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. پرونده مقاله

The returns to scale (RTS) is an economic issue that would play a crucial role in the expansion or limitation of the decision-making unit (DMU) under-evaluation in data envelopment analysis (DEA). In this paper, we study an inverse DEA problem in which besides finding the appropriate amount of increase in output, preserving the primary classification of returns to scale for the DMU under-evaluation is considered. This research discusses two cases: when the DMU operates under constant returns to scale (CRS), and the other case considers DMUs with increasing returns to scale (IRS). Respectively for DMUs with CRS the upper bound obtained from the sensitivity analysis method is applied to determine the maximum amount of authorized output increase to preserve the primary classification of RTS. Then, we present two methods for the case of DMUs operating under the IRS. In the first one, we use an upper limit of the authorized amount of output's increase for modeling the problem in such a way that the IRS has remained unchanged. Then, the second method provides a model based on the closest most productivity scale size (MPSS) to the projection of the DMU under evaluation to solve the output estimation problem with maintaining the IRS. Finally, we give a numerical example to examine the application of the presented models.

پرونده مقاله