Clustering decision making units (DMUs) in data envelopment analysis (DEA) with integer data in order to benchmark them through a series of steps
摘要
Data Envelopment Analysis (DEA) is a technique used to calculate the relative efficiency of a set of homogeneous decision-making units(DMU). Using this technique and the determined hyperplanes, all units are divided into categories of strongly efficient, weakly efficient, and inefficient. In this type of categorization, all inefficient and weakly efficient units must accept a point from the strongly efficient frontier as a benchmark(BM) and make necessary changes for improvement, which may not be practically feasible due to the large distance from the efficiency frontier. In this paper, a method for categorizing decision-making unitsis presented. This categorization is based on the definition of positive(A+) and negative(A−) ideal points in the production possibility set and layering the production possibility set(PPS) using separating hyperplanes. Accordingly, an algorithm for categorizing units with integer inputs and outputs was designed. This categorization can be applied for feasible improvement and the selection of the nearest benchmark. Finally, the proposed algorithm is applied to an example with one input and one output, as well as a dataset of bank branches.