Javad Gerami - Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Mohammad Reza Mozaffari - Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.

In this paper, we present an Additive Slacks-Based Measure (ASBM) model for measuring efficiency Decision-Making Unit (DMU) in the presence of undesirable outputs based on DEA Ratio based (DEA-R) model. In order to obtain a reasonable measure of efficiency, this paper proposes a concept for determining the minimum number of undesirable outputs that a DMU is allowed to generate based on the assertion of weak disposability. We show theeffect of producing excessive amounts of undesirable outputs on efficiency. We propose an alternative form of the ASBM model to measure efficiency based on DEA-R models. In the first stage, we introduce counterpart (hypothetic) units corresponding to each DMUs. We obtain the true efficiency scores and slack variables regarding the input and output components of each of the DMUs. In the second stage, we obtain the efficiency scores in the presence of undesirable outputs based on ASBM-DEA-R model. In the following, we illustrate the proposed approach with a numerical example. At the end, the results of the research are given.

Data Envelopment Analysis, DEA-R, Ratio data, undesirable output, Efficiency, Non-radial DEA, ASBM