Modelling Inter-city Road Distances by Mathematical Functions

Love, Robert F.; Morris, James G.

doi:10.1057/jors.1972.6

Cited by 138 publications

(62 citation statements)

References 9 publications

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“…In reality, customers usually drive to the facility, and therefore network distances are more appropriate for modeling. When p distances are used, it is empirically found that p = 1.78 provides the best fit to road distances (Love and Morris [69]). In many cases, customers make their choice by time rather than by distance.…”

Section: The Distancementioning

confidence: 99%

Modeling Competitive Facility Location Problems: New Approaches and Results

Berman¹,

Drezner²,

Drezner³

et al. 2009

Decision Technologies and Applications

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The gravity model as applied to competitive facility location is described in this tutorial. The gravity model is used mainly by marketers to estimate the market share attracted by competing retail facilities. A demand area consists of potential customers who spend their discretionary buying power at competing retail facilities. We discuss the gravity model and issues related to the determination of the parameters of the models. The basic model is to find the best locations for new facilities that would attract the maximum buying power from customers in the area. Extensions to this basic model include modeling uncertainty about future market conditions, minimizing the probability that the attracted market share falls short of a certain target, demand generated by intercepting a flow of customers, market expansion and lost demand, and allocation of a given budget among one's facilities to improve their attractiveness. We describe special tools that are utilized in the solution procedures. These are the generalized Weiszfeld procedure, the big triangle small triangle global optimization approach, and the tangent line approximation.

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Section: The Distancementioning

confidence: 99%

Modeling Competitive Facility Location Problems: New Approaches and Results

Berman¹,

Drezner²,

Drezner³

et al. 2009

Decision Technologies and Applications

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show abstract

“…A new study by Love and Walker [14] shows that although marginally better results can be obtained by using a block norm with eight or more parameters than by using the kl p norm, the computation cost of fitting the block norms can be prohibitive. Conversely, the original studies by Love and Morris [10,11] show that the kl p norm usually gives much superior results compared to other simpler norms such as the weighted Euclidean or weighted rectangular norms.…”

Section: Introductionmentioning

confidence: 95%

“…Love and Morris [10,11,12] applied several distance norms including the weighted l p (kl p ) norm to Germany and several régions of the United States. Let x = (xi, x%) , y = (yi, 2/2) be any two points in the plane.…”

Section: Introductionmentioning

confidence: 99%

Properties of ordinary and weighted sums of order $p$ used for distance estimation

Brimberg¹,

Love²

1995

RAIRO-Oper. Res.

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“…The criterion not only provides a numerical value so that different distance predicting functions can be compared but also provides the means for determining any empirical parameters of a distance predicting function. Researchers are presently using three goodness-of-fit criteria [1], [2], [3], [5], [11], [12], [18], [23], [24 In addition, AD and SD have been used by Love and Morris [11], [12] to develop tests for statistically comparing the accuracy of different distance predicting functions.…”

Section: Introductionmentioning

confidence: 99%

“…For example, it has been assumed that if the AD criterion is used, the weighted p -norm will predict long distances more accurately than short distances. The SD criterion has been characterized as having prediction errors with better statistical properties but still being similar to the AD criterion in terms of its accuracy in predicting long distances [11], [12]. The NAD criterion, on the other hand, has been assumed to predict short distances as accurately as long distances [3], [5], [15], [18].…”

Section: Introductionmentioning

confidence: 99%

A statistical comparison of three goodness-of-fit criteria used in modelling distances

Love

Üster

2001

Journal of Applied Mathematics and Decision Sciences

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Abstract. Distance predicting functions may be used in a variety of applications for estimating travel distances between points. To evaluate the accuracy of a distance predicting function and to determine its parameters, a goodness-of-fit criteria is employed. AD (Absolute Deviations), SD (Squared Deviations) and NAD (Normalized Absolute Deviations) are the three criteria that are mostly employed in practice. In the literature some assumptions have been made about the properties of each criterion. In this paper, we present statistical analyses performed to compare the three criteria from different perspectives. For this purpose, we employ the kpθ -norm as the distance predicting function, and statistically compare the three criteria by using normalized absolute prediction error distributions in seventeen geographical regions. We find that there exist no significant differences between the criteria. However, since the criterion SD has desirable properties in terms of distance modelling procedures, we suggest its use in practice.

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Modelling Inter-city Road Distances by Mathematical Functions

Cited by 138 publications

References 9 publications

Modeling Competitive Facility Location Problems: New Approaches and Results

Modeling Competitive Facility Location Problems: New Approaches and Results

Properties of ordinary and weighted sums of order $p$ used for distance estimation

A statistical comparison of three goodness-of-fit criteria used in modelling distances

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