A method to rank the efficient units based on cross efficiency matrix without involving the zero weights

Abstract

One of the basic objections of the previous models of cross efficiency (CE) is the possibility for the weights to equal zero. This case takes place for the inputs and the outputs in the efficient responses in CE models. Therefore, the input and the output weights which equal zero do not play a role in computing the score of the CE. In this paper, to overcome this problem, an idea to prevent the optimal weights to equal zero in the CE method is offered. This new method can be expanded to all CE models. Based on the offered method, a zero-one mixed linear programming problem is proposed to obtain a set of non-zero weights among the optimal solutions of the preliminary CE model. Following, the zero-one mixed linear programming problem is changed into an equivalent linear program. Then, according to a consistent CE matrix the efficient units are ranked. In order to explain the model and indicate its advantage, an example is given.