On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Model and algorithm for solving real time dial-a-ride problem

This research studies a static and real-time dial-a-ride problem with time varying travel times, soft time windows, and multiple depots. First, a static DARP model is formulated as a mixed integer programming and in order to validate the model, several random small network problems are solved using commercial optimization package, CPLEX. Three heuristic algorithms based on sequential insertion, parallel insertion, and clustering first-routing second are proposed to solve static DARP within a reasonable time for implementation in a real-world situation. Also, the results of three heuristic methods are compared with the results obtained from exact solution by CPLEX to validate and evaluate three heuristic algorithms. Computational results show that three heuristic algorithms are superior compared to the exact algorithm in terms of the calculation time as the problem size (in terms of the number of demands) increases. Also among the three heuristic algorithms, the heuristic algorithm based on sequential insertion is more efficient than other heuristic algorithms that are based on parallel insertion and clustering first-routing second. For the case study, Maryland Transit Administration (MTA)'s real operation of Dial-a-ride service is introduced and compared with the results of developed heuristic. The objective function values from heuristic based on clustering first- routing second are better than those from MTA's operation for all cases when waiting cost, delay cost, and excess ride cost are not included in the objective function values. Also, the algorithm for real-time DARP considering dynamic events such as customer no shows, accidents, cancellations, and new requests is developed based on static DARP. The algorithm is tested in a simulation framework. In the simulation test, we compared the results of cases according to degree of gap between expected link speeds and real link speeds. Also for competitive analysis, the results of dynamic case are compared with the results of static case, where all requests are known in advance. The simulation test shows that the heuristic method could save cost as the uncertainty in new requests increases

Innovative systems for the transportation disadvantaged: towards more efficient and operationally usable planning tools

When considering innovative forms of public transport for specific groups, such as demand responsive services, the challenge is to find a good balance between operational efficiency and 'user friendliness' of the scheduling algorithm even when specialized skills are not available. Regret insertion-based processes have shown their effectiveness in addressing this specific concern. We introduce a new class of hybrid regret measures to understand better why the behaviour of this kind of heuristic is superior to that of other insertion rules. Our analyses show the importance of keeping a good balance between short- and long-term strategies during the solution process. We also use this methodology to investigate the relationship between the number of vehicles needed and total distance covered - the key point of any cost analysis striving for greater efficiency. Against expectations, in most cases decreasing fleet size leads to savings in vehicle mileage, since the heuristic solution is still far from optimality

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

Minimum Makespan Multi-vehicle Dial-a-Ride

Dial a ride problems consist of a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs, where each object requires to be moved from its source to destination vertex. We consider the multi-vehicle Dial a ride problem, with each vehicle having capacity k and its own depot-vertex, where the objective is to minimize the maximum completion time (makespan) of the vehicles. We study the "preemptive" version of the problem, where an object may be left at intermediate vertices and transported by more than one vehicle, while being moved from source to destination. Our main results are an O(log^3 n)-approximation algorithm for preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation for its special case when there is no capacity constraint. We also show that the approximation ratios improve by a log-factor when the underlying metric is induced by a fixed-minor-free graph.Comment: 22 pages, 1 figure. Preliminary version appeared in ESA 200

A double dynamic fast algorithm to solve multi-vehicle Dial a Ride Problem

Abstract In this work a two level heuristic algorithm is described for a nearly real-time multi-vehicle many-to-many Dial-A-Ride Problem (DARP). This algorithm is ready to support a Demand Responsive Transportation System in which we face the problem of quickly evaluate a good-quality schedule for the vehicles and provide fast response to the users. The insertion heuristic is double dynamic nearly real-time and the objective function is to minimize the variance between the requested and scheduled time of pickup and delivery. In the first level, after a customer web-request, the heuristic returns an answer about the possibility to insert the request into the accepted reservations, and therefore in a vehicle schedule, or reject the request. In the second level, during the time elapsed between a request and the following, and after a reshuffling of the order of the incoming accepted requests, the same heuristic works for the whole set of accepted requests, trying to optimize the solution. We intensively tested the algorithm with a requests-generating software that has allowed us to show the competitive advantage of this web-based architecture

A Study on the application of genetic algorithms on the Dial-A-Ride Problem

[[abstract]]The Dial-a-Ride Problem (DARP) is a vehicle routing problem faced in arranging Dial-a-Ride services. The DARP has been proven a NP-Hard problem; therefore, most research has used heuristic solution methods to address this issue. The purpose of this study is to evaluate of the application of a Diversity Control Adaptive Genetic Algorithm (DCAGA) and Family Competition Genetic Algorithm (FCGA) on the DARP. This study proposed two solution procedures, which were integrated approach and cluster approach. A series of case studies with different characteristics, such as demand density and demand size, were used to test the solution capability of the proposed algorithms. Based on the results of the case studies, the Diversity Control Adaptive Genetic Algorithm is identified as the best algorithm in solution quality. Overall, the solution of the integrated procedure is better than, those of the two-phase procedure.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]US