Abstract
Many production activities generate undesirable outputs apart from desirable outputs. In addition, the data related to undesirable outputs may be fuzzy (imprecise) in some cases. Based on the fuzzy data theory, we propose a group of additive integer-valued data envelopment analysis (DEA) models with fuzzy undesirable outputs. The advantages of the proposed models are as follows: (1) they enable decision-makers to evaluate the efficiency of decision making units (DMUs) with integer-valued variables and fuzzy undesirable outputs; (2) they can be easily solved without any transformation because they are linear programming models; (3) they are better than radial DEA models as they can identify inefficiencies in all the selected inputs and outputs. Particularly, minimum distance-based additive integer-valued DEA models with fuzzy undesirable outputs are developed in this paper to find the closest benchmarking targets for inefficient DMUs, and additive super-efficiency integer-valued DEA models with fuzzy undesirable outputs are presented to differentiate and rank efficient DMUs. The validity of the proposed models is examined by an empirical application in the pallet rental industry.
Highlights
Data envelopment analysis (DEA) is a widely applied nonparametric programming technique for evaluating the performance of decision making units (DMUs) [1], [2]
In this paper we intend to contribute to the body of knowledge by proposing a group of additive integer-valued DEA models with fuzzy undesirable outputs (FU-addIDEA). The advantages of these additive integer-valued DEA models are as follows: (1) they enable decision-makers to non-proportionally change inputs and outputs, so they can identify inefficiencies in all the selected inputs and outputs [6,7,8,9,10]; (2) they can deal with integervalued variables and fuzzy undesirable outputs; (3) they can be solved without any transformation because they are linear programming models; (4) a DMU is additive-efficient only if it is radial-efficient [6]
The results of the case study show that (1) the efficiency scores obtained from our models are more accurate than those resulting from DEA models without considering fuzzy undesirable outputs; (2) real benchmarking targets for real-valued variables and integer benchmarking targets for integer-valued variables can be obtained from our models, and these targets are the closest; (3) using the proposed models, decision-makers can fully rank DMUs and figure out how many input savings, desirable output surpluses, and undesirable output savings exist in efficient DMUs
Summary
Data envelopment analysis (DEA) is a widely applied nonparametric programming technique for evaluating the performance of decision making units (DMUs) [1], [2]. In this paper we intend to contribute to the body of knowledge by proposing a group of additive integer-valued DEA models with fuzzy undesirable outputs (FU-addIDEA). The advantages of these additive integer-valued DEA models are as follows: (1) they enable decision-makers to non-proportionally change inputs and outputs, so they can identify inefficiencies in all the selected inputs and outputs [6,7,8,9,10]; (2) they can deal with integervalued variables and fuzzy undesirable outputs; (3) they can be solved without any transformation because they are linear programming models; (4) a DMU is additive-efficient only if it is radial-efficient [6].
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