Models to estimate average route lengths in different geographical environments

Hindle, A.; Worthington, David

doi:10.1057/palgrave.jors.2601751

Cited by 12 publications

(9 citation statements)

References 5 publications

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“…However, the models have only been tested for rectangular areas and very specific information on the input, the ratio between length and width of the area, has to be known for these tour length approximations limiting their practical use. Hindle and Worthington (2004) used simulation to refine Eq. ( 14) for a 100 x 100 square area by including a term with the natural logarithm of the number of customers.…”

Section: Discussionmentioning

confidence: 99%

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Baller

Dabia

Dullaert

et al. 2019

European Journal of Operational Research

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Section: Discussionmentioning

confidence: 99%

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Baller

Dabia

Dullaert

et al. 2019

European Journal of Operational Research

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“…Percus and Martin derived the TSP instances for the eight n values between 12 and 100; iterations were conducted between five and 12 runs ( 15 ). Unlike other researchers, Hindle and Worthington conducted the iterations with n increments of one ( 25 ).…”

Section: Literature Reviewmentioning

confidence: 99%

“…It is noted that the NN model was difficult to interpret geometrically owing to its characteristic as a so-called black box. Alternative expressions for estimating TSP tour lengths were developed by Hindle and Worthington, as presented in Equation 2 ( 25 ),…”

Section: Literature Reviewmentioning

confidence: 99%

Review of Length Approximations for Tours with Few Stops

Choi

Schonfeld

2021

Transportation Research Record: Journal of the Transportation R

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The shortest tour distance for visiting all points exactly once and returning to the origin is computed by solving the well-known traveling salesman problem (TSP). Owing to the large computational effort needed for optimizing TSP tours, researchers have developed approximations that relate the average length of TSP tours to the number of points, n, visited per tour. The existing approximations are used in transportation system planning and evaluation for estimating the distance for vehicles with large capacities (e.g., delivery trucks) where n is relatively large. However, the average TSP tour lengths would be inaccurately estimated if the approximations were derived for a wide range of n values since the tour lengths increase at a decreasing rate (i.e., with [Formula: see text]) as n increases. A comprehensive review is presented here of existing studies approximating TSP tour lengths for low n values, which have become important for some recently favored delivery alternatives (e.g., deliveries by bikes, drones, and robots).

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“…The operational research method used has been the (SMOSS) approach Simplified Modelling of Spatial Systems. 7–9 The essence of this approach is the derivation and application of relatively simple mathematical functions that can be shown to yield reasonably accurate approximations of the travel distances and times that would be obtained from the application of more exact routing algorithms in spatially distributed service situations.…”

Section: Operational Modellingmentioning

confidence: 99%

Travel-related costs of population dispersion in the provision of domiciliary care to the elderly: a case study in English Local Authorities

Hindle¹,

Hindle

Spollen

2009

Health Serv Manage Res

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The aim of this research has been to make a contribution to deliberations concerning the relative costs of provision of domiciliary services for the elderly in local authorities in England and the implications for funding. The main services considered have been day-centre services and home-care services, and the particular cost areas investigated have been travel-related costs as associated with distances travelled by day-centre vehicles and care workers and with worker travelling hours. These costs are influenced by the population settlement and dispersion characteristics of the areas served and funding mechanisms are needed (and are in place) to compensate service providers. However, current mechanisms have been widely criticized and the research reported here reaches conclusions about whether such criticisms are justified and how improvements might be brought about. The methods used have involved detailed operational modelling of the selected services in a sample of local authority areas and the generalization of the findings to England as a whole.

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Models to estimate average route lengths in different geographical environments

Cited by 12 publications

References 5 publications

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Review of Length Approximations for Tours with Few Stops

Travel-related costs of population dispersion in the provision of domiciliary care to the elderly: a case study in English Local Authorities

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