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Purpose When a large-scale outbreak such as the COVID-19 pandemic happens, organizations that are responsible for delivering relief may face a lack of both provisions and human resources. Governments are the primary source for the humanitarian supplies required during such a crisis; however, coordination with humanitarian NGOs in handling such pandemics is a vital form of public-private partnership (PPP). Aid organizations have to consider not only the total degree of demand satisfaction in such cases but also the obligation that relief goods such as medicine and foods should be distributed as equitably as possible within the affected areas (AAs). Design/methodology/approach Given the challenges of acquiring real data associated with procuring relief items during the COVID-19 outbreak, a comprehensive simulation-based plan is used to generate 243 small, medium and large-sized problems with uncertain demand, and these problems are solved to optimality using GAMS. Finally, post-optimality analyses are conducted, and some useful managerial insights are presented. Findings The results imply that given a reasonable measure of deprivation costs, it can be important for managers to focus less on the logistical costs of delivering resources and more on the value associated with quickly and effectively reducing the overall suffering of the affected individuals. It is also important for managers to recognize that even though deprivation costs and transportation costs are both increasing as the time horizon increases, the actual growth rate of the deprivation costs decreases over time. Originality/value In this paper, a novel mathematical model is presented to minimize the total costs of delivering humanitarian aid for pandemic relief. With a focus on sustainability of operations, the model incorporates total transportation and delivery costs, the cost of utilizing the transportation fleet (transportation mode cost), and equity and deprivation costs. Taking social costs such as deprivation and equity costs into account, in addition to other important classic cost terms, enables managers to organize the best possible response when such outbreaks happen.