Capacitated Vehicle Routing with Non-Uniform Speeds

The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having non-uniform speeds (that we call Heterogenous CVRP), and present a constant-factor approximation algorithm. The technical heart of our result lies in achieving a constant approximation to the following TSP variant (called Heterogenous TSP). Given a metric denoting distances between vertices, a depot r containing k vehicles with possibly different speeds, the goal is to find a tour for each vehicle (starting and ending at r), so that every vertex is covered in some tour and the maximum completion time is minimized. This problem is precisely Heterogenous CVRP when vehicles are uncapacitated. The presence of non-uniform speeds introduces difficulties for employing standard tour-splitting techniques. In order to get a better understanding of this technique in our context, we appeal to ideas from the 2-approximation for scheduling in parallel machine of Lenstra et al.. This motivates the introduction of a new approximate MST construction called Level-Prim, which is related to Light Approximate Shortest-path Trees. The last component of our algorithm involves partitioning the Level-Prim tree and matching the resulting parts to vehicles. This decomposition is more subtle than usual since now we need to enforce correlation between the size of the parts and their distances to the depot

The stochastic vehicle routing problem : a literature review, part II : solution methods

Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems. Keywords: vehicle routing (VRP), stochastic programmingm, SVRPpublishedVersio

School bus selection, routing and scheduling.

The aim of this thesis is to develop formulations and exact algorithms for the school bus routing and scheduling problem and to develop an integrated software implementation using Xpress-MP/CPLEX and ArcGIS of ESRI, a geographical information system software package. In this thesis, bus flow, single commodity flow, two-commodity flow, multi-commodity flow, and time window formulations have been developed. They capture all of the important elements of the School Bus Routing and Scheduling Problem (SBRSP) including homogeneous or heterogeneous bus fleets, the identification of bus stops from a large set of potential bus stops, and the assignment of students to stops and stops to routes. They allow for the one stop-one bus and one stop-multi bus scenarios. Each formulation of the SBRSP has a linear programming relaxation and we present the relationships among them. We present a Branch-and-Cut exact algorithm which makes use of new linearization techniques, new valid inequalities, and the first valid equalities. We develop an integrated software package that is based on Geographical Information System (GIS) map-based interface, linking to an Xpress-MP/CPLEX solver. The interface between GIS and Xpress-MP is written in VBA and VC++.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .K4. Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6250. Thesis (Ph.D.)--University of Windsor (Canada), 2005

Using group role assignment to solve Dynamic Vehicle Routing Problem

The Dynamic Vehicle Routing Problem (DVRP) is a more complex problem than the traditional Vehicle Routing Problem (VRP) in the combinatorial optimization of operations research. With more degrees of freedom, DVRP introduces new challenges while judging the merit of a given route plan. This thesis utilized the time slice strategy to solve dynamic and deterministic routing problems. Based on Group Role Assignment (GRA) and two different routing methods (Modified Insertion heuristic routing and Modified Composite Pairing Or-opt routing), a new ridesharing system has been designed to provide services in the real world. Simulation results are presented in this thesis. A qualitative comparison has been made to outline the advantages and performance of our solution framework. From the numerical results, the proposed method has a great potential to put into operation in the real world and provides a new transit option for the public.Master of Science (MSc) in Computational Scienc

SOLVING MULTI-SCHOOL BUS ROUTING AND SCHEDULING PROBLEM

School bus routing and scheduling is of huge importance in school transportation system operations. It is usually treated as two separated problems and is solved sequentially. But it is shown that such separation will lead to a worse solution than solving them together with respect to the number of buses and travel time. The rationale behind it and the key point connecting routing and scheduling problem – trip compatibility – is thus deeply studied. A Mixed Integer Programming model is proposed along with a School Decomposition Algorithm. The model and algorithm are tested on eight sets of randomly-generated mid-size problems in comparison to the existing models. The results show that the proposed model and algorithm can find a better solution using up to 30% fewer buses than the best traditional models in a reasonable amount of time

Real-time Multi-period truckload routing problems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering; and, (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 99-102).In this thesis we consider a multi-period truckload pick-up and delivery problem dealing with real-time requests over a finite time horizon. We introduce the notion of postponement of requests, whereby the company can postpone some requests to the next day in order to improve its operational efficiency. The postponed requests must then be served on the next day. The daily costs of operation include costs associated with the trucks' empty travel distances and costs associated with postponement. The revenues are directly proportional to the length of job requests. We evaluate the profits of various re-optimization policies with the possibility of postponement. Another important notion of trucking operation corresponds to repositioning strategies which exploit probabilistic knowledge about future demands. A new repositioning strategy is proposed here to provide better decisions. For both notions, extensive computational results are provided under a general simulation framework.by Tanachai Limpaitoon.S.M

Design of vehicle routing problem domains for a hyper-heuristic framework

The branch of algorithms that uses adaptive methods to select or tune heuristics, known as hyper-heuristics, is one that has seen a large amount of interest and development in recent years. With an aim to develop techniques that can deliver results on multiple problem domains and multiple instances, this work is getting ever closer to mirroring the complex situations that arise in the corporate world. However, the capability of a hyper-heuristic is closely tied to the representation of the problem it is trying to solve and the tools that are available to do so. This thesis considers the design of such problem domains for hyper-heuristics. In particular, this work proposes that through the provision of high-quality data and tools to a hyper-heuristic, improved results can be achieved. A definition is given which describes the components of a problem domain for hyper-heuristics. Building on this definition, a domain for the Vehicle Routing Problem with Time Windows is presented. Through this domain, examples are given of how a hyper- heuristic can be provided extra information with which to make intelligent search decisions. One of these pieces of information is a measure of distance between solution which, when used to aid selection of mutation heuristics, is shown to improve results of an Iterative Local Search hyper-heuristic. A further example of the advantages of providing extra information is given in the form of the provision of a set of tools for the Vehicle Routing Problem domain to promote and measure ’fairness’ between routes. By offering these extra features at a domain level, it is shown how a hyper-heuristic can drive toward a fairer solution while maintaining a high level of performance

Design of vehicle routing problem domains for a hyper-heuristic framework

The branch of algorithms that uses adaptive methods to select or tune heuristics, known as hyper-heuristics, is one that has seen a large amount of interest and development in recent years. With an aim to develop techniques that can deliver results on multiple problem domains and multiple instances, this work is getting ever closer to mirroring the complex situations that arise in the corporate world. However, the capability of a hyper-heuristic is closely tied to the representation of the problem it is trying to solve and the tools that are available to do so. This thesis considers the design of such problem domains for hyper-heuristics. In particular, this work proposes that through the provision of high-quality data and tools to a hyper-heuristic, improved results can be achieved. A definition is given which describes the components of a problem domain for hyper-heuristics. Building on this definition, a domain for the Vehicle Routing Problem with Time Windows is presented. Through this domain, examples are given of how a hyper- heuristic can be provided extra information with which to make intelligent search decisions. One of these pieces of information is a measure of distance between solution which, when used to aid selection of mutation heuristics, is shown to improve results of an Iterative Local Search hyper-heuristic. A further example of the advantages of providing extra information is given in the form of the provision of a set of tools for the Vehicle Routing Problem domain to promote and measure ’fairness’ between routes. By offering these extra features at a domain level, it is shown how a hyper-heuristic can drive toward a fairer solution while maintaining a high level of performance