Mean and mean square location models along a coordinate line

Many simple location models involve optimization through minimizing an objective function that determines mean travel distance. Such problems often involve locating a single service unit at the median of a demand variable. This paper considers the role of the mean of a demand variable. We investigate situations in which the demand mean and demand median are substantially separated and show that such separation is accompanied by large travel expected travel distances and large travel variances. Expected travel distances and expected travel variances are connected in a natural way to expected mean square travel distances. Optimal location with respect to mean square is considered in a general setting and such locating is shown to have interesting properties with respect to mean travel distance and mean travel variance. The use of multiple service units is assumed.