The COVID-19 outbreak has raised concerns over the global pharmaceutical supply chain where raw ingredients are produced in a few geographically concentrated regions. Disturbance in upstream production along with the surging demand for medical treatments have increased the risk of medicine shortfalls, and this situation has prompted the need for a more diversified supply chain with geographically dispersed competing suppliers. In this research, we investigate how disturbance spans a supply chain network where supply quantities are endogenously determined by competition behaviors. We evaluate the expected shortfall between post-disturbance supply and intrinsic demand, with an adapted algorithm which pushes pseudoflows in the network and partitions nodes into strong and weak branches in a spanning tree, to solve the equivalent maximum flow problem. Parametric analysis based on simulations reveals that the severity of disturbance loss can be significantly offset with supplier competitions, although the marginal benefit of competition decreases fast in the number of suppliers. In addition, configuration inefficiencies can magnify upstream shortfalls and supply chain efficiency can be improved by pushing high-cost firms to stop production. Our findings indicate that a supply chain with a moderate level of competition and balanced configuration can be robust against disturbance and demand volatility.