Avoiding dissimilarity between the weights of the optimal DEA solutions

Abstract

The zero weights in data envelopment analysis evaluation causes some problems such as ignoring the some inputs and/or outputs of DMUs under evaluation. Moreover, some authors claimed that the great differences in weights might be a problem. The aim of this paper is to extend the multiplier bound approach to avoid zero weights and great differences in the values of multipliers more. We show that our proposed model is equivalent to the type I assurance region model that will be used in the evaluation efficiency.

Appendix: Computational aspects

The objective function and constraints of the model (6) are fractional and linear, respectively. With the following change of variables (see Charnes and Cooper [13]); the model (6) converted to the LP model (11) whose optimal value is the same to the (6):

$$\begin{aligned}&\begin{array}{l} \beta =\frac{1}{\omega _I},\\ \tilde{v}_i=\beta v_i,\\ \tilde{u}_i=\beta u_i,\\ \tilde{l}_i=\beta l,\\ \end{array} \\&\begin{array}{rlllc} \max &{}\tilde{\phi }_{j_0}=\tilde{l}_I\\ s.t.&{} \sum\limits_{i=1}^{m}\tilde{v}_{i}x_{ij_0}=1,&{}&{}\\ &{} \sum\limits_{r=1}^{s}\tilde{u}_{r}y_{rj_0}=1,&{}&{}\\ &{} \sum\limits_{r=1}^{s}\tilde{u}_{r}y_{rj}-\sum\limits_{i=1}^{m}\tilde{v}_{i}x_{ij}\le 0,&{}j\in E\\ &{}\tilde{l}_I\le \tilde{v}_{i}\le 1,&{}i=1,\ldots ,m\\ &{}v_{i}, u_{r}, l_I, \omega _I\ge 0. \end{array} \end{aligned}$$

(11)