We study how supply disruptions interact with monopoly pricing, inventory management, and consumer stockpiling in a continuous-time model. Preemption incentives---consumers prefer to stock up before a price hike while the firm prefers to hike before consumers stock up---lead to an equilibrium with gradual stockpiling and endogenous uncertainty over the timing of a price hike, which can trigger a run at the disruption onset. Consumer storage introduces welfare losses from randomized pricing, but can also strengthen the firm's incentive to hold buffer stock. Rationing, price controls, and reserve mandates can each improve welfare, but only strategic government reserves can implement the social optimum.