Additive Integer-Valued DEA Models With Fuzzy Undesirable Outputs: Closest Benchmarking Targets and Super-Efficiency

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. INDEX TERMS additive DEA, undesirable output, fuzzy variable, integer, pallet.

The New Model of Game Cross Efficiency DEA With Index Groups and an Application to Land Utilization Efficiency

“…In the process of solving the ratio, DEA fulfills a non-parameter estimation [2][3][4]. Since DEA method is feasible, practicable and effective, it attracts much attention and is applied to many fields such as, the root cause identification for vibration and noise failure of washing machine [5], the evaluation on the performance of pallet rental companies [6,7], the performance evaluation on system of logistics enterprises [8], the selection of the most suitable locations to host wind power plants [9], etc.…”