Estimation of cost efficiency for firms in different technologies using data envelopment analysis

Data envelopment analysis (DEA) is a method for evaluating the relative efficiency of a set of firms in a production process. Estimation of cost efficiency is one of the branches of performance evaluation. Cost efficiency evaluates the ability of producing current output with minimum available cost. Now let's assume that there are several groups of firms that operate separately and have different technologies, but are centrally managed, or in other words, their source of raw materials is shared, but each of these groups has different costs for these resources. Traditional DEA models do not offer any suggestions for calculating the cost efficiency in such situations where firms are grouped into different technological groups and the input's costs are different. In this paper, using the concepts of cost efficiency and meta-frontier and using the rational relation between cost efficiency and technical efficiency, a method is proposed to calculate the cost efficiency of firms in different technological conditions. There is also a way to use the transfer of units to improve their performance. The method presented in this study is used in a numerical example and a real case application and their results are explained.