The pharmaceutical industry is subject to many unique constraints, due in part to both product characteristics and regulatory guidelines. Nevertheless, pharmaceutical companies are expected to be able to serve customers that rely on their products, even as demand can be unpredictable and erratic. Pharmaceutical companies have choices in how they deal with demand uncertainty, but two schools of thought dominate: hold additional inventory or employ additional capacity. Finding the right balance between additional inventory and excess capacity proves difficult given product shelf-life constraints and long production ramp-up lead times. This study develops a mixed-integer linear program that optimizes inventory policy and production capacity policy under stochastic demand scenarios at a single node of the supply chain by minimizing inventory costs, production costs, and anticipated write-off costs. Scenarios of demand uncertainty with different probabilities are simulated to provide insights into key drivers of the model behavior and guide insights into useful inventory policies. Findings demonstrate that in an environment characterized by long production ramp-up lead times and products constrained by shelf life, neither additional inventory or excess production capacity alone is sufficient for hedging demand uncertainty. Therefore, pharmaceutical companies should consider employing the two strategies together to meet market demand with the optimal cost.