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This paper proposes a new mathematical model for locating k-obnoxious facilities Here a vertex covering k-obnoxious facilities location problem on a plane has been modelled by combining it as a combination of three interacting criteria as follows: 1) maximise the minimum distances between any existing point and any variable point as well as between any pair of variable points; 2) maximise the number of existing points covered by various respective variable points; 3) minimise the overall importance of the various existing points associated to the various variable facility points. A nonlinear programming iterative algorithm for locating k-obnoxious facilities has been developed. The algorithm developed here is a generalised iterative algorithm. It has been proved that the optimal solution obtained by the algorithm is the non-dominated solution of the original multi-objective problem. Rectilinear distance norm has been considered as the distance measure as it is more appropriate to the various realistic situations.

Operation Management and Quantitative Techniques

International Journal of Operational Research

A mathematical model for locating k-obnoxious facilities on a plane

In this paper k-obnoxious facility location problem has been modeled as a pure planner location problem.  Area restriction concept has been incorporated by inducting a convex polygon in the constraints set. A linear programming iterative algorithm for k- obnoxious facility locations has been developed. An upper bound has been incorporated in the algorithm to get the  optimal solution. Also the concept of upper bound has reduced  the number of linear programming problems to solved in the algorithm. Rectilinear distance norm has been considered as the distance measure as it is more appropriate to the various realistic situations. 

Fulltext

Transportation Management

Solving k-obnoxious facility location problem on a plane

Industrial Engineering Journal

Teaching Linear Programming

In the present investigation a vertex covering center location model has been
developed and modeled in stochastic environment. The problem has been dealt
after relaxing the restrictions of the network and modeled as a multi-objective
location problem where the existing demand points are not known but are
instead random variables specified by probability distributions. Both bivariate
uniform and bi-variate exponential distributions have been considered
to design the models. Compromise solution methods for the different
probability distributions have been developed. It has been proved that the
solutions obtained by these procedures will give global optimal solutions.
Recti-linear distance norm has been considered as the distance measure as it
is more appropriate in different realistic situations.

International Journal of Operations and Quantitative Management

A center location model with stochastic demand points

This paper presents two approaches for solving both the minimax and minisum location problems and as well as a bi-objective location problem. The bi-objective location problem is a combination of both minimax and minisum location problems with recti-linear distances and randomly distributed destinations. Wesolowsky. G.O. [Journal of Regional Science 18: 53–60, 1977] has considered the stochastic extension of Weber problem with rectilinear distance norm and suggested some iterative method after dividing the problem into two parts, one for the X coordinates and other for the Y coordinates, where these co-ordinates may be correlated. In the present investigation exact approaches for both Minisum and Minimax objectives with randomly distributed destinations have been considered separately with both bi-variate exponential and bi-variate uniform distributions and formulated as a non-linear programming problem. Also the area restriction concept has been introduced so that the facility to be located should be within certain restricted area. The consideration of area restrictions has been implemented by incorporating a convex polygon as the constraint set. It has been proved that the solution obtained by this method will give the global optimal solution. The second part of this investigation is the bi-objective problem. The aim of the bi-objective problem is to find the satisfying solution which is desired in many realistic situations. Situation in which the proposed model is applicable is the location of a new warehouse where the sources of goods shipped to the warehouse and also the supply points to which the goods will be shipped is not known in advance. Due to the volatile and competitive nature of the market the supply and the demand points or in other words the variable points are not known in advance but some probability distribution can be predicted. It is required to find the location of a new warehouse which is closer to the variable points and simultaneously the total shipping cost per month from the warehouse to the variable points is minimum. For both single as well as bi-objective problems rectilinear distance norm has been considered as it is more appropriate to the different realistic situations. Two types of compromise solution methods have been suggested to get a satisfactory solution of the bi-objective problem.

OPSEARCH

Location models with stochastic demand points

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.

American Journal of Operations Research

A Multi-Objective Obnoxious Facility Location Modelon a Plane

World University root node

Industrial Engineering Journal.

Investor's Dilemma- Great Eastern Shipping Co. Ltd

This paper presents a model which has been designed to decide the number of advertisement in different advertising media and the optimal allocation of the budget assigned to the different media. The main objective of this problem is to maximize the reach to the desired section of people for different media within their maximum allowable budget without violating the max and min number of advertisement goals. The media have been considered as different newspapers and different channels in Televisions. Here in this article the model has been formulated in such a way that the advertisement should reach to those who are suitable for the product instead of going to those section who are not considered suitable for the product as well. A chance constrained goal programming model has been designed after considering the parameter corresponding to reach for different media as random variables. The random variables in this case has been considered as values which have known mean and standard deviations. A case for an upcoming institution who are interested to advertise for its two years Post Graduate Diploma in Management (PGDM) programme to the different newspapers and television channels has been designed to illustrate the solution methodology.