Introduction
After large-scale natural disasters, the lack and/or unfair distribution of supply causes various damages and hinders the functioning of the humanitarian supply chain. The affected areas located at a long distance cannot be ignored for receiving aid in case of limited resources or increased costs in properly managing the humanitarian supply chain. The distribution of the necessary livelihood items must be fair. To deal with disasters such as earthquakes, some places can be created for medical supplies, food, and other necessities for the survivors in the shelters. Therefore, in this study, a framework based on mathematical modeling is presented for the fair distribution of different relief items from different centers to the affected areas during an earthquake in Tehran, Iran. 

Methods 
In this study, a mathematical model for the fair distribution of relief items in a humanitarian supply chain is presented at two levels of high and low. For this purpose, a multi-purpose and multi-level humanitarian supply chain was first developed. The proposed model had three objective functions that were solved by the weighted sum method. LINGO software is used to implement the model. We examined three dimensions of humanitarian logistics indicators: Access cost, unmet demand rate in each period, and the gap between the order fill rate and the ideal demand satisfaction rate over the entire period. 

Results 
The distribution of four essential items (blankets, tents, food, and water) in 7 affected neighborhoods in the 1st district of Tehran is done by two special support centers and one multi-purpose support center, belonged to the crisis management organization and located in the Sohank and Babaei neighborhoods. According to the results, with the decrease in the supply parameter, the amount of unmet demand increased, and there was a shortage of essential items in all periods. This shortage affected the desirability of distribution among recipients and had a negative effect on the performance of the humanitarian supply chain and fair distribution. On the other hand, with the increase in supply parameter, there was a surplus of items, and considering the time window, there may be no demand for some food items, which can lead to their spoilage. In this case, an additional cost is imposed on the chain.  

Conclusion
The model proposed in this paper is suitable for large-scale local (not national) natural disasters in urban areas (with a high number of residents). The results provide valuable information to managers and planners to make valuable decisions after earthquake to control the situation.

Ethical Considerations

Compliance with ethical guidelines
In this study, the information of participants was kept confidential. 

Funding
This paper was extracted from a PhD. thesis. This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Authors' contributions
Software: Reza Narimani and Hossein Amoozad Khalili; Investigation and writing original draft: Reza Narimani; conceptualization, sources, review & editing: Majid Motamedi; Review & and editing: Hossein Amoozad Khalili. 

Conflicts of interest
The authors declare no conflict of interest.


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