2016/05/31 by Piotr Matl, Richard F. Hartl, Thibaut Vidal · 141 citations
Engineering · Mathematics · #Axiom #Computer science #Econometrics #Economics #Equity (law) #Mathematical optimization #Mathematics #Operations research #Pareto principle #Routing (electronic design automation) #Set (abstract data type) #Smart Parking Systems Research #Transportation and Mobility Innovations #Vehicle Routing Optimization Methods #Vehicle routing problem #Workload #math.OC
paper · pdf · doi:10.1287/trsc.2017.0744
published in Transportation Science 52(2), 239-260 (Institute for Operations Research and the Management Sciences) · Accepted Manuscript
openalex publication_date 2017/09/15 · arxiv created 2018/03/05 · arxiv updated 2018/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 the context of 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 by providing 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 of equity, and point out important connections between their properties and the properties 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 remain 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 on equity in logistics. The data are available at 10.1287/trsc.2017.0744 .