The impacts of disasters have recently attracted increased attention from researchers and policy makers. However, there has been little consensus about how an efficient inventory management model can be developed for postdisaster conditions. Victims of a disaster are generally gathered into shelters during and after a severe disaster to ensure their security. Many evacuees do not have the financial resources to leave the disaster area or to find food, drugs, and other necessities. Hence, their vital needs should be supplied efficiently throughout the disaster and postdisaster periods. Without an adequate stock of goods, satisfying the daily requirements of the victims without disruption might be problematic. To solve this problem, humanitarian inventory control models that can aid in adequately responding to a disaster or a humanitarian crisis are needed. In this context, response represents preparedness, planning, assessment, appeal, mobilization, procurement, transportation, warehousing, and distribution. This paper is concerned with the development of a subproblem of the general humanitarian supply chain problem: an efficient and quick-response humanitarian inventory management model able to determine the safety stock that will prevent disruptions at a minimal cost. The humanitarian inventory management problem is first mathematically formulated as a version of the Hungarian Inventory Control Model. A solution to this time-dependent stochastic model is then proposed by using the p-level efficient points algorithm. The single commodity case results are given, and a sensitivity analysis of the model vis-à-vis various model parameters that affect safe inventory levels is conducted.