Ranking ranges, performance maverick and diversity for decision-making units with interval cross-efficiency matrix

An alternative strategy in cross-efficiency evaluation is to take into consideration all the possible choices of data envelopment analysis weights that all decision-making units (DMUs) can make, thus eliminate the non-uniqueness issue of cross-efficiency scores, and also avoid the need of the decision maker's preference in choosing aggressive or benevolent strategy among various alternative secondary goals. We are interested in this alternative strategy and continue investigating it. With the derived interval cross-efficiency matrix for all the DMUs, we determine cross-efficiency intervals, ranking ranges, performance maverick and diversity for each DMU, which could provide more insightful information in cross-efficiency evaluation for decision makers. Our developed cross-efficiency interval and ranking ranges are useful for assessing the stability of the cross-efficiency scores. Besides, our developed interval performance maverick and diversity extend previous study to consider all possible weights space, which make results more acceptable for supplier rationalisation. Two examples of data on 18 Chinese cities and 23 suppliers are presented for illustrations.