  Goods can exhibit positive externalities impacting decisions of customers in
socials networks. Suppliers can integrate these externalities in their pricing
strategies to increase their revenue. Besides optimizing the prize, suppliers
also have to consider their production and maintenance costs. Predictive
maintenance has the potential to reduce the maintenance costs and improve the
system availability. To address the joint optimization of pricing with network
externalities and predictive maintenance scheduling based on the condition of
the system, we propose a bi-level optimization solution based on game theory.
In the first level, the manufacturing company decides about the predictive
maintenance scheduling of the units and the price of the goods. In the second
level, the customers decide about their consumption using an optimization
approach in which the objective function depends on their consumption, the
consumption levels of other customers who are connected through the graph, and
the price of the network which is determined by the supplier. To solve the
problem, we propose the leader-multiple-followers game where the supplier as a
leader predicts the strategies of the followers. Then, customers as the
followers obtain their strategies based on the leader's and other followers'
strategies. We demonstrate the effectiveness of our proposed method on a
simulated case study. The results demonstrate that knowledge of the social
network graph results in an increased revenue compared to the case when the
underlying social network graph is not known. Moreover, the results demonstrate
that obtaining the predictive maintenance scheduling based on the proposed
optimization approach leads to an increased profit compared to the baseline
decision-making (perform maintenance at the degradation limit).
