Humanitarian organizations (HOs) face operational challenges during sudden-onset disasters, such as constraints on staff, storage, and transportation, delaying critical donations to people in need (PIN). These inefficiencies create a trade-off: centralized operations enable accurate demand estimation but face bottlenecks, while decentralized donations, where individual donors distribute supplies based on preferences, offer faster responses but risk supply-demand mismatches. To address this, we propose a model that partially decentralizes humanitarian operations while accounting for random demand. In the deterministic case, the optimal decentralization level reduces to a one-dimensional piecewise-linear convex optimization problem, enabling a novel algorithm to find all solutions efficiently. We prove that the objective function has at most 3n + 2 pieces, leading to an improved O(n)-complexity algorithm for n affected zones. These results extend to the stochastic case, accommodating |Ω| demand scenarios with complexity O(|Ω|n). We derive closed-form expressions for the optimal decentralization level, facilitating detailed comparative analyses. Our model effectively incorporates demand uncertainty, donor preferences, and fairness considerations, all of which can be efficiently addressed using the proposed algorithms. As a case study, we apply this framework to early-stage humanitarian aid distribution in Ukraine during the 2022 Russo-Ukrainian War. Results show that partial decentralization, when HO efficiency discounts are high, is nearly three times more effective than full centralization. A 33% decentralization level can reduce demand shortage costs by up to 80% compared to full decentralization via postal services. This highlights the potential of partial decentralization in improving disaster relief operations.