Inventory decisions for humanitarian aid materials considering budget constraints

Abstract

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.