Applying a Mathematical Model for the Distribution of Earthquake Relief Items to the Affected Areas of Tehran

Background and objective After a large-scale natural disaster, the lack of supply and unfair distribution of relief items can cause high human casualties and hinder the function of the humanitarian supply chain. Therefore, this study aims to present a framework based on mathematical modeling for the proper distribution of relief items among the affected areas in Tehran Method In this study, mathematical modeling was used for the distribution of relief items in a humanitarian supply chain at two high and low levels. Therefore, this article aims to provide an optimization model for the distribution of livelihood packages in the humanitarian supply chain to deal with the crisis. 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. Results 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 proposed model is suitable in the event of natural disasters locally in urban areas of Tehran (with a certain number of residents). The results of this study can be useful for managers to make appropriate decisions after disasters and control the situation.