The Variance Location Problem on a Network with Continuously distributed demand

Most location problems on networks consider discrete nodal demand. However, for many problems, demands are better represented by continuous functions along the edges, in addition to nodal demands. Several papers consider the optimal location problem of one or more facilities when demands are continuously distributed along the network, and the objective function dealt with is the median one. Nevertheless, in location of public services it is desirable to use an equity criterion. One of the latter is variance of distance distribution which has been studied only for discrete nodal demands. In this paper the variance problem has been generalized to the case where one allows the demand to arise discretely on the nodes as well as continuously along the edges. Properties and behaviour of the objective function are studied. Likewise we present an exact algorithm for solving this problem in a network, which reduces the complexity of the exhaustive procedure.