A structured review and analysis of the researches conducted in the field of productivity changes in units with undesirable output using the Malmquist Luenberger productivity index

Evaluation of performance and productivity and the process of its changes over time is considered essential in the process of improvement in organizations, production, industrial and service units. Regarding the calculation of productivity and changes in productivity over time, different models, methods, approaches, and indices have been presented; one of the most important, common and widely used is the Malmquist productivity index. On the other hand, during production processes, undesirable products and outputs are obtained simultaneously with desirable products. Therefore, an index called Malmquist Luenberger was presented with the development of Malmquist's productivity index, which took into account the undesirable outputs while seeking to reduce them and, at the same time, aimed at expanding the desirable outputs. Therefore, the current research has been compiled with the aim of a structured and systematic review and analysis of articles and research that have made a scientific effort on the subject of calculating productivity changes in units with undesirable output using the Malmquist productivity index and especially the Malmquist Luenberger productivity index. This research is based on PRISMA methodology with the aim of structured analysis of studies that have made a scientific effort in the field of calculating productivity changes in units with undesirable output using the Malmquist/Malmquist Luenberger productivity index. This research is a review type that was conducted through searching in domestic and foreign databases such as academic information, Scopus, Science Direct, Elsevier, and Google Scholar in the period from 1980 to 2022 with the approach of selecting the most important, valid, and prominent domestic and foreign scientific and applied articles and researches. In terms of the quantity and quality of the articles, the present article seems to be unprecedented and unique because, due to the breadth and diversity of published articles and research, the void of the current structured research among the published efforts is quite noticeable, and by using this article, on the one hand, researchers can study the latest actions and research efforts in the mentioned field in a completely categorized and structured manner, and on the other hand, the existing scientific gaps and future proposals regarding the evaluation of benefits. See the productivity using the Malmquist/Malmquist Luenberger productivity index, which is the result of the scientific investigations of the authors of this article. Therefore, this research, in the form of a structured review and analysis article, is considered a kind of road map for researchers interested in the field of productivity.Originality/Value: Considering that this article is a structured review of existing research, the output of the current research is a roadmap for researchers and researchers in the field of calculating productivity changes using the Malmquist/Malmquist Luenberger index in order to understand the current problems, challenges and problems of current research as well as future scientific proposals.