Consensus modeling with probability and cost constraints under uncertainty opinions

Goal programming is often applied into uncertain group decision making to achieve the optimal solution. Exiting models focus on either the minimum cost (guaranteeing negotiation budget) or the maximum utility (improving satisfaction level). This paper constructs a stochastic optimization cost consensus group decision making model adopting the minimum budget and the maximum utility as objective function simultaneously to study the negotiation consensus with decision makers' opinions expressed in the forms of multiple uncertain preferences such as utility function and normal distribution. Thus, the proposed model is a generalization of the existing cost consensus model and utility consensus model, respectively. Furthermore in this model, utility priority coefficients cause acceptable budget range and chance constraint shows the probability of reaching consensus. Differing from previous optimization models, the proposed model designs a Monte Carlo simulation combined with Genetic Algorithm to reach an optimal solution, which makes it more applicable to real-world decision making.