A neutral cross-efficiency measurement for general parallel production system

There are some problems in the efficiency evaluation for parallel systems. From the applicability of existing models, the parallel models based on self-evaluation may produce the low distinguishing power and unreasonable input–output weights. From the accuracy of efficiency, the weights of partial production-units may be assigned zero values, and thereby the fail of the production-units will lead to the incomprehensibility of system efficiency. The neutral cross-efficiency model maximizes the evaluated decision-making unit (DMU) and simultaneously makes each output of the DMU being as efficient as possible, which effectively avoids the difficulty in choosing between aggressive and benevolent models, and reduces the number of zero output weights. Based on this, this paper proposes the neutral cross-efficiency evaluation method fo r general parallel systems. First, the self-evaluation models for parallel system and its production-units are developed, and the model can enable each production-unit to participate in the evaluation effectively. Then, the neutral cross-efficiency model is proposed to overcome the defects of self-evaluation model. Particularly, the proposed model is also suitable to special general parallel systems with shared resources. More importantly, the proposed models assign different input–output weights for the production-units to avoid the production-units being forced to run under identical production mechanism. Finally, two real-world examples prove the availability and effectiveness of the proposed method.