Meta cost Malmquist Index with variable relative importance as a function of time in different period and FDH models of DEA

Meta Cost Malmquist Index explains change of cost productivity of Decision Making Unit (DMUs) in several time periods. The Trade Offs approach is an advanced tool for the improvement of the discrimination of Data Envelopment Analysis (DEA) models. They used CRS models in DEA for computing this index, since the convexity assumption is strong condition for computing, so for solving this problem in this paper we use Free Disposal Hull (FDH) models in DEA for computing Meta Cost Malmquist Index. Also in this paper Meta Cost Malmquist Index is evaluated considering in fact that relative importance of input and outputs id different periods are different. In the papers concerning Meta Cost Malmquist Index this fact is not considered, which is very important from managerial point of you. The main advantage this index is that, it is circular.