Workload Equity in Vehicle Routing: The Impact of Alternative Workload Resources

In practical vehicle routing problems (VRPs), important non-monetary benefits can be achieved with more balanced operational plans which explicitly consider workload equity. This has motivated practitioners to include a wide variety of balancing criteria in decision support systems, and researchers to examine the properties of these criteria and the trade-offs made when optimizing them. As a result, previous studies have provided a much-needed understanding of how different equity functions affect the resulting VRP solutions. However, by focusing exclusively on models which balance tour lengths, a critical aspect has thus far remained unexplored -- namely the impact of the workload resource subject to the balancing. In this work, we generalize previous studies to different workload resources, extend the scope of those analyses to additional aspects of managerial and methodological significance, and reevaluate accordingly previous conclusions and guidelines for formulating a balance criterion. We propose a classification of workload resources and equity functions, and establish which general types of balanced VRP models can lead to unintended optimization outcomes. To explore in greater detail the differences between models satisfying the given guidelines, we conduct an extensive numerical study of 18 alternative balance criteria. We base our observations not only on smaller instances solved to optimality, but also on larger instances solved heuristically, to gauge the extent to which our conclusions hold also for larger VRPs. Overall, our study counter-balances the focus of previous works and reveals the importance of selecting the right workload resource.