Unrestricted Selection of the Sizes

Abstract

The problems that arise if the sizes are to be chosen without a restriction on their relative position are far more complex than those we met in the previous chapters. This is mainly caused by the fact that the shape of the service areas is now in general not the same as was the case when using one of the restrictions. Since the shapes depend on the position of the sizes, the change of the position of one of the sizes might have the consequence that the shape of one or more of the service areas also changes considerably. This means that when an iterative method is used to solve the model the new shapes of the service areas have to be determined after each iteration. In order to complicate matters not too much, we will consider only those loss functions which lead to service areas whose boundaries consist of a number of horizontal and vertical line segments.