In the early stages of a major disaster, where demand at disaster sites is uncertain, roads are damaged in affected areas, and the fairness and timeliness of rescue operations must be considered, the SNS algorithm is applied to solve the emergency supply distribution model to achieve rapid and effective distribution of emergency supplies. First, an emergency supply distribution model was constructed, with the objective of minimizing the total cost of emergency rescue and the evaluation of humanitarian aid under the background of fuzzy demand and damaged roads. Then, the SNS algorithm was introduced to solve the model, and an improved SNS(ISNS) algorithm with a reinforcement learning rate strategy was proposed. Finally, taking the 2022 Luding Earthquake in Sichuan as an example, the SNS algorithm, ISNS algorithm, discrete particle swarm optimization, genetic algorithm, and simulated annealing algorithm were applied to solve this case, respectively. The results indicate that the ISNS algorithm demonstrates stability. Compared with other algorithms, the total cost of emergency rescue is reduced by at least 6 410 yuan, and the evaluation of the humanitarian aid evaluation target is improved by at least 50.6%, highlighting the superiority of the ISNS algorithm. The ISNS algorithm is beneficial for solving emergency supply distribution problems.