NETWORK LOCATION PROBLEMS INVOLVING STRUCTURES (SUBTREE-COVER, S-MEDIAN)
Abstract
Most of the network location problems studied have been point location studies. The nature of the facility to be constructed such as an electrical communication system or an evacuation route may be better represented by a structure (such as a tree or a path) rather than just a point. Similarly, the facility may be required to serve structures or areas within the network and not just points. In this thesis, we study location problems which involve one or more structures on trees and general networks. The first problem considers the location of a single facility for which the objective is to minimize the total weighted distances to structures. An efficient algorithm is developed by exploiting the underlying graph structure. A second aspect of our research is to consider central facility location where the facility takes the form of a subtree of the network. Three versions of this problem are introduced. In the first problem, the objective is to find a facility of minimal length such that the distance from each demand point to the facility does not exceed a given constant. The second problem is a median type problem for which the cost of each served demand is the weighted distance to the facility, and the setup cost of establishing a facility is proportional to its length. The objective is to minimize the total costs over all possible facilities. Efficient algorithms for solving these problems are developed. The third problem is also a covering problem where in addition to the setup cost of a facility, a positive penalty cost is applied for each unserved demand, and the objective is to find a facility with the minimum total costs. A dynamic programming algorithm is presented for solving this version of the problem on a tree network.
Degree
Ph.D.
Subject Area
Management
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