Kohonen maps for solving a class of location–allocation problems

Location–allocation problems occur whenever more than one facility need be located to serve a set of demand centers and it is not known or fixed a priori their allocation to the supply centers. This paper deals with a continuous space problem in which demand centers are independently served from a given number of independent, uncapacitated supply centers. Installation costs are assumed not to depend on the actual location or the actual throughput of the supply centers. Transportation costs are considered to be proportional to the square Euclidean distance travelled and a minisum criterion is adopted. The problem is recognized as identical to certain Cluster Analysis and Vector Quantization problems. Such a relationship leads to applying Kohonen Maps, which are Artificial Neural Networks capable of extracting the main features, i.e. the structure, of the input data through a self-organizing process based on local adaptation rules. This approach has previously been applied to other combinatorial problems such as the Travelling Salesperson Problem.