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Humanmade or natural catastrophes such as droughts, floods, earthquakes, storms, coups, economic and political crises, wars, and so forth impact various areas of the world annually. Furthermore, the lack of adequate preparations and proper coping against them causes nations to suffer heavy losses and casualties, which are sometimes irrecoverable. Consequently, as an essential activity in crisis management, humanitarian relief logistics has been of particular importance and has taken a good deal of notice at the international level during recent years. Aid facilities location and the storage of necessary commodities before a disaster and the proper distribution of relief commodities among demand points following a disaster are critical logistical strategies to improve performance and reduce latency when responding to a given disaster. In this regard, this study presents a stochastic multi-objective mixed-integer non-linear programming model in a two-level network that includes warehouses and affected areas. The model aims at minimizing total social costs, which include the expense of founding warehouses, the expense of procuring commodities, and deprivation cost, as well as maximizing fulfilled demands and warehouses utility. In this study, several pre-disaster periods, a limited budget for establishing warehouses and procuring relief commodities with their gradual injection into the system, the time value of money, various criteria for evaluating warehouses, the risk of disruption in warehouses and transportation networks, and heterogeneous warehouses are considered. The maximization of warehouses utility is done according to a data envelopment analysis model. Moreover, a multi-objective fuzzy programming model called the weighted max-min model is applied to solve the proposed model. Ultimately, the outcomes of the evaluation and validation of the proposed model show its appropriate and efficient performance.