Minimum Makespan Multi-vehicle Dial-a-Ride

Inge Li Gørtz, Viswanath Nagarajan, R. Ravi

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    Abstract

    Dial-a-Ride problems consist of a set V of n vertices in a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs {(si,ti)}mi=1, where each object requires to be moved from its source to destination vertex. In the multi-vehicle Dial-a-Ride problem, there are q vehicles each having capacity k and where each vehicle j ∈ [q] has its own depot-vertex rj ∈ V. A feasible schedule consists of a capacitated route for each vehicle (where vehicle j originates and ends at its depot rj) that together move all objects from their sources to destinations. The objective is to find a feasible schedule that minimizes the maximum completion time (i.e. makespan) of vehicles, where the completion time of vehicle j is the time when it returns to its depot rj at the end of its route. We consider the preemptive version of multi-vehicle Dial-a-Ride, where an object may be left at intermediate vertices and transported by more than one vehicle, while being moved from source to destination. Approximation algorithms for the single vehicle Dial-a-Ride problem (q = 1) have been considered in [3,10]. Our main results are an O(log3n)-approximation algorithm for preemptive multi-vehicle Dial-a-Ride, and an improved O(logt)-approximation for its special case when there is no capacity constraint (here t ≤ n is the number of distinct depot-vertices). There is an Ω(log1/4n) hardness of approximation known [9] even for single vehicle capacitated preemptive Dial-a-Ride.

    We also obtain an improved constant factor approximation algorithm for the uncapacitated multi-vehicle problem on metrics induced by graphs excluding any fixed minor (eg. planar metrics). In this case, we obtain improved guarantees of O(log2 n) for capacitated multi-vehicle Dial-a-Ride, and O(1) for the uncapacitated problem.
    Original languageEnglish
    Title of host publicationAlgorithms - ESA 2009
    PublisherSpringer
    Publication date2009
    Pages540-552
    ISBN (Print)978-3-642-04127-3
    DOIs
    Publication statusPublished - 2009
    Event17th European Symposium on Algorithms - København, Denmark
    Duration: 7 Sep 20099 Sep 2009
    Conference number: 17
    http://algo2009.itu.dk/esa-2009

    Conference

    Conference17th European Symposium on Algorithms
    Number17
    CountryDenmark
    CityKøbenhavn
    Period07/09/200909/09/2009
    Internet address
    SeriesLecture Notes in Computer Science
    NumberVolume 5757/2009
    ISSN0302-9743

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