27 research outputs found

    On the vehicle routing problem with time windows

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    Routing and delivery planning: algorithms and system implementation.

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    Wong Chi Fat.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 107-115).Abstracts in English and Chinese.List of Tables --- p.ixList of Figures --- p.xChapter 1. --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Literature Review --- p.3Chapter 1.2.1 --- Shortest Path Problem --- p.4Chapter 1.2.2 --- Vehicle Routing Problem with Time Windows --- p.6Chapter 1.3 --- Thesis Outline --- p.9Chapter 2. --- Time-varying Shortest Path with Constraints in a 2-level Network --- p.11Chapter 2.1 --- Introduction --- p.11Chapter 2.2 --- Problem Formulation of TCSP --- p.12Chapter 2.3 --- Arbitrary Waiting Time --- p.13Chapter 2.4 --- TCSP in a 2-level Network --- p.15Chapter 2.4.1 --- Problem Formulation of TCSP in a 2-level Network --- p.17Chapter 2.5 --- Algorithms Solving TCSP in a 2-level Network --- p.20Chapter 2.5.1 --- Exact Algorithm --- p.21Chapter 2.5.2 --- Heuristic Algorithm --- p.23Chapter 2.6 --- Concluding Remarks --- p.30Chapter 3. --- Vehicle Routing Problem with Time Windows and Stochastic Travel Times --- p.32Chapter 3.1 --- Introduction --- p.32Chapter 3.2 --- Problem Formulation --- p.34Chapter 3.3 --- General Branch-and-cut Algorithm --- p.42Chapter 3.4 --- Modified Branch-and-cut Algorithm --- p.44Chapter 3.4.1 --- Prefixing --- p.45Chapter 3.4.2 --- Directed Partial Path Inequalities --- p.47Chapter 3.4.3 --- Exponential Smoothing --- p.50Chapter 3.4.4 --- Fast Fathoming --- p.54Chapter 3.4.5 --- Modified Branch-and-cut algorithm --- p.56Chapter 3.5 --- Computational Analysis --- p.57Chapter 3.5.1 --- "Performance of Prefixing, Direct Partial Path Inequalities and Exponential Smoothing" --- p.57Chapter 3.5.2 --- Performance of Fast Fathoming --- p.63Chapter 3.5.3 --- Summary of Computational Analysis --- p.67Chapter 3.6 --- Concluding Remarks --- p.67Chapter 4. --- System Features and Implementation --- p.69Chapter 4.1 --- Introduction --- p.59Chapter 4.2 --- System Features --- p.70Chapter 4.2.1 --- Map-based Interface and Network Model --- p.70Chapter 4.2.2 --- Database Management and Query --- p.73Chapter 4.3 --- Decision Support Tools --- p.75Chapter 4.3.1 --- Route Finding --- p.75Chapter 4.3.2 --- Delivery Planning --- p.77Chapter 4.4 --- System Implementation --- p.80Chapter 4.5 --- Further Development --- p.82Chapter 5. --- Vehicle Routing Software SurveyChapter 5.1 --- Introduction --- p.83Chapter 5.2 --- Essential Features in CVRS Nowadays --- p.84Chapter 5.2.1 --- Common Features --- p.34Chapter 5.2.2 --- Advanced Features --- p.90Chapter 5.3 --- Concluding Remarks --- p.94Chapter 6. --- Summary & Future Work --- p.97Appendix A --- p.101Appendix B --- p.104Bibliography --- p.10

    Branch-and-Cut for the split delivery vehicle routing problem with time windows

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    The split delivery vehicle routing problem with time windows (SDVRPTW) is a notoriously hard combinatorial optimization problem. First, it is hard to find a useful compact mixed-integer programming (MIP) formulation for the SDVRPTW. Standard modeling approaches either suffer from inherent symmetries (mixed-integer programs with a vehicle index) or cannot exactly capture all aspects of feasibility. Because of the possibility to visit customers more than once, the standard mechanisms to propagate load and time along the routes fail. Second, the lack of useful formulations has rendered any direct MIP-based approach impossible. Up to now, the most effective exact algorithms for the SDVRPTW have been branch-and-price-and-cut approaches using path-based formulations. In this paper, we propose a new and tailored branch-and-cut algorithm to solve the SDVRPTW. It is based on a new, relaxed compact model, in which some integer solutions are infeasible for the SDVRPTW. We use known and introduce some new classes of valid inequalities to cut off such infeasible solutions. One new class is path-matching constraints that generalize infeasible-path constraints. However, even with the valid inequalities, some integer solutions to the new compact formulation remain to be tested for feasibility. For a given integer solution, we build a generally sparse subnetwork of the original instance. On this subnetwork, all time-window-feasible routes can be enumerated, and a path-based residual problem then solved to decide on the selection of routes, the delivery quantities, and thereby the overall feasibility. All infeasible solutions need to be cut off. For this reason, we derive some strengthened feasibility cuts exploiting the fact that solutions often decompose into clusters. Computational experiments show that the new approach is able to prove optimality for several previously unsolved instances from the literature

    Facets of the polytope of the asymmetric travelling salesman problem with replenishment arcs

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    The Asymmetric Travelling Salesman Problem with Replenishment Arcs (RATSP) is a new class of problems arising from work related to aircraft routing. Given a digraph with cost on the arcs, a solution of the RATSP, like that of the Asymmetric Travelling Salesman Problem, induces a directed tour in the graph which minimises total cost. However the tour must satisfy additional constraints: the arc set is partitioned into replenishment arcs and ordinary arcs, each node has a non-negative weight associated with it, and the tour cannot accumulate more than some weight limit before a replenishment arc must be used. To enforce this requirement, constraints are needed. We refer to these as replenishment constraints.In this paper, we review previous polyhedral results for the RATSP and related problems, then prove that two classes of constraints developed in V. Mak and N. Boland [Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs, Technical Report TR M05/03, School of Information Technology, Deakin University, 2005] are, under appropriate conditions, facet-defining for the RATS polytope.<br /

    Operational Research: Methods and Applications

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    Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes
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