Location Dominance on Spherical Surfaces

Aly, Adel A.; Kay, David C.; Litwhiler, Daniel W.

doi:10.1287/opre.27.5.972

Cited by 29 publications

(3 citation statements)

References 4 publications

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“…A subset of the sphere is spherically convex if it contains the geodesics between any two points in the subset, and the (spherical) convex hull of a subset is the smallest convex set containing the subset. Aly, Kay, and Litwhiler [1] prove that if x 1 , . .…”

Section: Hubs On a Spherementioning

confidence: 99%

The FedEx Problem

Morrison

2010

The College Mathematics Journal

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In April of 1973 a small company, Federal Express, began package delivery operations by flying 186 packages to 25 cities in the U.S. from Memphis. In order to deliver small packages quickly the company used a novel strategy in the shipping business. Every day packages picked up from all over the country were flown to Memphis where they were sorted and then flown to their destinations for delivery the next day. The strategy has been extremely successful and has been adopted by other shippers such as UPS, which established a shipping hub in Louisville. Meanwhile, Federal Express has grown into a large company, now known as FedEx, with worldwide operations.According to the company website [6], Memphis was selected for its geographical center to the original target market cities for small packages. In addition, the Memphis weather was excellent and rarely caused closures at Memphis International Airport. The airport was also willing to make the necessary improvements for the operation and had additional hangar space readily available.It is the question of the "geographical center" that is the focus of this article. Suppose that FedEx were choosing its hub today with the assumption that anyone in the U.S. is equally likely to ship a package to anyone else in the country. The goal is to minimize the average distance the package must be shipped. Since we are assuming that the sender's and receiver's locations are independent and identically distributed, the average distance that a package travels is twice the average distance from the sender to the hub location, and so the optimal location is a point located with minimal average distance to the population. This is equivalent to a point that minimizes the sum of all the distances to the members of the population. Such a point we will call a hub for the population. By the term FedEx problem, we mean the related questions of the existence, uniqueness, and determination of hubs.In the first section we deal with the FedEx problem for a population in R n using the Euclidean distance, and in section 2 we actually find the hub for the U.S. population based on the data from the 2000 census and with the distance between points measured along great circles. In the last * College Math.

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Section: Hubs On a Spherementioning

confidence: 99%

The FedEx Problem

Morrison

2010

The College Mathematics Journal

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“…The minimizer X * of J 1 ðXÞ is known as the Fermat-Weber [7] point or 1-median. The Fermat-Weber problem has drawn much attention from mathematicians and facility location scientists and engineers; see, for instance [8][9][10][11][12][13][14][15][16][17][18][19][20] and the references therein. For Euclidean metric dðx, yÞ =…”

Section: Introductionmentioning

confidence: 99%

An Optimized Discrete Data Classification Method in $N$ -Dimensional

Kim

2022

Computational and Mathematical Methods

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We propose a discrete data classification method of scattered data in N -dimensional by solving the minimax problem for a set of points. The current research is extended from 2-dimensional and 3-dimensional to N -dimensional. The problem can be applied to artificial intelligence classification problems (machine learning, deep learning), point data analysis problems (data science problem), the optimized design of nanoscale circuits, and the location of facility problems, circle detection on 2D image, or sphere detection on depth image. We generalized the discrete data classification methodology in N -dimensional. Finally, we resolved to find an exact solution of the location of a manifold for our suggested problem in N -dimensional.

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“…These are: the minisum (or Weber) [1,2,[4][5][6][7][8][9][10][11], the minimax (or Rawls) [4,5,[11][12][13][14][15][16][17][18], and the maximin (or obnoxious facility) [11,12,19] problems. In a minisum problem, a facility must be located where the sum of the weighted distances between it and a set of points with known locations is minimized.…”

Section: Introductionmentioning

confidence: 99%

Spherical minimax location problem using the Euclidean norm: Formulation and optimization

Patel

1995

Comput Optim Applic

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Abstract. The minimax spherical location problem is formulated in the Cartesian coordinate system using the Euclidean norm, instead of the spherical coordinate system using spherical arc distance measures. It is shown that minimizing the maximum of the spherical arc distances between the facility point and the demand points on a sphere is equivalent to minimizing the maximum of the corresponding Euclidean distances. The problem formulation in this manner helps to reduce Karush-Kuhn-Tucker necessary optimality conditions into the form of a set of coupled nonlinear equations, which is solved numerically by using a method of factored secant update with a finite difference approximation to the Jacobian. For a special case when the set of demand points is on a hemisphere and one or more point-antipodal point pair(s) are included in the demand points, a simplified approach gives a minimax point in a closed form.

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Location Dominance on Spherical Surfaces

Cited by 29 publications

References 4 publications

The FedEx Problem

The FedEx Problem

An Optimized Discrete Data Classification Method in $N$ -Dimensional

Spherical minimax location problem using the Euclidean norm: Formulation and optimization

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Location Dominance on Spherical Surfaces

Cited by 29 publications

References 4 publications

The FedEx Problem

The FedEx Problem

An Optimized Discrete Data Classification Method in N -Dimensional

Spherical minimax location problem using the Euclidean norm: Formulation and optimization

Contact Info

Product

Resources

About

An Optimized Discrete Data Classification Method in $N$ -Dimensional