Approximate formulas of average distances associated with regions and their applications to location problems

Koshizuka, Takeshi; Kurita, Osamu

doi:10.1007/bf01582882

Cited by 35 publications

(21 citation statements)

References 8 publications

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“…where P and Q are probability measures in R 2 and even in the most simple case of uniform distributions, the évaluation of these formulae, when possible, is very time-consuming [16].…”

Section: \\X-y\\dp(x)dq(y)mentioning

confidence: 99%

“…For example, existing facility or demands may be points, although each point is a random variable with a probability measure over an area. This is the case of location problems under conditions of uncertainty [6,9,14], Secondly the facilities may have areas instead of points, as suggested for instance in [16]. A third interprétation is that the problem deals with a very large number of demand and facility points clustered in some neighborhoods, thus being more appropriate to model it as an area-demand and area-facility problem rather than a conglomerate of many points [7].…”

Section: Introductionmentioning

confidence: 99%

“…Aly and Marucheck [1,18] deal with the problem of demand uniformly distributed over rectangular régions with the Manhattan norm. Recently Koshizuka and Kurita [16] have studied the Weber problem with uniform demand on circular areas using approximate formulas for average distances.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The generalized Weber problem with expected distances

Carrizosa¹,

Conde²,

Munõz-Márquez³

et al. 1995

RAIRO-Oper. Res.

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“…where P and Q are probability measures in R 2 and even in the most simple case of uniform distributions, the évaluation of these formulae, when possible, is very time-consuming [16].…”

Section: \\X-y\\dp(x)dq(y)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The generalized Weber problem with expected distances

Carrizosa¹,

Conde²,

Munõz-Márquez³

et al. 1995

RAIRO-Oper. Res.

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“…This is a special case of the expected distance when interactions are equally likely from all locations in both objects (Koshizuka and Kurita 1991). Average distances are useful when measuring interaction ''cost'' (time, money, energy) between two objects.…”

Section: Geographic Relationshipsmentioning

confidence: 99%

Representation and Spatial Analysis in Geographic Information Systems

Miller

Wentz

2003

Annals of the Association of American Geographers

137

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A common-perhaps modal-representation of geography in spatial analysis and geographic information systems is native (unexamined) objects interacting based on simple distance and connectivity relationships within an empty Euclidean space. This is only one possibility among a large set of geographic representations that can support quantitative analysis. Through the vehicle of GIS, many researchers are adopting this representation without realizing its assumptions or its alternatives. Rather than locking researchers into a single representation, GIS could serve as a toolkit for estimating and exploring alternative geographic representations and their analytical possibilities. The article reviews geographic representations, their associated analytical possibilities and relevant computational tools in the combined spatial analysis and GIScience literatures. The discussion identifies several research and development frontiers, including analytical gaps in current GIS software.A common-perhaps modal-representation of geography in spatial analysis (SA) and geographic information systems (GIS) is native (unexamined) objects interacting based on simple distance and connectivity relationships within an empty Euclidean plane. This representation has essentially remained untouched since its inception during the birth of quantitative geography and computer cartography, an era characterized by scarce geographic data, weak computers, and crude spatial algorithms. It is only one possibility among a large set that can support ''analysis,'' or the ability to measure and infer quantitative properties and relationships. 1 The Euclidean model is useful in many contexts, such as cartography, navigation, and many types of analysis. However, there may be latent explanatory power in geographic space not captured by the Euclidean model and consequently missed by SA techniques and GIS-based analysis based on this georepresentation. Representation and analysis are closely linked: mathematical and computational tools, however powerful, cannot extract more information than is latent in a representation.Through the vehicle of GIS, many researchers are adopting the Euclidean model and its related analytical possibilities without realizing its assumptions or its alternatives. Rather than locking researchers into a single representation, GIS could serve as a toolkit for estimating and exploring alternative geographic representations and their analytical possibilities for a given geographic phenomenon or problem. Reconsidering and expanding the geographic representation model underpinning both SA and GIS is an unexplored avenue for improving analytical capabilities of both.Theories and techniques for alternative geographic representations and analyses exist in the SA and geographic information science (GIScience) literatures. 2 SA has a small but steady current of literature on representation issues in analysis, including theories of geographic space and techniques for estimating distance metrics, analyzing geographic relationships between spatial...

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“…A number of problems can be addressed with geometric probability, including finding the optimal location of taxi stations given the distribution of pickup calls, and the design of a response district for ambulances given the distribution of medical assistance requirements (Larson and Odoni, 1981). Other works estimate average distances between points under different assumptions about the area where the objects are distributed (e.g., Vaughan, 1984;Koshizuka and Kurita, 1991). None of these studies analyses the case of pedestrian movements in a city, which is the object of this paper.…”

Section: Introductionmentioning

confidence: 97%

Probability distribution of walking trips and effects of restricting free pedestrian movement on walking distance

Tirachini

2015

Transport Policy

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Approximate formulas of average distances associated with regions and their applications to location problems

Cited by 35 publications

References 8 publications

The generalized Weber problem with expected distances

The generalized Weber problem with expected distances

Representation and Spatial Analysis in Geographic Information Systems

Probability distribution of walking trips and effects of restricting free pedestrian movement on walking distance

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