Theory of binary-valued data envelopment analysis: an application in assessing the sustainability of suppliers

Purpose The 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/approach The authors address integer inputs and outputs in the proposed approach by introducing a new PPS. Findings To 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.