Self-organizing feature maps for solving location–allocation problems with rectilinear distances

Abstract

This study deals with solving uncapacitated location–allocation (LA) problems with rectilinear distances by using a method based on Kohonen self-organizing feature maps (SOFMs). By treating LA problems as clustering problems, this method has the advantage of extracting the structure of the input data by a self-organizing process based on adaptation rules. In this paper, a heuristic method is constructed by using SOFMs with a guided refining procedure, and its performance is compared with simulated annealing. The experimental results using the proposed guided refining procedure to reinforce the SOFM method show that the proposed method is excellent in terms of quality of solution and speed of computation. In addition, the experimental results suggest that SOFMs may provide an excellent approach when generating initial solutions for other heuristic or exact algorithms. This conjecture is made because most of the solutions yielded by SOFM are close to the optimal solution in all experiments. Scope and purpose Given the location of a set of customers with different demands, the LA problem is to select the locations of a number of supply centers to serve the customers and to decide the corresponding allocation of the customers to supply centers under a given optimization criterion. The LA problem may arise in fire stations, hospitals, police stations, telecommunication networks, and warehouses relative to production facilities and customers. In addition, the recent rapid growth of demand for supply chain management, which can decrease the total cost, while improving the quality of goods and services of various organizations, has drawn significant research attention. As an important part of supply chain management, the LA problem is related to the facility management service, logistics and distribution, order entry and customer service operations. Therefore, it should be indicated much more than before for organizations to improve their competitive advantage. In solving the LA problem, the costs of transportation between customers and supply centers are proportional to an appropriately determined distance, e.g. the Euclidean distance or rectilinear distance. The location of supply centers and the allocation of customers to supply centers must be considered simultaneously. The capacities of supply centers in LA problems can either be fixed or treated without any limitation if the capacity of each supply center can be adjusted according to the amount of allocated service demands of customers, which are referred to as capacitated and uncapacitated problems, respectively. In addition, the assumption of no interaction between supply centers makes LA problems different from p-hub problems. Currently, existing algorithms for solving the LA problems cannot meet the demands of rapidly changing industrial or market environments, since they are either time consuming or provide poor-quality solutions. Therefore, in this article, we propose a heuristic method using Kohonen's feature maps, which are artificial neural networks capable of mapping the distribution of input data to specified neurons, with a guided refining procedure to solve uncapacitated LA problems. In addition, the investigation of appropriateness of using Kohonen's feature maps (called SOFMs) as an initial solution-generating method for another heuristic or exact method is also provided.