Efficiency Assessment for a Line Location Problem with positive/negative weights with Interval Coordination

Subject Areas : International Journal of Industrial Mathematics

haleh moradi ¹ , فرهاد حسین زاده لطفی ² , M. Rostamy Malkhalifeh ³

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Received: 2022-04-30 Accepted : 2024-08-05 Published : 2024-09-21

Keywords: Line location problem, Semi-obnoxious, DEA, Interval data, efficiency, median line,

Abstract :

A line location problem as a subdivision of facility location problem deals with finding a straight line in the plane, so that sum of weighted distances or maximum weighted distances from the line to the demand points is minimized. This paper provides a novel approach to study the semi-obnoxious median line location problem with Euclidean norm by using data envelopment analysis method. Since the presented procedure would consider lines as decision making units, so efficiency of lines is taken into account instead of their optimality. Moreover, due to the inherent uncertainty of the parameters of the line location problem in the real world such as weights or/and coordinates of demand points, the problem under interval data is studied in viewpoint of data envelopment analysis as well. Furthermore, some propositions and a numerical example are provided to investigate the problem. Finally, conclusion is given.