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Spatial optimization approaches for solving the continuous Weber and multi-Weber problems

Description
Facility location models are usually employed to assist decision processes in urban and regional planning. The focus of this research is extensions of a classic location problem, the Weber problem, to address continuously distributed demand as well as multiple facilities. Addressing continuous demand and multi-facilities represents major challenges. Given advances…

Facility location models are usually employed to assist decision processes in urban and regional planning. The focus of this research is extensions of a classic location problem, the Weber problem, to address continuously distributed demand as well as multiple facilities. Addressing continuous demand and multi-facilities represents major challenges. Given advances in geographic information systems (GIS), computational science and associated technologies, spatial optimization provides a possibility for improved problem solution. Essential here is how to represent facilities and demand in geographic space. In one respect, spatial abstraction as discrete points is generally assumed as it simplifies model formulation and reduces computational complexity. However, errors in derived solutions are likely not negligible, especially when demand varies continuously across a region. In another respect, although mathematical functions describing continuous distributions can be employed, such theoretical surfaces are generally approximated in practice using finite spatial samples due to a lack of complete information. To this end, the dissertation first investigates the implications of continuous surface approximation and explicitly shows errors in solutions obtained from fitted demand surfaces through empirical applications. The dissertation then presents a method to improve spatial representation of continuous demand. This is based on infill asymptotic theory, which indicates that errors in fitted surfaces tend to zero as the number of sample points increases to infinity. The implication for facility location modeling is that a solution to the discrete problem with greater demand point density will approach the theoretical optimum for the continuous counterpart. Therefore, in this research discrete points are used to represent continuous demand to explore this theoretical convergence, which is less restrictive and less problem altering compared to existing alternatives. The proposed continuous representation method is further extended to develop heuristics to solve the continuous Weber and multi-Weber problems, where one or more facilities can be sited anywhere in continuous space to best serve continuously distributed demand. Two spatial optimization approaches are proposed for the two extensions of the Weber problem, respectively. The special characteristics of those approaches are that they integrate optimization techniques and GIS functionality. Empirical results highlight the advantages of the developed approaches and the importance of solution integration within GIS.
ContributorsYao, Jing (Author) / Murray, Alan T. (Thesis advisor) / Mirchandani, Pitu B. (Committee member) / Kuby, Michael J (Committee member) / Arizona State University (Publisher)
Created2012
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Deriving an obstacle-avoiding shortest path in continuous space: a spatial approach

Description
The shortest path between two locations is important for spatial analysis, location modeling, and wayfinding tasks. Depending on permissible movement and availability of data, the shortest path is either derived from a pre-defined transportation network or constructed in continuous space. However, continuous space movement adds substantial complexity to identifying the…

The shortest path between two locations is important for spatial analysis, location modeling, and wayfinding tasks. Depending on permissible movement and availability of data, the shortest path is either derived from a pre-defined transportation network or constructed in continuous space. However, continuous space movement adds substantial complexity to identifying the shortest path as the influence of obstacles has to be considered to avoid errors and biases in a derived path. This obstacle-avoiding shortest path in continuous space has been referred to as Euclidean shortest path (ESP), and attracted the attention of many researchers. It has been proven that constructing a graph is an effective approach to limit infinite search options associated with continuous space, reducing the problem to a finite set of potential paths. To date, various methods have been developed for ESP derivation. However, their computational efficiency is limited due to fundamental limitations in graph construction. In this research, a novel algorithm is developed for efficient identification of a graph guaranteed to contain the ESP. This new approach is referred to as the convexpath algorithm, and exploits spatial knowledge and GIS functionality to efficiently construct a graph. The convexpath algorithm utilizes the notion of a convex hull to simultaneously identify relevant obstacles and construct the graph. Additionally, a spatial filtering technique based on intermediate shortest path is enhances intelligent identification of relevant obstacles. Empirical applications show that the convexpath algorithm is able to construct a graph and derive the ESP with significantly improved efficiency compared to visibility and local visibility graph approaches. Furthermore, to boost the performance of convexpath in big data environments, a parallelization approach is proposed and applied to exploit computationally intensive spatial operations of convexpath. Multicore CPU parallelization demonstrates noticeable efficiency gain over the sequential convexpath. Finally, spatial representation and approximation issues associated with raster-based approximation of the ESP are assessed. This dissertation provides a comprehensive treatment of the ESP, and details an important approach for deriving an optimal ESP in real time.
ContributorsHong, Insu (Author) / Murray, Alan T. (Thesis advisor) / Kuby, Micheal (Committee member) / Rey, Sergio (Committee member) / Arizona State University (Publisher)
Created2015
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Investigating the Relationship between Neighborhood Socioeconomic Status and Proximity to Public Services

