A Multi-Objective Obnoxious Facility Location Modelon a Plane

Affiliation(s)

Indian Institute of Management Indore, Rau, Pigdamber, Indore, Madhya Pradesh 453331, India.

Indian Institute of Management Indore, Rau, Pigdamber, Indore, Madhya Pradesh 453331, India.

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.

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.

Cite this paper

nullU. Bhattacharya, "A Multi-Objective Obnoxious Facility Location Modelon a Plane,"*American Journal of Operations Research*, Vol. 1 No. 2, 2011, pp. 39-45. doi: 10.4236/ajor.2011.12006.

nullU. Bhattacharya, "A Multi-Objective Obnoxious Facility Location Modelon a Plane,"

References

[1] E. Erkut and S. Neuman, “Analytical Models for Locating Undesirable Facilities,” European Journal of Operational Research, Vol. 40, No. 3, 1989, pp. 275-291. doi:10.1016/0377-2217(89)90420-7

[2] M. I. Shamos, “Computational Geometry,” Ph.D. Dissertation, Department of Computer Science, Yale University, New Haven, 1977.

[3] B. Dasarathy and L. White, “A Maximin Location Problem,” Operations Research, Vol. 28, No. 6, 1980, pp. 1385-1401. doi:10.1016/0377-2217(89)90420-7

[4] Z. Drezner and G. O. Wesolowsky, “A Maximin Location Problem with Maximum Distance Constraints,” AIIE Transaction, Vol. 12, No. 3, 1980, pp. 249-252. doi:10.1080/05695558008974513

[5] E. Melachrinoudis and T. P. Cullinane, “Locating an Undesirable facility within a Geographical Region Using the Maximin Criterion,” Journal of Regional Science, Vol. 25, No. 1, 1985, pp. 115-127. doi:10.1111/j.1467-9787.1985.tb00297.x

[6] Z. Drezner and G. O. Wesolowsky, “The Location of an Obnoxious Facility with Rectangular Distance,” Journal of Regional Science, Vol. 23, No. 2, 1983, pp. 241-248. doi:10.1111/j.1467-9787.1983.tb00800.x

[7] E. Melachrindis, “An Efficient Computational Procedure for the Rectilinear Maximin Location Problem,” Transportation Science, Vol. 22, No. 3, 1988, pp. 217-223. doi:10.1287/trsc.22.3.217

[8] A. Mehrez, Z. Sinuany-Stern and A. Stulman, “An Enhancement of the Drezner-Wesolowsky Algorithm for Single Facility Location with Maximin of Rectangular Distance,” Journal of Operations Research Society, Vol. 37, No. 10, 1986, pp. 971-977.

[9] A. Tamir, “Locating Two Obnoxious Facilities using the Weighted Maximin Criterion,” Operations Research Letter, Vol. 34, No. 1, 2006, pp. 97-105. doi:10.1016/j.orl.2005.02.004

[10] J. M. Diaz-Banez, M. A. Lopez and J. A. Sellaves, “Locating an Obnoxious Plane,” European Journal of Operations Research, Vol. 173, No. 2, 2006, pp. 556-564. doi:10.1016/j.ejor.2005.02.048

[11] F. Plastria, and E. Carrizosa, “Undesirable Facility Location with Minimal Covering Objectives,” European Journal of Operational Research, Vol. 119, No. 1, 1999, pp. 158-180. doi:10.1016/S0377-2217(98)00335-X

[12] C. S. ReVelle, H. A. Eiselt, M. S. Daskin, “A Bibliography for Some Fundamental Problem Categories in Discrete Location Science,” European Journal of Operational Rsearch, Vol. 184, No. 3, 2008, pp. 817-848. doi:10.1016/j.ejor.2006.12.044

[1] E. Erkut and S. Neuman, “Analytical Models for Locating Undesirable Facilities,” European Journal of Operational Research, Vol. 40, No. 3, 1989, pp. 275-291. doi:10.1016/0377-2217(89)90420-7

[2] M. I. Shamos, “Computational Geometry,” Ph.D. Dissertation, Department of Computer Science, Yale University, New Haven, 1977.

[3] B. Dasarathy and L. White, “A Maximin Location Problem,” Operations Research, Vol. 28, No. 6, 1980, pp. 1385-1401. doi:10.1016/0377-2217(89)90420-7

[4] Z. Drezner and G. O. Wesolowsky, “A Maximin Location Problem with Maximum Distance Constraints,” AIIE Transaction, Vol. 12, No. 3, 1980, pp. 249-252. doi:10.1080/05695558008974513

[5] E. Melachrinoudis and T. P. Cullinane, “Locating an Undesirable facility within a Geographical Region Using the Maximin Criterion,” Journal of Regional Science, Vol. 25, No. 1, 1985, pp. 115-127. doi:10.1111/j.1467-9787.1985.tb00297.x

[6] Z. Drezner and G. O. Wesolowsky, “The Location of an Obnoxious Facility with Rectangular Distance,” Journal of Regional Science, Vol. 23, No. 2, 1983, pp. 241-248. doi:10.1111/j.1467-9787.1983.tb00800.x

[7] E. Melachrindis, “An Efficient Computational Procedure for the Rectilinear Maximin Location Problem,” Transportation Science, Vol. 22, No. 3, 1988, pp. 217-223. doi:10.1287/trsc.22.3.217

[8] A. Mehrez, Z. Sinuany-Stern and A. Stulman, “An Enhancement of the Drezner-Wesolowsky Algorithm for Single Facility Location with Maximin of Rectangular Distance,” Journal of Operations Research Society, Vol. 37, No. 10, 1986, pp. 971-977.

[9] A. Tamir, “Locating Two Obnoxious Facilities using the Weighted Maximin Criterion,” Operations Research Letter, Vol. 34, No. 1, 2006, pp. 97-105. doi:10.1016/j.orl.2005.02.004

[10] J. M. Diaz-Banez, M. A. Lopez and J. A. Sellaves, “Locating an Obnoxious Plane,” European Journal of Operations Research, Vol. 173, No. 2, 2006, pp. 556-564. doi:10.1016/j.ejor.2005.02.048

[11] F. Plastria, and E. Carrizosa, “Undesirable Facility Location with Minimal Covering Objectives,” European Journal of Operational Research, Vol. 119, No. 1, 1999, pp. 158-180. doi:10.1016/S0377-2217(98)00335-X

[12] C. S. ReVelle, H. A. Eiselt, M. S. Daskin, “A Bibliography for Some Fundamental Problem Categories in Discrete Location Science,” European Journal of Operational Rsearch, Vol. 184, No. 3, 2008, pp. 817-848. doi:10.1016/j.ejor.2006.12.044