Dominance and ranking interval in DEA parallel production systems

Traditional network data envelopment analysis (DEA) on parallel production systems uses extreme weights to measure performance of decision-making units (DMUs) considering their inner structure. The results of considering inner structure can give further insights into the performance relative to the black-box DEA approach. However, the employment of extreme weights may reduce the informativeness of network DEA evaluation, since it ignores other optimal weights of the evaluation model. This paper concerns using all possible input/output weights in DEA to measure the performance of parallel production systems with considering inner structure. The proposed approach can make performance evaluation less dependent on any specific weights and give more meaningful results. A family of dominance relations has been defined, and we propose ratio-based efficiency analysis models to show how to compute these. One of these dominance relations, namely the R-dominance relation, can reflect the characteristic of the inner parallel structure and can be used to identify benchmarks for DMUs based on subsystems. The ranking intervals of DMUs are calculated based on the acyclic dominance relation, namely the efficiency dominance relation. Our proposed approach is demonstrated by applying it to measure performance of Chinese provinces.