On Characterizing weak defining hyperplanes (weak Facets) in DEA with Constant Returns to Scale Technology

TL;DR

This paper investigates the characterization of weak defining hyperplanes in the Production Possibility Set of DEA under CCR technology, providing properties, an algorithm, and numerical examples for practical implementation.

Contribution

It introduces a new method for identifying weak facets in DEA's PPS, with proven properties and an algorithm compatible with existing optimization software.

Findings

The proposed algorithm effectively identifies weak facets.

Properties of weak hyperplanes are formally established.

Numerical examples demonstrate practical applicability.

Abstract

The Production Possibility Set (PPS) is defined as a set of inputs and outputs of a system in which inputs can produce outputs. The Production Possibility Set of the Data Envelopment Analysis (DEA) model is contain of two types defining hyperplanes (facets); strong and weak efficient facets. In this paper, the problem of finding weak defining hyperplanes of the PPS of the CCR-technology is dealt with. We state and prove some properties relative to our method. To illustrate the applicability of the proposed model, some numerical examples are finally provided. Our algorithm can easily be implemented using existing packages for operation research, such as GAMS.