Approximation Algorithms for Capacitated Facility-Placement and Vehicle-Routing Problems in Transportation Networks

Becker, Amariah

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Year:: 2019
Contributor:: Becker, Amariah (creator); Klein, Philip (Advisor); Mathieu, Claire (Reader); Upfal, Eli (Reader); Werneck, Renato (Reader); Brown University. Department of Computer Science (sponsor)
Genre:: theses
Subject:: Approximation Algorithms; Vehicle routing problem; Transportation Network; Graph algorithms
Extent:: xi, 170 p.
DOI: https://doi.org/10.26300/q4t9-3v32

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Abstract:: Facility-placement and route-planning optimization problems aim to minimize the cost of providing a service to a set of clients. These problems arise frequently in a variety of contexts across computer science and operations research. Some of the most classic and well-studied of these including k-Center and the Traveling Salesperson Problem (TSP), though versatile, fail to adequately model the fact that actual service-providers have limited capacities. Facilities and vehicles have limited size (e.g. hospitals and buses can only hold so many people) as well as limited resources (e.g. staff, supplies, fuel, fleet size etc.), so are often unable to serve all clients at once. Most placement and route-planning algorithms cannot easily be extended to accommodate these considerations without drastic sacrifices to performance. In this thesis, we present approximation algorithms that provide guaranteed near-optimal solutions to these types of planning problems. Moreover, our algorithms are specifically designed for metrics that model transportation networks: planar and bounded-genus graphs, graphs with bounded treewidth, and graphs with bounded highway dimension. We capitalize on the structure of these metrics to improve the performance of our algorithms. We first consider Capacitated Domination problems, which aim to minimize the number of facilities required to serve all clients without exceeding facility capacities. For fixed capacities, we present an approximation scheme for planar graphs. Next, we address Capacitated Vehicle Routing, in which vehicles can only visit a limited number of clients in each trip. For arbitrary capacities, we improve the best-known approximation ratio for vehicle routing in trees. For fixed capacities, we design the first approximation schemes for vehicle routing in planar graphs and graphs of bounded highway dimension. Finally, we present a framework for designing vehicle-routing approximation schemes in tree metrics that can be customized to address many different vehicle-routing problems. In particular, the framework accommodates such constraints as vehicle distance (e.g. those imposed by fuel limits or driver fatigue), vehicle capacity, fleet size, and client regret.
Notes:: Thesis (Ph. D.)--Brown University, 2019

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Rights: In Copyright
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Becker, Amariah, "Approximation Algorithms for Capacitated Facility-Placement and Vehicle-Routing Problems in Transportation Networks" (2019). Computer Science Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.26300/q4t9-3v32

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Computer Science Theses and Dissertations

Theses and Dissertations for the Computer Science department.
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