A new slacks-based measure of Malmquist–Luenberger index in the presence of undesirable outputs

• Published in: Omega (Oxford) Vol. 51; pp. 29 - 37
• Main Authors: Arabi, Behrouz, Munisamy, Susila, Emrouznejad, Ali
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2015; Pergamon Press Inc
• Subjects: Algorithms; Data Envelopment Analysis; Directional Distance Function; Eco-Efficiency Change; Mathematical models; Productivity; Steam power; Studies; Eco-Efficiency Change; Directional Distance Function; Data Envelopment Analysis
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2014.08.006

In the majority of production processes, noticeable amounts of bad byproducts or bad outputs are produced. The negative effects of the bad outputs on efficiency cannot be handled by the standard Malmquist index to measure productivity change over time. Toward this end, the Malmquist–Luenberger index (MLI) has been introduced, when undesirable outputs are present. In this paper, we introduce a Data Envelopment Analysis (DEA) model as well as an algorithm, which can successfully eliminate a common infeasibility problem encountered in MLI mixed period problems. This model incorporates the best endogenous direction amongst all other possible directions to increase desirable output and decrease the undesirable outputs at the same time. A simple example used to illustrate the new algorithm and a real application of steam power plants is used to show the applicability of the proposed model. •A DDF type model is introduced which uses optimal directions compared to exogenously given ones.•A SBM incorporating bad outputs equivalent to above DDF model is introduced.•A new SBM model is presented for DMU׳s located above frontier in the MLI measurement process.•This pair of SBM׳s is used in a new algorithm tackles the prevalent infeasibility problem in the MLI measurement.•The new models and algorithm are successfully applied in a real sample of power plants data.