Minisum Location Problem Research Articles

Duality for constrained multifacility location problems with mixed norms and applications

A dual problem is developed for the constrained multifacility minisum location problems involving mixed norms. General optimality conditions are also obtained providing new algorithms based on the concept of partial inverse of a multifunction. These algorithms which are decomposition methods, generate sequences globally converging to a primal and a dual solution respectively. Numerical results are reported.

The minisum location problem on an undirected network with continuous link demands

In the one-median problem, a facility is to be located on a network minimizing total travel distances from the facility to customer demands restricted to nodal locations. In reality, however, demands do occur on links of a network. Thus, aggregation of or restriction to nodal demands may not be a satisfactory approximation. In this paper, we generalize the one-median problem to a network with discrete nodal as well as general continuous link demands. Properties of the total travel distance, as a function of the facility's location, are examined. We introduce an exact and a heuristic procedure to find an optimal location for the facility. An efficient algorithm is developed when the network is a tree.

The Solution of Distance Constrained Mini-Sum Location Problems

The problem considered in this paper requires determining the location of a given number of centers or facilities to minimize the sum of weighted distances to customers being served, subject to the constraint that no customer receives inadequate service. The method proposed is a partial enumerative procedure that employs both a graph-coloring algorithm (to generate feasible partitions) and an iterative location procedure with feasibility tests (to determine optimal locations). The procedure ensures the global optimum to this otherwise non-convex location-allocation problem. The procedure has been programmed and computational results are presented.

Sequential location-allocation problems on chains and trees with probabilistic link demands

In this paper, we consider multiperiod minisum location problems on networks in which demands can occur continuously on links according to a uniform probability density function. In addition, demands may change dynamically over time periods and at most one facility can be located per time period. Two types of networks are considered in conjunction with three behavioral strategies. The first type of network discussed is a chain graph. A myopic strategy and long-range strategy for locatingp-facilities are considered, as is a discounted present worth strategy for locating two facilities. Although these problems are generally nonconvex, effective methods are developed to readily identify all local and global minima. This analysis forms the basis for similar problems on tree graphs. In particular, we construct algorithms for the 3-facility myopic problem and the 2-facility long-range and discounted cost problems on a tree graph. Extensions and suggestions for further research on problems involving more general networks are provided.

A Solution to the Weber Location Problem on the Sphere

In this paper we present an algorithm for the solution of the minisum location problem on the sphere. The algorithm is finite for the solution within a given accuracy of the optimal solution.

State of the Art—Location on Networks: A Survey. Part II: Exploiting Tree Network Structure

The discussion of the fundamental p-center and p-median problems in Part I of this paper provides the basis for the work surveyed in Part II. Part II deals with the minimax and minisum location problems with mutual communication, location problems involving multiple objectives, the distance constraints problem and problems involving the location of paths. In addition, convexity issues in network location problems are discussed. Virtually all of this work exploits network structure. Specifically it is based on the assumption that the network is a tree. The conclusion section gives a brief discussion of the state of the art and of current trends in network location research.

The minisum location problem for the Jaccard metric

The well-known Jaccard metric for binary vectors can also be used for nonnegative vectors. This metric is a special case of a whole class of metrics obtainable from a given one by a certain transformation. For the Jaccard metric, the continuous optimization problem of finding an optimal location is reduced to a discrete one. The impact of this result on a multiple location-allocation problem from cluster analysis is discussed.

Heuristic Methods for Location-Allocation Problems

Heuristic Methods for Location-Allocation Problems