Neutral cross-efficiency evaluation regarding an ideal frontier and anti-ideal frontier as evaluation criteria

Cross-efficiency evaluation methods have long been suggested as an alternative for the ranking of decision making units (DMUs) in data envelopment analysis (DEA). Neutral cross-efficiency evaluation methods have been developed in a way that is only concerned with their own interests and are indifferent to other DMUs. This paper proposes a new cross-efficiency evaluation method in which each DMU has a neutral attitude to its peers. This is done by introducing an ideal virtual frontier (IVF) and an anti-ideal virtual frontier (AVF). Unlike current neutral cross-efficiency evaluation methods, this cross-efficiency evaluation method determines one set of input and output weights for each DMU, aiming to improve the DMU's performance by taking the IVF and AVF as evaluation criteria. This is done by minimizing the deviation of a DMU from the IVF and maximizing the deviation of the DMU from the AVF. As a result, the cross-efficiencies measured by these new DEA models are neutral and more logical. Numerical examples are provided to illustrate the potential applications of these new DEA models and their effectiveness in ranking DMUs.