关键词: 群体决策与协商, 最小成本共识模型, 不确定成本, 两阶段随机规划, 鲁棒优化

Abstract: Consensus plays a crucial role in group decision-making.For decision-making problems that need to be solved in reality, the opinions of decision-makers may differ greatly from each other, and it is difficult to obtain an acceptable solution directly. For possible future situations, decision-makers will prepare multiple decision options in advance, but cannot accurately predict the actual situation. In addition, due to the interference of external factors, it is difficult to obtain the exact value of the adjustment cost in each case. This suggests that it is challenging for decision-makers to obtain real data, and the obtained data are often inaccurate. In the application of real-world decision problems, the decision-makers often don’t know the exact values of the parameters in the optimization model before giving the initial opinions. In order to effectively address the individual characteristics of uncertainty and complexity, two-stage stochastic programming and robust optimization are applied to deal with uncertainty in decision-making problems, and both techniques excel in solving such uncertainty problems. The former considers stochastic scenarios during the decision-making process, and it uses expectation as a preference criterion to minimize the expected total cost of obtaining the preferred solution. The latter considers parameter uptake throughout the decision-making process, where uncertainty can be modeled by the worst-case scenario in the cost uncertainty set, and finds a stable solution that satisfies all the optimization constraints in the worst-case scenario.
Firstly, the key influencing factors of the uncertain decision-making environment are analyzed. We generate several stochastic scenarios and introduce perturbations to unit costs in each scenario. This is used to improve a situation where it is difficult to accurately carry out modeling based on model-driven approaches. Secondly, robust optimization and stochastic programming are combined to focus on the constraints of asymmetric adjustment costs and uncertain decision environments. By introducing box set, polyhedral set and intersection set, a robust two-stage minimum cost consensus model based on asymmetric adjustment costs is constructed. The specific robust counterpart model under each uncertainty set is given, which provides the corresponding strategies in terms of cost compensation and optimal opinion adjustment. Finally, by combining the survey data of carbon emission reduction governance under uncertain background, the effectiveness of the robust two-stage minimum cost consensus model in the carbon emission reduction governance problem is verified. Based on this, the optimal opinion adjustment strategy of the experts representing each company in the manufacturing industry in uncertain environments is proposed. In order to better illustrate the effectiveness of the proposed model, it is compared with the previous models in the numerical experiment section, and it is found that the novel consensus model under the intersection set can cost less to reach consensus. However, if the decision-makers are more conservative, they can refer to the model under the box set.
This paper is concerned with the impact of uncertainty influences and stochastic scenarios on consensus costs and consensus in the context of asymmetric adjustment costs. A robust two-stage minimum cost consensus model that considers asymmetric cost uncertainty is constructed. The experimental results show that the novel model is more suitable for uncertain decision-making environments and can help decision-makers obtain more reliable choices. This paper does not take into account other factors that influence uncertainty in real-world decision-making situations. Future research can further investigate the impact of other uncertainty factors on total cost and consensus by considering extended models with uncertainty and information asymmetry, such as initial opinions, total adjustment cost thresholds and experts’ tolerance levels.

Key words: group decisions and negotiations, minimum cost consensus model, uncertainty cost, two-stage stochastic programming, robust optimization