Frontier improvement in the DEA models

TL;DR

This paper develops an algorithm to improve DEA model frontiers by utilizing the concept of terminal units, addressing inaccuracies in efficiency scores caused by finite data sets and artificial units.

Contribution

It introduces a new algorithm based on terminal units to enhance DEA frontiers, improving efficiency score accuracy in finite data contexts.

Findings

Algorithm effectively improves DEA frontiers

Results verified with real-life data sets

Graphical examples confirm theoretical findings

Abstract

Applications of data envelopment analysis (DEA) show that many inefficient units are projected onto the weakly efficient parts of the frontier when efficiency scores are computed. However this fact disagrees with the main concept of the DEA approach, because the efficiency score of an inefficient unit has to be measured relative to an efficient unit. As a consequence inaccurate efficiency scores may be obtained. This happens because a non-countable (continuous) production possibility set is determined on a basis of a finite number of production units. It has been proposed in the literature to use artificial production units in the primal space of inputs and outputs as a starting point in order to improve the frontier of the DEA models. Farrell was the first who introduced artificial units in the primal space of inputs and outputs in order to secure convex isoquants. In previous papers we introduced the notion of terminal units. Moreover, some relationships were established between terminal units and other sets of units that were proposed for improving envelopment. In this paper we develop an algorithm for improving the frontier. The construction of algorithm is based on the notion of terminal units. Our theoretical results are verified by computational experiments using real-life data sets and also confirmed by graphical examples.