Humanitarian aid organizations generally need to decide how to allocate their limited budget among different materials for disaster preparedness and disaster response. The budget can either be used before the disaster for stocking decisions under uncertainty or it can be used after the disaster to satisfy the required demand at a higher cost when the uncertainty is resolved. In this study, we aim to decide how many of each type of material to procure before and after the disaster considering the budget limitations. For this purpose, we first develop single product models with and without budget constraints using a newsvendor approach. Then, we build a two-stage stochastic model with budget constraint for the two-product case and determine its optimal solution by first solving the second stage problem to allocate the remaining budget among the products after the disaster. Then, we solve the first stage problem using KKT conditions for the resulting constrained nonlinear optimization problem. Finally, we extend our analysis for multiple product cases and propose approximation algorithms utilizing the optimal solutions derived for the single and two-product cases. We provide managerial insights using our results through detailed numerical experiments, and also present a case study with real life data. It is observed that, contrary to expectations, higher quantities need to be purchased before the disaster when there is a limited budget, as compared to the unlimited budget case. When multiple products are considered, it is important to consider the interactions between the products, especially when the budget is moderate.

人道主义援助组织通常需要决定如何在不同的备灾和救灾物资中分配有限的预算。预算既可以在灾难发生前用于不确定性情况下的库存决策，也可以在灾难发生后用于在解决不确定性时以更高的成本满足所需的需求。在这项研究中，我们的目标是在考虑到预算限制的情况下，决定在灾难前后采购每种材料的数量。为此，我们首先使用报摊方法开发有和没有预算限制的单一产品模型。然后，我们为双产品情况建立了一个具有预算约束的两阶段随机模型，并通过首先解决第二阶段问题来确定其最优解，以便在灾难发生后在产品之间分配剩余预算。然后，我们使用 KKT 条件来解决第一阶段问题，从而得到约束非线性优化问题。最后，我们扩展了对多个产品案例的分析，并提出了利用针对单个和两个产品案例得出的最优解的近似算法。我们通过详细的数值实验使用我们的结果提供管理见解，并提供一个包含现实生活数据的案例研究。据观察，与预期相反，与预算无限制的情况相比，在预算有限的情况下，需要在灾难前购买更多数量。