Abstract
The inverse Data Envelopment Analysis (InvDEA) is an exciting and significant topic in the DEA area. Also, uncertain data in various real-life applications can degrade the efficiency results. The current work addresses the InvDEA in the presence of stochastic data. Under maintaining the efficiency score, the inputs/outputs-estimation problem is investigated when some or all of its outputs/inputs increase. A novel optimality concept for multiple-objective programming problems, stochastic (weak) Pareto optimality in the level of significance α ∈[0,1], is introduced to derive necessary and sufficient conditions for input/output estimation. Furthermore, the performance of the developed theory in a banking sector application is verified.
Highlights
Data envelopment analysis (DEA), as an excellent nonparametric efficiency measurement method, has been employed to determine the efficiency scores of a class of homogeneous decision-making units (DMUs) under several inputs and outputs [7, 13]
It is worth noting that DEA is one of the most powerful tools used for efficiency evaluation, some researchers debate on the three main components of the DEA technique as follows [3, 34, 35]: (i) DEA is a nonparametric technique, so the usual conclusions comparing with a parametric function are impossible
Formulation for any parametric function related to the production including cost, or profit function evaluation of marginal products, marginal costs, and partial elasticities is impossible almost. (ii) The conventional DEA is based on linear programming (LP)
Summary
Data envelopment analysis (DEA), as an excellent nonparametric efficiency measurement method, has been employed to determine the efficiency scores of a class of homogeneous decision-making units (DMUs) under several inputs and outputs [7, 13]. The main advantage of the mentioned model is its linearity This model can calculate the relative efficiency of units at a significant specific level and identify efficient DMUs. It is notable that the aim of a conventional InvDEA model is to estimate the input and output levels are deterministic types, which does not take the random errors of data into account in the production process. This study presents a theoretical and practical framework of InvDEA under random data and focuses on the key thematic areas of resource allocation management, handling investment analysis problems, the implication of new performance strategies, and the motivations.
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