global malmquist productivity index for evaluation of multistage series systems with undesirable and non-discretionary data

Data envelopment analysis measures relative efficiency, in which the performances of the dmus in a group are compared. in this approach, an efficient unit in one group may be considered inefficient compared to the units of other groups and vice versa. to solve this weakness, two known productivity indexes, the malmquist and luenberger, have been introduced to evaluate units (or systems) from one period to another. the existence of special types of data such as undesirable and non-discretionary in some multi-stage series systems is unavoidable. the evaluation of such systems in the simultaneous presence of the mentioned data and different periods has not been done so far. therefore, in this study, we have presented a model with a new approach to evaluate them. at the end of the study, we checked the proposed model’s ability by providing comparative and structural examples. we have shown that without undesirable and non-discretionary data, the proposed is better than other models. also, this model has been used for the first time and obtained acceptable results in the presence of these data.