Interruptions in supply can have a severe impact on company performance. Their mitigation and management is therefore an important task. Reasons for interruptions can be machine breakdowns, material shortages, natural disasters, and labour strikes. Sourcing from multiple suppliers is a strategy to deal with and reduce supply disruption risk. We study a supply chain with one buyer facing Poisson demand who can procure from a set of potential suppliers who are not perfectly reliable. Each supplier is fully available for a certain amount of time (ON periods) and then breaks down for a certain amount of time during which it can supply nothing at all (OFF periods). The problem is modeled by a Semi-Markov decision process (SMDP) where demands, lead times and ON and OFF periods of the suppliers are stochastic. The objective is to minimize the buyer's long run average cost, including purchasing, holding and penalty costs. In a numerical study, we investigate the trade-off between single and multiple sourcing, as well as keeping inventory and having a back-up supplier. The results illustrate the benefit from dual souring compared to single sourcing and show the influence of the suppliers’ characteristics cost, speed and availability on the optimal policy. Further, the value of full information about the supplier status switching events is analyzed and the performance of the optimal policy is compared to an order-up-to-S policy. As the optimal policy is very complex, a simple heuristic providing good results compared to the optimal solution is developed.