Being interested in supporting social consensus making, in this paper, we have proposed a group decision making procedure through conflict resolution in the following situation : each group has a different privilege with decision making; the final goal should be evaluated by a few qualitative sub-goals besides quantitative ones. For this purpose, we have developed a step-wise procedure that has been popularly adapted when encountered with complicated and large-scale problem-solving. As well as at the value system design phase, we applied the analytic hierarchy process AHP to decide weights standing for the privilege at the decision making phase, Then, after rearranging the hierarchy of the sub-goals depending on the nature, we have provided an iterative procedure to derive a final solution from a discrete optimization problem. To reduce the difficulties of multi-objective decision making thereat, we took a scoring method for total evaluation and applied the genetic algorithm as a solution method. Through numerical experiments applied to a planning problem of the radioactive waste management system we have shown numerically the proposed approach is very promising for social consensus making.