Two-stage stochastic minimum cost consensus models with asymmetric adjustment costs

Abstract

When dealing with consensus cost problems with asymmetric adjustment costs, the uncertain scenarios with certain probabilities which are becoming a serious problem decision-makers have to face. However, existing optimization-based consensus models have failed to consider uncertain factors that could influence the final consensus and total consensus cost. In order to better deal with these issues, it is necessary to develop practical consensus optimal models. Thus, we establish three two-stage stochastic minimum cost consensus models with asymmetric adjustment costs that may eventually lead the way to better consensus outcomes. The impact of uncertain parameters (such as individual opinions, unit asymmetric adjustment costs, compromise limits, cost-free thresholds) are investigated by modeling three kinds of uncertain consensus models. We solve the proposed two-stage stochastic consensus problem iteratively using the L-shaped algorithm and show the convergence of the algorithm. Furthermore, a case of pollution control negotiations verifies the practicability of the proposed models. Moreover, the comparison of results with the L-shaped algorithm and CPLEX shows that the L-shaped algorithm is more effective in solving time. Some discussions and comparisons on local and global sensitivity analysis of the uncertain parameters are presented to reveal the features of the proposed models. Finally, the relationships between the minimum cost consensus model and minimum cost consensus models with asymmetric adjustment costs and the proposed models are also provided.