The under-performance of supply chains presents a significant hindrance to disease control in developing countries. Stock-outs of essential medicines lead to treatment interruption which can force changes in patient drug regimens, drive drug resistance and increase mortality. This study is one of few to quantitatively evaluate the effectiveness of supply chain policies in reducing shortages and costs. This study develops a systems dynamics simulation model of the downstream supply chain for amikacin, a second-line tuberculosis drug using 10 years of South African data. We evaluate current supply chain performance in terms of reliability, responsiveness and agility, following the widely-used Supply Chain Operation Reference framework. We simulate 141 scenarios that represent different combinations of supplier characteristics, inventory management strategies and demand forecasting methods to identify the Pareto optimal set of management policies that jointly minimize the number of shortages and total cost. Despite long supplier lead times and unpredictable demand, the amikacin supply chain is 98% reliable and agile enough to accommodate a 20% increase in demand without a shortage. However, this is accomplished by overstocking amikacin by 167%, which incurs high holding costs. The responsiveness of suppliers is low: only 57% of orders are delivered to the central provincial drug depot within one month. We identify three Pareto optimal safety stock management policies. Short supplier lead time can produce Pareto optimal outcomes even in the absence of other optimal policies. This study produces concrete, actionable guidelines to cost-effectively reduce stock-outs by implementing optimal supply chain policies. Preferentially selecting drug suppliers with short lead times accommodates unexpected changes in demand. Optimal supply chain management should be an essential component of national policy to reduce the mortality rate.