad

En la actualidad las empresas, entidades gubernamentales, la comunidad academica y cientifi ca, enfocan su atención en el desarrollo sostenible. Uno de los sectores de mayor interés en este enfoque es la logística, especificamente el area de transporte. La inclusión de consideraciones de desarrollo sostenible implica cambiar la planeación, diseño y operación de sus procesos lo que impacta directamente en la e ficiencia y competitividad..