One of the most critical tasks after a natural disaster is to organize and execute humanitarian relief operations effectively and efficiently while reaching an equitable outcome. However, due to limited resources in the initial stage of response, it becomes challenging for logistics planning authorities to target needed individuals. The concerns would be with providing an unbiased platform to make decisions about equitable distribution schedules. Therefore, developing an effective and efficient disaster relief plan that tries to treat individuals as equitable as possible was the main motivation in this research. For this purpose, this dissertation studied a novel last mile distribution plan in the initial response phase where the key focus is the preservation of lives. An integrated vehicle routing and resource allocation problem was investigated and formulated in an routing-allocation model (RAP). The theoretical foundation of RAP is formulated as an egalitarian model where resources are to be distributed so as to maximize the welfare of those in greatest need. The strategic goal is to alleviate human deprivation and suffering by minimizing the response time in regard to each beneficiary’s needs fulfillment and delivery delay on the route. Equity is quantified with a min-max objective on a deprivation cost, which is a non-linear function of deprivation time. The objective function is set to minimize the maximum deprivation cost of the deliveries so that supplies arrive in a cyclical manner while all demand sites are treated equitably.