A sudden-onset disaster such as hurricane, tidal wave, or earthquake creates a nearly insurmountable challenge in bringing humanitarian relief to those who desperately need it. This paper seeks to assess the last-mile of the supply chain to ensure relief is delivered to those who need it. A model utilising a stochastic process is developed to study the supply chain distribution process as dependent on the humanitarian relief concerns. This model is analysed and critical considerations are recognised. A stochastic model was used to assess whether a last-mile relief station could run indefinitely. The answer to this question is no. The station will eventually reach a state of under-stock or overstock; both scenarios indicate ineffectiveness. Various aspects of this problem have been studied from the perspective of supply chain management to optimal facility location. This paper focuses on the last critical mile and its distribution needs.