What question did this study set out to answer?

The aim is to explore how output levels of a Decision-Making Unit (DMU) should change in response to increased inputs, affecting efficiency scores.

February 5, 2026Open Access

Applying an enhanced hybrid interval slacks-based model to solve inverse DEA to estimate outputs

Key Points

The aim is to explore how output levels of a Decision-Making Unit (DMU) should change in response to increased inputs, affecting efficiency scores.
Utilized an enhanced non-radial slack-based model for data analysis.
Incorporated both continuous and integer interval data as hybrid information.
Applied necessary and sufficient conditions derived from multi-objective nonlinear programming (MONLP).
Established a framework for estimating output changes in response to input variations.
Illustrated challenges associated with hybrid interval data through a practical example.

Abstract

Abstract This paper focuses on inverse data envelopment analysis (DEA) under the following question: ” If the inputs of DMUₒ DMU o increase, how much should the outputs of DMUₒ DMU o increase to decrease the efficiency score of DMUₒ DMU o? In these problems, a non-radial enhanced slack-based model is employed in the presence of hybrid interval data, which includes both continuous and integer interval data. Under this scenario, novel necessary and sufficient conditions to estimate outputs are considered based on the Pareto solution of related multi-objective nonlinear programming (MONLP). Furthermore, an example is presented to illustrate the problems associated with hybrid interval data. Finally, the conclusion and future work are presented

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