Abstract. Data Envelopment Analysis (DEA) is a mathematical programming approach for measuring efficiency of Decision Making Units (DM U s). In traditional DEA, a ratio of weighted outputs to inputs is examined and, for each DM U , some optimal weights are obtained. The method of cross-efficiency is an extension to DEA by which a matrix of scores is computed. The elements of the matrix are computed by means of the weights obtained via usual models of DEA. The cross-efficiency may have some drawbacks, e.g., the cross-efficiency scores may be multiple due to the presence of several optima. To overcome this issue, secondary goals are used. However, this method has never been used for peer evaluation of DMUs with undesirable outputs. In this paper, our objective is to bridge this gap. For this end, we introduce a new secondary goal, test it on an empirical example with undesirable outputs, report the results, and finally, we give some concluding remarks.
PurposeThe objective of this study is to present a binary-valued data envelopment analysis (DEA) theory. The authors’ proposed approach, for the first time, combines binary-valued and integer-valued theories concurrently in the DEA context. To do so, new production possibility sets (PPSs) with some distinguished features are developed.Design/methodology/approachThe authors address integer inputs and outputs in the proposed approach by introducing a new PPS.FindingsTo take into account the binary data, the authors develop axiomatic DEA principles. The binary production principles guarantee any combination of convexity and feasibility. Furthermore, the authors develop a new DEA model to consider integer and real data. A case study is presented to show the usefulness of the developed models. Using the proposed models, the authors obtained benchmarks to solve the sustainable supplier selection problems.Originality/value(1) For the first time, binary-valued and integer-valued theories are presented in an integrated DEA model. (2) To deal with the pure binary data, a new PPS is proposed. (3) To consider real, integer and binary data, a new PPS is introduced. (4) New technologies are developed to propose feasible solutions. (5) The proposed models can project inefficient decision-making units (DMUs) on efficiency frontier given binary, integer and real data. (6) A case study is given for the performance evaluation of sustainable suppliers.
The existence of equivalent scalar problems for properly efficient point of a given multiobjective optimization problem over arbitrary cones is studied by so many authors. This paper emphasizes two scalarizations, i.e., linear scalarization and conic scalarization, and studies geometrical viewpoint on the relationship between proper efficiency and these scalarizations. We also show that conic scalarization is a generalization of linear scalarization based on augmented dual cone which provides a new type of trade-off for properly efficient solutions.
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