Disaster response aims to address the immediate needs of the affected populations quickly in highly uncertain circumstances. In disaster relief supply chains, the demand comes from disaster victims (typically considered as internally dis-placed populations), while the supply mostly consists of in-kind donations. This dissertation focuses on finding a fair mechanism to distribute a scarce relief item among a set of demand points under supply uncertainty. Primary concerns, restrictive elements, and unknown parameters change throughout the response phase, which substantially affects the structure of the underlying problems. Thus, the first part of this study provides a temporal classification of disaster response (e.g., into subphases) based on evolving features of demand and supply. As the next step, a donation management problem is structured considering the characteristics of a selected subphase. We first focus on the deterministic donation management problem, which is formulated as a multi-criteria multi-period location-inventory problem with service distance constraints. A set of mobile facilities, called points of distribution (PoDs), is used to distribute the collected supply. In particular, two decisions are made for every period of the planning horizon: (i) where to locate a limited number of mobile PoDs and (ii) what quantity to deliver to each demand node from each PoD. We consider three criteria. The first two involve the so-called deprivation cost, which measures a population’s “suffering” due to a shortage. The third objective is related to the total travel time. Two resulting vectorial optimization models are solved using the ε-constraint method, and the corresponding Pareto frontiers are obtained. Computational results are presented that result from applying the proposed methodological developments to an instance of the problem using real data as well as a generated one. Finally, the stochastic counterpart of the problem is addressed with the aim of minimizing a deprivation cost-based objective. The uncertain supply parameters are integrated into the model using a multi-stage stochastic programming (MSSP) approach. The MSSP model is tested on a real data set to assess and evaluate possible policies that can be adopted by decision-makers. Two matheuristic approaches are employed to handle the exponential growth of the scenario trees: a rolling horizon algorithm and a scenario tree reduction algorithm. A set of computational experiments is performed to evaluate the performance of the proposed methodologies. Overall, the results show that the proposed algorithms can better support the decision-making process when fairness is of relevance.