Using slacks-based model to solve inverse DEA with integer intervals for input estimation

Atefeh Younesi (), Farhad Hosseinzadeh Lotfi () and Manuel Arana-Jiménez ()
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Atefeh Younesi: University of Cádiz
Farhad Hosseinzadeh Lotfi: Islamic Azad University
Manuel Arana-Jiménez: University of Cádiz

Fuzzy Optimization and Decision Making, 2023, vol. 22, issue 4, No 2, 587-609

Abstract: Abstract This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of $$DMU_o$$ D M U o increases from $$Y_o$$ Y o to $$\beta _o$$ β o , such the new DMU is given by $$(\alpha _o^*,\beta )$$ ( α o ∗ , β ) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables.

Keywords: Data envelopment analysis (DEA); Inverse DEA; Integer interval; Multiple-objective nonlinear programming (MONLP); Slacks-based model (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10700-022-09403-1

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