Serving regional demand in facility location

Papers in Regional Science

2022

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This paper introduces a bi‐objective strategic location problem to address access and coverage. While previous research in continuous location modelling considered access coverage independently, none has approached such a problem in an integrated fashion. In this paper, a new mathematical formulation considering access and coverage is derived, and a solution algorithm to find the entire set of optimal tradeoff solutions is developed. Application findings are reported for several case studies, varying in problem size. The developed approach is shown to provide critical insights for real‐time decision‐making, facilitating planning, management and policy development.

Section: Mathematical Modelmentioning

confidence: 99%

Locating a facility to simultaneously address access and coverage goals

Baik

Papers in Regional Science

2022

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“…The caveat is that (X κ , Y κ ) can be found. Solving for each face Weber point (X κ , Y κ ) is possible using the unconstrained regional (classic) Weber point, X, Ŷ , which can be found using the iterative approach of Weiszfeld (see Schaefer & Hurter Jr, 1974;Church & Murray, 2009;Yao & Murray, 2014;Church, 2019;Murray et al, 2020;Murray, 2021). Since the classic Weber problem, (3), is convex, it is true that the optimal face Weber point (X κ , Y κ ) can be derived using the nearest point operatory,…”

Section: Formalization and Solutionmentioning

confidence: 99%

Urban informatics and spatial optimization

Baik

2022

Urban Info

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There has been much concern for sustainability issues, recognizing the significant impacts that humans have had and continue to have on the Earth. Urban informatics has much to offer city systems in terms of understanding, management and design, particularly associated with sustainability. Efficiency that characterizes sustainable systems, and strategic goals to achieve them, does not happen by chance, but rather is the byproduct of concerted efforts driven by informed decision making. This paper focuses on strategic decision making, and the role of spatial optimization as a component of urban informatics. Strategic siting involving access and coverage demonstrates the capabilities of spatial optimization, but more importantly highlights the significance of an urban informatics perspective.

“…When applying basic calculus, however, its solution is more complicated. Weiszfeld () demonstrated that the derivative information could be used to devise an iterative solution scheme, where an initial guess at the best‐point center location could be systematically refined and improved, eventually converging to the optimum site (see also Church & Murray , Yao & Murray ). This solution method relies on the following simplified derivatives:

(X^{(t + 1)}, Y^{(t + 1)}) = (\frac{\sum_{i = 1}^{n} \frac{a_{i} x_{i}}{\sqrt{{(X^{(t)} - x_{i})}^{2} + {(Y^{(t)} - y)}^{2}}}}{\sum_{i = 1}^{n} \frac{a_{i}}{\sqrt{{(X^{(t)} - x_{i})}^{2} + {(Y^{(t)} - y)}^{2}}}}, \frac{\sum_{i = 1}^{n} \frac{a_{i} y_{i}}{\sqrt{{(X^{(t)} - x_{i})}^{2} + {(Y^{(t)} - y)}^{2}}}}{\sum_{i = 1}^{n} \frac{a_{i}}{\sqrt{{(X^{(t)} - x_{i})}^{2} + {(Y^{(t)} - y)}^{2}}}})

…”

Section: Technical Specificationmentioning

confidence: 99%

Complexities in spatial center derivation

2018

Transactions in GIS

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The center of a spatial object or set of objects is a rather straightforward and well understood descriptor. Beyond providing a statistically oriented interpretation of the middle of something, the center often has much significance in terms of locating services and activities, but may also represent a place of political/historical importance, a site that | 1337 MURRAY distribution facility, not to mention the time required to process, fill, and deliver once a supply request has been made. Good access is essential and may well be the difference in the success of the company, keeping costs low and providing the best service to customers possible. While a slightly different interpretation of costs and benefits, one can similarly view residential emergency aid and/or evacuation in the event of a crisis/disaster, such as the recent fire and mudslides experienced in Santa Barbara, CA. There is a time and/or cost for people to get to and from a spatial center that provides a service. Finding the most efficient site relative to costs is clearly important in economic terms, but also critical for saving lives and property when it reflects such a context. This is precisely why place significance of a geographic center is highlighted in Rogerson (2015a) because a political designation of a county seat, as an example, ultimately exists to provide good (and economical) access to public services and other functions.In addition to summary and efficiency, a spatial center may also have explanatory meaning as well as design and communication significance. With respect to explanatory meaning, the spatial center of crime incidents may identify the residence or employment location of a perpetrator. Rossmo (2000) details a range of contexts along these lines, where the spatial center assists in solving or explaining cases involving arson, blackmail, rape, robbery, and murder, among others. A challenge in design and communication involves the labeling of features in mapbased display. The default placement of a feature label in most commercial GIS is, in fact, at or along the object center for polygon-based features. The reason for this is that it often represents a location of minimal potential conflict with neighboring labels, enhancing legibility and visual aesthetics.This article explores ontological and semantic issues associated with identifying a spatial center. Section 2 details aspects of definitional variability, emphasizing distinctions associated with direct and indirect summary, homogeneous and heterogeneous spatial characteristics, as well as interpretation of a center beyond the oftenconceived single point. Section 3 follows, with technical specifications that highlight the criteria used to quantify what constitutes the best center. Select illustrative examples of core ideas are provided in Section 4. The article ends with a discussion and concluding comments in Section 5.