Research Reports from the Department of Operations

Authors

K.P. K. Nair

Document Type

Report

Publication Date

10-1-1970

Abstract

Considering communities to be interconnected by road network, Hakimi provided a graph theoretic method for finding the optimal location of a single service center, such as hospital or police station, minimizing largest distance from the service center. The same problem is considered in this paper when the region to be served is represented by a convex polygon with finite number of corner points and the distance between any pair of points in the polygon is taken to be the straight path between the two points. This problem is shown to be exact in certain cases though in some other cases it is only approximate. The optimal solution is obtained from the covering circle of the convex polygon and the properties of the solution are established. Two methods of solution - geometric method and quadratic programming - are presented. Practical applications of importance in cases of certain types of service centers are outlined besides indicating useful extensions of the present solution method for solving more general problems.

Keywords

Operations research, Industrial location, Graph theory, Mathematical optimization, Quadratic programming

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 207

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

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