A two-stage structure with undesirable outputs: slacks-based and additive slacks-based measures DEA models

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
² Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O.Box 41938-19141, Rasht, Iran
³ Department of Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
⁴ Department of Computer Engineering, Faculty of Mathematical Sciences, Technical and Vocational University (TVU), Tehran, Iran

^* Coresponding author: salahim@guilan.ac.ir, salahi.maziar@gmail.com

Received: 11 January 2022
Accepted: 10 July 2022

Abstract

The slacks-based measure (SBM) and additive SBM (ASBM) models are two widely used DEA models acting based on inputs and outputs slacks and giving efficiency scores between zero and unity. In this paper, we use both models with the application of the weak disposability axiom for outputs to evaluate efficiency in a two-stage structure in the presence of undesirable outputs. In the external evaluation, the SBM model is reformulated as a linear program and the ASBM model is reformulated as a second-order cone program (SOCP) that is a convex programming problem. In the internal evaluation, the SBM model for a specific choice of weights is linearized while the ASBM model is presented as an SOCP for arbitrary choice of weights. Finally, the proposed models are applied on a real dataset for which efficiency comparison and Pearson correlation coefficients analysis show advantages of the ASBM model to the SBM model.