Introduction
One of the most important goals of the crisis management headquarters is the proper preparation and distribution of food to the affected people during a disaster. During these disasters, there are challenges in the preparation and distribution of foods among the victims, due to limitations in terms of food storage and consumption, which makes it more difficult for the service providers. Therefore, it is very important to use a suitable network or cold supply chain for food items. Logistics plays an essential and decisive role in the perishable food supply chain and crisis management support; its disruption can negatively affect the entire crisis management process. Logistic support during a crisis  includes the processes of estimation, supply, transportation, maintenance and distribution of goods, equipment and services for the victims and relief teams. Since the management of cold supply chain is different from other chain systems and its entire process is subject to special conditions considering the type of foods and the lack of attention to various principles can lead to food damages such as spoilage, loss of quality, poisoning, etc., a comprehensive system or model is needed. In this study, we aim to develop a mathematical model using integer linear programming for the optimization of cold food supply chain during disasters. 

Methods
This is a cross-sectional quantitative/qualitative study using the operational research approach. We designed a two-objective mixed integer linear programming model for a cold, stable and multi-level supply chain in the food industry in the conditions of uncertainty and crisis. In this programming model, the economic order quantity (EOQ) performance optimization method was used to determine the optimal order point. The indicators affecting the performance of cold supply chain model included cost and service, distance, carbon dioxide emissions, capacity and demand. The proposed supply chain included: Suppliers, producers, distributors and service centers. In the supply chain, the selected food were prepared from primary suppliers and sent to procurement centers (n=16 in Iran). These centers were able to provide different food products in multiple periods and the crisis management headquarters could receive the products they need directly from the suppliers or from the distribution channels (n=5 in Iran). The central crisis management headquarters, (n=35 in Iran), receive the products they need in two ways, either directly from the supplier or through the distribution channels. The presented model was solved based on the real data obtained from the crisis management headquarters in Iran and implemented as a pilot for 16 supply centers, 5 distribution channels, and 35 crisis management headquarters with two LP-metric and augmented epsilon constraint (AEC) methods. 

Results
Ten numerical examples were used with different objective function values at different times for both LP-metric and AEC methods. The results showed that the LP-metric method had better performance for objective functions compared to the AEC method. The findings of testing research hypotheses using one-way analysis of variance showed that the use of mathematical models had a positive and significant effect on the optimization of the cold food supply chain during disasters. In this regard, there was no significant difference between LP-metric and AEC methods (P>0.05). Also, the use of mathematical models had a positive and significant effect on improving the quality of food industry. Optimizing the supply chain by the mathematical model has a positive and significant effect on the performance of food industries.

Conclusion
The findings showed that by using the presented mathematical model, it is possible to achieve the optimization of the cold food supply chain during disasters. The model has high efficiency and can solve high-quality solutions in a reasonable time. It has a higher performance compared to traditional approaches. It is expected that by using the presented mathematical model, relief operations and food distribution during disasters can be facilitated and optimized.

Ethical Considerations

Compliance with ethical guidelines
In this study, all ethical principles were observed. Since no experiments on animal or human samples were conducted, no ethical code was obtained.

Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Authors' contributions
The authors contributed equally to preparing this paper.

Conflicts of interest
The authors declared no conflict of interest.