Minimum cost with consensus constraint to support multi-attribute product design

Classical discrete multi-attribute product design (DMAPD) problem aims to design the product with the maximum number of approval individuals. However, the consensus constraint, which measures the uniformity of the opinions among different individuals, is rarely considered in the existing DMAPD studies. To fill this gap, we propose a novel minimum cost discrete multi-attribute product design (MCDMAPD) model with consensus constraint. Firstly, we provide a method to determine the multi-attribute satisfaction degrees and the satisfaction threshold. Then, under the constraint of the limited design budget, the DMAPD model maximizing the number of approval individuals is developed. Next, we define a consensus measure on the designed product, and provide the method for determining the unit adjustment cost of individuals. Furthermore, by considering the strategic proof and the envy-free constraints, the MCDMAPD model with consensus constraint is developed to reach the acceptable consensus. Finally, we conduct the simulation analysis and comparison analysis to justify the MCDMAPD model