a measure of the luenberger productivity indicator in the presence of undesirable outputs

Checking the regression or progression of production, also called total factor productivity (tfp) growth, over discrete time periods is an interesting concept in data envelopment analysis (dea). in recent dea literature, the method of incorporating undesirable outputs into assessments and their impact on tfpresults has been approached by many researchers. one application of these techniques is the luenberger productivity indicator. in this paper, we introduced a new method under the assumption of variable returns to scale (vrs) to remedy an infeasibility problem of the directional distance function (ddf) over hybrid periods of time. then, an algorithm based on the new models was presented for determining the luenberger productivity indicator in the presence of undesirable outputs. the proposed new method successfully removed ill-defined problems in measuring the luenberger productivity indicator while considering all economic implications. finally, a simple example was used to illustrate the proposal algorithm compared to the results using another method.