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

Timely Data Delivery in a Realistic Bus Network

Abstract—WiFi-enabled buses and stops may form the backbone of a metropolitan delay tolerant network, that exploits nearby communications, temporary storage at stops, and predictable bus mobility to deliver non-real time information. This paper studies the problem of how to route data from its source to its destination in order to maximize the delivery probability by a given deadline. We assume to know the bus schedule, but we take into account that randomness, due to road traffic conditions or passengers boarding and alighting, affects bus mobility. We propose a simple stochastic model for bus arrivals at stops, supported by a study of real-life traces collected in a large urban network. A succinct graph representation of this model allows us to devise an optimal (under our model) single-copy routing algorithm and then extend it to cases where several copies of the same data are permitted. Through an extensive simulation study, we compare the optimal routing algorithm with three other approaches: minimizing the expected traversal time over our graph, minimizing the number of hops a packet can travel, and a recently-proposed heuristic based on bus frequencies. Our optimal algorithm outperforms all of them, but most of the times it essentially reduces to minimizing the expected traversal time. For values of deadlines close to the expected delivery time, the multi-copy extension requires only 10 copies to reach almost the performance of the costly flooding approach. I

Intelligent Safety Transport Framework for Schools: A Review of Route Planning and Tracking Systems

This work presents a review of recent literature in intelligent school transportation frameworks, particularly focusing on route planning, real time vehicle and children tracking. The focus on route planning and tracking is to identify the hidden practical problems and threats present in school transportation, bearing in mind safety. Different methods and technologies used for route planning and vehicle as well as children tracking are reviewed. A discussion is provided on the current frameworks along with the challenges and future research direction

Optimization of a city logistics transportation system with mixed passengers and goods

International audienceIn this paper, we propose a mathematical model and an adaptive large neighborhood search to solve a two{tiered transportation problem arising in the distribution of goods in congested city cores. In the rst tier, goods are transported in city buses from a consolidation and distribution center to a set of bus stops. The main idea is to use the buses spare capacity to drive the goods in the city core. In the second tier, nal customers are distributed by a eet of near{zero emissions city freighters. This system requires transferring the goods from buses to city freighters at the bus stops. We model the corresponding optimization problem as a variant of the pickup and delivery problem with transfers and solve it with an adaptive large neighborhood search. To evaluate its results, lower bounds are calculated with a column generation approach. The algorithm is assessed on data sets derived from a eld study in the medium-sized city of La Rochelle in France

Mathematical Formulation Model for a School Bus Routing Problem with Small Instance Data

This paper aims to describe the mathematical formulation model and an exact optimal solution analyses for a school bus routing problem with small instance data. The formulated model has been used  to compute the optimal solution of time spent by students at all bus stops, apart from that the bus stops are not necessary be linearly ordered. We also listed down five procedures of mathematical formulation model to reach an exact optimal solution for a school bus routing problem with small instance data. We assume that each bus has fixed pick up points, these generates the many possible routes for a bus, the number of routes that generated is equal to permutation of pick up points, for each route of a bus we computing the objective function and the route with smallest objective function value can be optimal route of a bus. The sample data from two schools located at Dar es Salaam are collected and validated in the model to shows the good performing of that model. The optimal solution results obtained shows that the students spent minimal minutes in new planned routes compared to current routes. Keywords: bus stop, students, buses, optimal value, optimal solution, set, pick up