A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs

This paper is primarily concerned with data envelopment analysis (DEA) of systems where negative outputs and negative inputs arise naturally. Examples of situations in which both negative inputs and negative outputs occur are given. More attention has been paid, in the literature, to the former type of problem. Most available DEA software does not solve this type of problem or copes with negative outputs and possibly negative inputs by assigning zero weights to them. A modified slacks-based measure (MSBM) model is presented, in which both negative outputs and negative inputs occur. The MSBM model overcomes the lack of translation invariance in the slacks-based measure model by drawing on the ideas from the range directional model (RDM). The MSBM model takes into account individual input and output slacks, which provides more precise evaluation of inefficient decision-making units (DMUs). It therefore, generally leads to lower efficiencies for inefficient DMUs than the RDM.