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

A large neighbourhood based heuristic for two-echelon routing problems

In this paper, we address two optimisation problems arising in the context of city logistics and two-level transportation systems. The two-echelon vehicle routing problem and the two-echelon location routing problem seek to produce vehicle itineraries to deliver goods to customers, with transits through intermediate facilities. To efficiently solve these problems, we propose a hybrid metaheuristic which combines enumerative local searches with destroy-and-repair principles, as well as some tailored operators to optimise the selections of intermediate facilities. We conduct extensive computational experiments to investigate the contribution of these operators to the search performance, and measure the performance of the method on both problem classes. The proposed algorithm finds the current best known solutions, or better ones, for 95% of the two-echelon vehicle routing problem benchmark instances. Overall, for both problems, it achieves high-quality solutions within short computing times. Finally, for future reference, we resolve inconsistencies between different versions of benchmark instances, document their differences, and provide them all online in a unified format

Birch bark tar in early Medieval England:continuity of tradition or technological revival?

International audienc

Fecal Enterobacteriales enrichment is associated with increased in vivo intestinal permeability in humans

Type 2 diabetes (T2D) has been linked with increased intestinal permeability, but the clinical significance of this phenomenon remains unknown. The objective of this study was to investigate the potential link between glucose control, intestinal permeability, diet and intestinal microbiota in patients with T2D. Thirty‐two males with well‐controlled T2D and 30 age‐matched male controls without diabetes were enrolled in a case–control study. Metabolic parameters, inflammatory markers, endotoxemia, and intestinal microbiota in individuals subdivided into high (HP) and normal (LP) colonic permeability groups, were the main outcomes. In T2D, the HP group had significantly higher fasting glucose (P = 0.034) and plasma nonesterified fatty acid levels (P = 0.049) compared with the LP group. Increased colonic permeability was also linked with altered abundances of selected microbial taxa. The microbiota of both T2D and control HP groups was enriched with Enterobacteriales. In conclusion, high intestinal permeability was associated with poorer fasting glucose control in T2D patients and changes in some microbial taxa in both T2D patients and nondiabetic controls. Therefore, enrichment in the gram‐negative order Enterobacteriales may characterize impaired colonic permeability prior to/independently from a disruption in glucose tolerance

Protostellar Evolution during Time Dependent, Anisotropic Collapse

The formation and collapse of a protostar involves the simultaneous infall and outflow of material in the presence of magnetic fields, self-gravity, and rotation. We use self-similar techniques to self-consistently model the anisotropic collapse and outflow by a set of angle-separated self-similar equations. The outflow is quite strong in our model, with the velocity increasing in proportion to radius, and material formally escaping to infinity in the finite time required for the central singularity to develop. Analytically tractable collapse models have been limited mainly to spherically symmetric collapse, with neither magnetic field nor rotation. Other analyses usually employ extensive numerical simulations, or either perturbative or quasistatic techniques. Our model is unique as an exact solution to the non-stationary equations of self-gravitating MHD, which features co-existing regions of infall and outflow. The velocity and magnetic topology of our model is quadrupolar, although dipolar solutions may also exist. We provide a qualitative model for the origin and subsequent evolution of such a state. However, a central singularity forms at late times, and we expect the late time behaviour to be dominated by the singularity rather than to depend on the details of its initial state. Our solution may, therefore, have the character of an attractor among a much more general class of self-similarity.Comment: 11 pages, 5 figures, To appear in MNRAS, Memorial paper for M. Aburiha

Goal-setting participation and goal commitment: examining the mediating roles of procedural fairness and interpersonal trust in a UK financial services organisation

This study investigates whether participation in goal-setting within performance measurement and evaluation processes affects goal commitment and if so, whether the effect is mediated by procedural fairness and interpersonal trust. Using a sample of 54 managers within a UK financial services organisation, this study finds that participation in goal-setting is positively associated with goal commitment. Further analysis arising from introducing procedural fairness and interpersonal trust as mediating variables reveals that the association is significantly mediated by procedural fairness. Overall, these findings offer empirical evidence on the importance of procedural fairness on the relationship between participation and goal commitment