Workload equity in vehicle routing: The impact of alternative workload resources - Matl, P.; Hartl, R.F.; Vidal, T. (Computers & operations research, 2019)
•The cost of balance depends primarily on the workload resource, and less on the equity function.•More complex equity functions, and balancing tour lengths, yield the most compromise solutions.•For the same workload resource, most solutions can be found with multiple equity functions.•Solutions optimized for one resource are usually poorly balanced in terms of another.•Solutions with similar cost and balance values tend to share many common arcs. In practical vehicle routing problems (VRPs), important non-monetary benefits can be achieved with more balanced operational plans that 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 that 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. Overall, our study counter-balances the focus of previous works and reveals the importance of selecting the right workload resource. Although the marginal cost of equity is low for all the examined models, the trade-off structure depends primarily on the workload resource, and less on the equity function. For the same resource, we observe a notable degree of overlap between the solutions found with different equity functions. Moreover, we find that there typically exists a set of low-cost VRP solutions that are well-balanced on average with respect to all the examined balance criteria. However, they are difficult to identify in practice as they are mostly Pareto-dominated by solutions optimized with respect to any single criterion. Finally, we observe that solutions with similar cost and balance tend to exhibit similar solution structure, a property that should be directly exploited by optimization methods.