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Probabilisticl p distances in location models

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Abstract

Modelling distances with thel p norm is very widespread in “site selecting” location problems. This paper deals with the concept of a probabilisticp parameter which permits uncertainty in the directness of the routes that can be taken between a facility and demand points. This paper establishes the rather surprising result that the expected distances can themselves be closely approximated byl p distances with appropriately chosenp parameters. This result is very useful when, as is often the case, expected distances are used in the optimization criterion.

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Brimberg, J., Wesolowsky, G.O. Probabilisticl p distances in location models. Ann Oper Res 40, 67–75 (1992). https://doi.org/10.1007/BF02060470

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