Location Science最新文献

For a given triangle ABC with ∠A>120°, the Simpson variant of Torricelli’s geometrical construction for solving a problem, allegedly first formulated by Fermat in the early 1600s, will identify a point which incorrectly was claimed by Courant and Robbins (Courant, R., Robbins, H., 1941. What is Mathematics? Oxford University Press, Oxford.) to solve the so-called Complementary problem: $\text{min}\text{{BX+CX−AX:X∈}\text{R}{}^2\text{}}$. The correct solution for any triangle is provided here.

The p-facility centdian network problem consists of finding the p points that minimize a convex combination of the p-center and p-median objective functions. The vertices and local centers constitute a dominating set for the 1-facility centdian; i.e., it contains an optimal solution for all instances of the problem. Hooker et al. (1991) give a theoretical result to extend the dominating sets for the 1-facility problems to the corresponding p-facility problems. They claim that the set of vertices and local centers is also a dominating set for the p-facility centdian problem. We give a counterexample and an alternative finite dominating set for p=2. We propose a solution procedure for a network that improves the complexity of the exhaustive search in the dominating set. We also provide a very efficient algorithm that solves the 2-centdian on a tree network with complexity O(n²).

The standard plant location problem requires choosing from a set of potential sites the locations of new facilities in order to serve all the demands specified on a network at a minimum total cost. In this paper, the standard model is replaced by a new model in which the acceptance of demands onto the location balance sheet becomes part of the decision process. The motivation for such an approach and its applicability in the decision process are elaborated. The mathematical formulation results in a bi-criterion model which can be used to study the trade-off between total cost and the proportion of the market to be served. Computational and theoretical results are reported which demonstrate the integer friendliness of the new model.

Consider a set L of potential locations for p facilities and a set U of locations of given users. The p-median problem is to locate simultaneously the p facilities at locations of L in order to minimize the total transportation cost for satisfying the demand of the users, each supplied from its closest facility. This model is a basic one in location theory and can also be interpreted in terms of cluster analysis where locations of users are then replaced by points in a given space. We propose several new Variable Neighborhood Search heuristics for the p-median problem and compare them with Greedy plus Interchange, and two Tabu Search heuristics.

This paper shows a computational method for optimizing a system of successively inclusive hierarchical facilities (a system in which the services provided by a certain rank of facilities include all services provided by lower rank facilities) on a continuous plane. The system is optimized with respect to not only the configuration of ranked facilities, but also its hierarchical structure (i.e. the composition of the number of ranks and the numbers of ranked facilities). The optimization procedure has two steps. The first step optimizes a system of exclusive hierarchical facilities by an analytical method. Using this optimal solution, the second step optimizes a system of successively inclusive hierarchical facilities by a computational search method. Numerical experiments show that the proposed method tends to reach a near optimal solution within a few iterations.