• Optimal policy can be proved for a two-supplier system with an unreliable supplier. • Stable (s,S) policy is robust outside of parameter conditions for optimality. • There is an easily computed condition for exclusive unreliable supplier ordering. • Optimal policies move from exclusive ordering to splitting as key parameters vary. We study a single-product, periodic-review inventory system with the presence of fixed ordering cost. There are two suppliers: One is perfectly reliable while the other offers a cost advantage but is subject to possible supply interruptions. We present a theoretical framework with mathematical proofs for the optimal ordering policy in the finite-horizon setting, which exhibits an ( s , S ) structure, but with multiple, sometimes overlapping, reorder points and order-up-to levels. Then, we analyze the limiting behavior of our ( s , S ) policy and show that both the optimal cost and ordering policy parameters converge over time. This steady-state ( s , S ) policy characterizes the optimal sourcing strategy for the infinite-horizon setting. Through computational studies, we investigate the effects of parameter changes on the optimal policy and demonstrate that our two-supplier ( s , S ) ordering policy is optimal under a wide range of system parameters beyond the conditions required in the optimality proof.