The main objective of this research is to propose a novel framework to approximate a discrete decision space, using optimization models in order to obtain an exact criterion for comparing the performance of Multi Attribute Decision Making (MADM) models. The framework, which is intact, an integration of qualitative and quantitative approach, is applied in a real world decision problem in context of Iran Insurance Company. Considering a multi attribute decision problem, the approximation method embeds the problem in an optimization problem to evaluate the proportional efficiency of decision alternatives, which can be considered as both output (if the criteria is positive) and input (if the criteria is negative) of the method. To evaluate the decision units' efficiency, an integration of Data Envelopment Analysis (DEA) and Analytical Hierarchy Process (AHP) is utilized. The output of the integrated method is, in fact, an exact solution in a continuous space which can be used as a reliable criterion to compare decision making techniques. Using the weights produced by Monte Carlo Simulation, the performance of decision techniques is evaluated and the best techniques are identified. In the last step of the research, the sensitivity analysis of AHP is examined on the basis of Monte Carlo results. It is shown that AHP is the most appropriate techniques which produce the closest results to DEA.