Natural disasters are accidental and unpredictable occurrences requiring particular procedure developments to minimise their impairment. Adequate capacity with appropriate location of medical centres, effective distribution of reliefs, and auxiliary equipment play an influential role in post-disaster relief and rescue operations. Pre-disaster efforts can be practical not only for Humanitarian Supply Chains (HSCs) but also supportive of Humanitarian Organizations (HOs) in the post-disaster phase. This study presents a two-stage stochastic programming model in which (1) the site and numeral of Temporary Medical Centers (TMCs) given the number of existing hospitals, the probability of damage to roads/hospitals besides categorising casualties (triage) are analyzed, and (2) the influence of a Quantity Flexibility (QF) contract is investigated for pre-positioning and procurement planning. After selecting reliable supplier(s), the model determines a suitable level for pre-positioning and ordering each relief item. Also, the model identifies the optimal TMCs positioning solution considering casualty types, demand, span between the affected regions, medical centres with available capacity, and multi-transportation modes. A case study is conducted in the earthquake-prone area of Tehran. Extensive sensitivity analyses are accomplished to gain valuable managerial insights. The results prove the proposed model can trade off strategic, tactical, and operational decisions in the pre-and-post-disaster phases.