Multi-objective optimization model in a heterogeneous weighted network through key nodes identification in overlapping communities

Abstract

Nowadays, it is possible to easily utilize positive and negative effects of neighbors on a social network to maximize diffusion of a novel product and profit of the seller. Hence, this paper aims to introduce a new mathematical model for a product pricing in non-competitive environment having multiple goals. The proposed model is designed while there are a monopole seller and several heterogeneous customers for a novel product. Considering various criteria, these customers are able to purchase the novel product including price, product quality, urgent need to have the product, and positive/negative externalities received from the neighbors. Moreover, they are able to comment in case of satisfaction or dissatisfaction with the product. However, the extent of influence depends on strength of the relations with neighbors that is considered in the proposed model with complete information and quantitative values. Proportionate to activating the neighbors, referral bonus is considered from the seller. To find influential nodes for the influence and exploit strategy implementation we propose a new overlapping community detection algorithm. In this algorithm, a new overlapping score based on non-member neighbor nodes connectivity is introduced to identify overlapping communities. Finally, we evaluate the efficiency of the proposed model, by implementing the proposed community detection algorithm in a real-world dataset. The results show that it is possible to obtain desired selling price in a fashion that maximum diffusion in the network happens and the seller achieves his desired profit under various management viewpoints.