Solving the 1-median problem on a network with continuous demand and demand surplus

Abstract

In this paper we address the problem of locating a delivery business with a production capacity. It is a variant of the 1-median location problem on a network, in which demand is assumed to be distributed along the edges and nodes of the network. However, instead of assuming that all the demand must be served, the location for a facility is sought minimizing the expected distance to a fraction of the demand.The problem is expressed as a Mixed Integer Nonlinear Optimization problem, solved by means of a geometric Branch and Bound algorithm.