Introduction
Natural and human-made disasters have long-term, negative, and sometimes irreparable impacts and consequences. Proper response to these disasters requires effective management of relief services. One way to achieve this goal is to ensure an optimal humanitarian supply chain. One of the determining factors in the quality and optimal performance of a humanitarian supply chain is the effective and timely cooperation and action of the parties involved in this chain. Influential parties in such operations include humanitarian organizations, donors, and the government. Governments help disaster victims either by providing goods directly, or by entrusting various types of aid, both in goods and financial, to humanitarian organizations. On the other hand, humanitarian organizations, due to their scope of activity, are the recipients of donors’ assistance and should earn and maintain the trust of these supporters by proper and effective performance. In order to build and maintain this trust, efforts to prepare and plan for potential disasters become increasingly important. One of the solutions to increase performance in emergency and humanitarian supply chains is to utilize the capacities of non-governmental organizations (NGOs). One of the fundamental research gaps is the existence of a model that considers the simultaneous cooperation of donors, humanitarian organizations, the government, and the private sector. Therefore, this study aims to present a collaborative model based on game theory that examines the cooperation between donors, humanitarian organizations, the government, and NGOs. 

Methods
The collaborative model is designed based on the problem of maximum coverage of damaged areas caused by a natural disaster. By considering the number and diversity of players, it takes into account the extent of the disaster and the number of affected areas in relief assistance. It also considers the quality of relief services and the competence of NGOs. This can allow for a default order to prioritize qualified NGOs with the required capacities in the event of a disaster. The developed model was solved using a hypothetical numerical example and GAMS software, version 24.1.2 and underwent a sensitivity analysis.

Results
The results obtained from the model provide valuable insights into the optimal actions of each player in the humanitarian supply chain during a disaster. This model takes into account the capacities and capabilities of each player, as well as the quality of services provided by the private sector, allowing for more efficient allocation of resources and ensuring maximum coverage of affected areas. The model also considers qualitative assessments conducted in the pre-disaster period and allows for prioritization of qualified NGOs during a disaster. This can significantly improve the effectiveness of disaster management efforts.

Conclusion
The results of this research show that the collaboration of parties involved in humanitarian supply chain can speed up and facilitate coverage of damaged areas during disasters. Involving players with different capacities leads to the utilization of existing capacities and facilitating assistance from the private sector. This research can be used as a basis for improving disaster management processes and increasing the efficiency of relief efforts in critical situations. To increase preparedness to deal with a disaster, it is recommended that an advertisement inviting interested NGOs be published to declare their readiness to assist in the event of a disaster in exchange for benefits such as tax exemptions from the government. International aid organizations, due to having the required capacities, can conduct a technical assessment of the volunteer NGOs and prepare a list of them. It is important to note that international organizations have a list of service/product vendors that they have worked with over time. Therefore, if private companies are on this list, they can be added to the list of candidates based on their previous performance evaluations. Companies that have a transportation and storage unit and are willing to provide assistance in the event of a disaster can also announce their readiness and participate in technical assessments. Then, their status and capacity should be updated periodically, for example annually, to take into account issues such as unit growth or the end of the company’s activities. Despite the difficulties and time-consuming nature of this process, based on the results of this research, it is worth the investment of time and money.

Ethical Considerations
Compliance with ethical guidelines
All ethical principles were considered in this study. Since there was no experiment on human or animal samples, the need for an ethical code was waived.

Funding
This paper was extracted from the master’s thesis of Golnush Jahromi Rajabi at Islamic Azad University, North Tehran Branch. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Authors' contributions
Validation, formal analysis, investigation, resources, data collection: Golnush Jahromi Rajabi; conceptualization and methodology: Razieh Keshavarzfard and Golnush Jahromi Rajabi; writing the original draft, review & editing, and supervision: Razieh Keshavarzfard.

Conflicts of interest
The authors declared no conflict of interest.


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