In practice, supplier actions are often taken to reduce the impact of disruption propagation in the supply chain and ensure continuity of material flows. However, these actions can be very costly. The selection of appropriate supplier actions to reduce the disruption risk is of great interest to both academics and practitioners. However, there is no study on optimally selecting supplier actions to find the best balance between the cost of these actions and the disruption risk. This work investigates a new bi-objective supply chain ripple effect management problem, considering supplier actions. The two objectives are to minimize the manufacturer's disruption risk and the expected total action cost. To efficiently address the problem, an integrated approach that combines Markov decision process (MDP), dynamic Bayesian network (DBN), and bi-objective nonconvex mixed-integer programming model, along with optimization techniques, is designed. From this study, the following managerial insights can be drawn: (i) for different desired risk reductions, cost-effective supplier actions are different and can be identified by the proposed approach to support decision-making; (ii) the risk decreases with the increase of the total action cost before the risk threshold is achieved, and the disruption risk cannot be smaller than the risk threshold, even if more costly actions are taken; (iii) the costs of supplier actions have no impact on the risk threshold, while the state probability distributions of suppliers and the manufacturer affect the risk threshold.