Finding Most Preferred Solution in Imprecise DESA

Abstract

The basic data envelopment analysis (DEA) determines the relative efficiency of a set of decision making units (DMUs) in exact input-output environments. For imprecise data, some methods have been developed to calculate the efficiency scores. The aim of this paper is showing an equivalence relation between one of the models of data envelopment analysis with imprecise data and multi-objective linear programming (MOLP). The Relation between DEA and MOLP conduced to use interactive multiple objective models for solving the DEA problem in exact situation and find the most preferred solution. This paper will establish an equivalence model between imprecise DEA (IDEA) and MOLP and show how an IDEA problem can be solved interactively without any prior judgements by transforming it into a MOLP formulation. Various interactive multi-objective models would be used to solve IDEA problems such that PROJECT method. This PROJECT method is able to generate any efficient solution (including nonsupported efficient solutions) and also to identify the most preferred solution (MPS), even in nonconvex cases. In addition to, we will use the data envelopment scenario analysis (DESA) model since this model focuses on decreasing total input consumption and increasing total output production which results in solving one mathematical model instead of n models.KeywordsData envelopment analysisImprecise dataInteractive multiple objective linear programmingPROJECT method