Consensus Decision Modeling with Distributionally Robust Chance Constraint in Uncertain Environments

Abstract

Group decision-making (GDM) in an ambiguous environment has consistently become a research focus in the decision science field during the past decade. Existing minimum cost consensus models either control the total budget in a deterministic context or focus on improving the utility of decision makers. In this study, a novel consensus model with a distributionally robust chance constraint (DRO-MCCM) is explored. First, two distributionally robust chance constraints consensus models are developed based on the varied utility preferences of decision-makers and taking into consideration the uncertainty of the unit adjustment cost. Next, construct conditional value-at-risk (CVaR) to approximate the cost chance constraint, simulate the viewpoint of decision makers with ambiguous preferences such as utility function and Gaussian distribution, and convert the model into a feasible semidefinite programming problem using dual theory and the moment method. Finally, the supply chain management scenario involving new product prices employs these models. Comparison and sensitivity analyses demonstrates the model’s superiority and effectiveness.