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In an emergency situation, fast and efficient logistics and distribution are essential for minimizing the impact of a disaster and for safeguarding property. When selecting a distribution center location, time satisfaction needs to be considered, in addition to the general cost factor. The improved jellyfish search algorithm (CIJS), which simulates the bionics of jellyfish foraging, is applied to solve the problem of an emergency logistics and distribution center site selection model considering time satisfaction. The innovation of the CIJS is mainly reflected in two aspects. First, when initializing the population, the two-level logistic map method is used instead of the original logistic map method to improve the diversity and uniform distribution of the population. Second, in the jellyfish search process, a Cauchy strategy is introduced to determine the moving distance of internal motions, which improves the global search capability and prevents the search from falling into local optimal solutions. The superiority of the improved algorithm was verified by testing 20 benchmark functions and applying them to site selection problems of different dimensions. The performance of the CIJS was compared to that of heuristic algorithms through the iterative convergence graph of the algorithm. The experimental results show that the CIJS has higher solution accuracy and faster solution speed than PSO, the WOA, and JS.