Maintenance scheduling of manufacturing systems based on optimal price of the network

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).