Modelling distances with the lp norm is very widespread in ‘site selecting’ location problems. This paper deals with the concept of a probabilistic p 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 by lp distances with appropriately chosen p parameters. This result is very useful when, as is often the case, expected distances are used in the optimization criterion.
