<p>Natural disasters lead to significant loss of life, widespread impact on communities, and enormous economic repercussions each year. This underscores the urgent need for effective disaster preparedness to prevent or mitigate their detrimental effects. A pivotal element of such preparedness involves the establishment of an integrated disaster relief supply chain (DRSC) network. Thus, this research designs a novel DRSC network operating within a multi-period uncertain environment and accounting for the perishability of relief items (RIs), the progressive allocation of the restricted budget, lateral transfers, and the time value of money at pre-disaster. In this context, a new two-stage mean-conditional value at risk (CVaR) stochastic-robust programming model is formulated. In each period, the first stage focuses on warehouses location and inventory management prior to a disaster, while the second stage is dedicated to the re-procurement and distribution of RIs in the aftermath of the disaster. To procure RIs, two novel contractual agreements are introduced, which are integrated with multi-sourcing and allow for two-part limited buybacks, multiple reservation options, deferred and installment disbursement, and quantity-based discounts on their terms. The model aims to maximize satisfied demands, minimize deprivation costs, and ensure fair service by employing novel service utility and balance measures. Additionally, a light robust optimization approach is utilized to solve the model effectively. The practical applicability and effectiveness of the model are demonstrated through an actual case study. Finally, valuable managerial insights are derived through conducting various tests and sensitivity analyses.</p>