AbstractThis article considers the problem of locating multiple new facilities to minimize the cost function consisting of the sum of weighted distances among new facilities and between new and existing facilities. The hyperboloid approximate procedure (HAP) is probably the most widely used approach for solving this problem. In this article, an optimality condition for this problem is derived and a method to accelerate the convergence rate of the HAP for the case of Euclidean distances is presented. From the numerical results presented in this article, it can be concluded that the performance of the new algorithm is superior to the performance of the original HAP.
AbstractAn iterative solution method is presented for solving the multifacility location problem with Euclidean distances under the minimax criterion. The iterative procedure is based on the transformation of the multifacility minimax problem into a sequence of squared Euclidean minisum problems which have analytical solutions. Computational experience with the new method is also presented.
AbstractThis paper considers the problem of locating multiple new facilities in order to minimize a total cost function consisting of the sum of weighted Euclidean distances among the new facilities and between the new and existing facilities, the locations of which are known. A new procedure is derived from a set of results pertaining to necessary conditions for a minimum of the objective function. The results from a number of sample problems which have been executed on a programmed version of this algorithm are used to illustrate the effectiveness of the new technique.
ABSTRACTIn this article, we propose a new product positioning method based on the neural network methodology of a self‐organizing map. The method incorporates the concept of rings of influence, where a firm evaluates individual consumers and decides on the intensity to pursue a consumer, based on the probability that this consumer will purchase a competing product. The method has several advantages over earlier work. First, no limitations are imposed on the number of competing products and second, the method can position multiple products in multiple market segments. Using simulations, we compare the new product positioning method with a quasi‐Newton method and find that the new method always approaches the best solution obtained by the quasi‐Newton method. The quasi‐Newton method, however, is dependent on the initial positions of the new products, with the majority of cases ending in a local optimum. Furthermore, the computational time required by the quasi‐Newton method increases exponentially, while the time required by the new method is small and remains almost unchanged, when the number of new products positioned increases. We also compute the expected utility that a firm will provide consumers by offering its products. We show that as the intensity with which a firm pursues consumers increases, the new method results in near‐optimal solutions in terms of market share, but with higher expected utility provided to consumers when compared to that obtained by a quasi‐Newton method. Thus, the new method can serve as a managerial decision‐making tool to compare the short‐term market share objective with the long‐term expected utility that a firm will provide to consumers, when it positions its products and intensifies its effort to attract consumers away from competition.