Description
With growing levels of income inequality in the United States, it remains as important as ever to ensure indispensable public services are readily available to all members of society. This paper investigates four forms of public services (schools, libraries, fire stations, and police stations), first by researching the background of…

With growing levels of income inequality in the United States, it remains as important as ever to ensure indispensable public services are readily available to all members of society. This paper investigates four forms of public services (schools, libraries, fire stations, and police stations), first by researching the background of these services and their relation to poverty, and then by conducting geospatial and regression analysis. The author uses Esri's ArcGIS Pro software to quantify the proximity to public services from urban American neighborhoods (census tracts in the cities of Phoenix and Chicago). Afterwards, the measures indicating proximity are compared to the socioeconomic statuses of neighborhoods using regression analysis. The results indicate that pure proximity to these four services is not necessarily correlated to socioeconomic status. While the paper does uncover some correlations, such as a relationship between school quality and socioeconomic status, the majority of the findings negate the author's hypothesis and show that, in Phoenix and Chicago, there is not much discrepancy between neighborhoods and the extent to which they are able to access vital government-funded services.
ContributorsNorbury, Adam Charles (Author) / Simon, Alan (Thesis director) / Simon, Phil (Committee member) / Department of Information Systems (Contributor) / Department of English (Contributor) / Department of Economics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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Location of refueling stations for alternative fuel vehicles considering driver deviation behavior and uneven consumer demand: model, heuristics, and GIS

Description

Concerns about Peak Oil, political instability in the Middle East, health hazards, and greenhouse gas emissions of fossil fuels have stimulated interests in alternative fuels such as biofuels, natural gas, electricity, and hydrogen. Alternative fuels are expected to play an important role in a transition to a sustainable transportation system.…

Concerns about Peak Oil, political instability in the Middle East, health hazards, and greenhouse gas emissions of fossil fuels have stimulated interests in alternative fuels such as biofuels, natural gas, electricity, and hydrogen. Alternative fuels are expected to play an important role in a transition to a sustainable transportation system. One of the major barriers to the success of alternative-fuel vehicles (AFV) is the lack of infrastructure for producing, distributing, and delivering alternative fuels. Efficient methods that locate alternative-fuel refueling stations are essential in accelerating the advent of a new energy economy. The objectives of this research are to develop a location model and a Spatial Decision Support System (SDSS) that aims to support the decision of developing initial alternative-fuel stations. The main focus of this research is the development of a location model for siting alt-fuel refueling stations considering not only the limited driving range of AFVs but also the necessary deviations that drivers are likely to make from their shortest paths in order to refuel their AFVs when the refueling station network is sparse. To add reality and applicability of the model, the research is extended to include the development of efficient heuristic algorithms, the development of a method to incorporate AFV demand estimates into OD flow volumes, and the development of a prototype SDSS. The model and methods are tested on real-world road network data from state of Florida. The Deviation-Flow Refueling Location Model (DFRLM) locates facilities to maximize the total flows refueled on deviation paths. The flow volume is assumed to be decreasing as the deviation increases. Test results indicate that the specification of the maximum allowable deviation and specific deviation penalty functional form do have a measurable effect on the optimal locations of facilities and objective function values as well. The heuristics (greedy-adding and greedy-adding with substitution) developed here have been identified efficient in solving the DFRLM while AFV demand has a minor effect on the optimal facility locations. The prototype SDSS identifies strategic station locations by providing flexibility in combining various AFV demand scenarios. This research contributes to the literature by enhancing flow-based location models for locating alternative-fuel stations in four dimensions: (1) drivers' deviations from their shortest paths, (2) efficient solution approaches for the deviation problem, (3) incorporation of geographically uneven alt-fuel vehicle demand estimates into path-based origin-destination flow data, and (4) integration into an SDSS to help decision makers by providing solutions and insights into developing alt-fuel stations.
ContributorsKim, Jong-Geun (Author) / Kuby, Michael J (Thesis advisor) / Wentz, Elizabeth (Committee member) / Murray, Alan T. (Committee member) / Arizona State University (Publisher)
Created2010