A Multi-Objective Obnoxious Facility Location Modelon a Plane

U K Bhattacharya

doi:10.4236/ajor.2011.12006

Abstract

In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing facility points; 2) Maximize the minimum distance from the facility to be located to the existing facility points; 3) Maximize the number of existing facility points covered. Area restriction concept has been incor-porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective problem. A transformed non- linear programming algorithm has been designed for the proposed non-linear model. Rectilinear dis-tance norm has been considered as the distance measure as it is more appropriate to various realistic situa-tions. A numerical example has been presented to illustrate the solution algorithm.

Highlights

For service facility location problems when the costs are the increasing function of distance, it is reasonable to consider either minimum of the sum of distances or the weighted distances
In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various existing facility points; 2) Maximize the minimum distance from the facility to be located to the existing facility points; 3) Maximize the number of existing facility points covered
The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region

Summary

Introduction

For service facility location problems when the costs are the increasing function of distance, it is reasonable to consider either minimum of the sum of distances or the weighted distances. Drezner and Wesolowsky [6] first introduced the rectilinear maximin problem for locating an obnoxious facility They developed a solution procedure by dividing the feasible region into rectilinear sub regions and solving a linear programming problem for each of this sub regions. In this present investigation a vertex covering obnoxious facility location model has been designed with multiple objectives. In this model weights as importance has been assigned to the various demand points and considers as a separate objective. Incorporation of the area restriction has been implemented by inducting a convex polygon in the feasible region Another advantage of introduction of a convex polygon in the constraint set is that it might reduce the number of transformed non-linear programming problems to be solved.

Preliminaries

Mathematical Formulation

Algorithm for Vertex Covering Obnoxious Facility Location Problem

Numerical Example

Concluding Remarks