In this research article postulates of Data Envelope Analysis (DEA) and factor minimal cost function and its properties are mentioned because they are prerequisites to understand the goal programming estimation of stochastic cost function. The LPP by which the factor minimum cost is obtained has been proposed here. This research paper includes the two stages of estimation of stochastic cost function. The properties satisfied by factor minimal cost function are stated and a diagram by which the concepts of technical, allocated and overall production efficiencies can be understood is proposed. The GP/CR model with single priority is specified and the GPP by which the estimation of full frontier can be estimated is presented. The LPP by which the output technical efficiency is estimated has been specified here. The goal programming problem by which DA can be formulated is derived and DEA-additive model is proposed. Furthermore some applications of goal programming in portfolio management have been proposed. © IJSTR 2019.