To address the emergency medical supply scheduling problem in public health emergencies， the psychological cost under trauma for disaster victims was introduced as an optimization objective based on minimizing transportation time and the number of vehicles， measuring the psychological stress difference experienced by victims due to delayed material delivery， and a multi-objective emergency medical supply scheduling model was proposed， aiming to minimize psychological cost under trauma， transportation time， and the number of vehicles. Given Non-deterministic Polynomial-time hard （NP-hard） nature of the model， a Multi-objective Discrete Hiking Optimization Algorithm （MDHOA） was designed. The emergency medical supply scheduling solution was encoded as a delimiter-free integer sequence， which was then decoded using the Split segmentation method. An improved nearest neighbor heuristic method was employed to optimize the initial solution， and a hiking population-driven multi-objective optimization mechanism was introduced to enhance the search capability. Experimental results show that the proposed algorithm overall outperforms comparison algorithms such as Non-dominated Sorting Genetic Algorithm Ⅱ （NSGA-Ⅱ）， Improved NSGA-Ⅱ （INSGA-Ⅱ）， and Improved Multi-Objective Honey Badger Algorithm （IMOHBA） in terms of three metrics： HyperVolume （HV）， Overall Nondominated Vector Generation （ONVG）， and Inverted Generational Distance （IGD） on the Solomon benchmark set， demonstrating superior solution coverage and stability. In a real-world case study of Haidian District， Beijing， the proposed model exhibits strong adaptability and practical feasibility. Sensitivity analysis results indicate that the psychological cost coefficient for disaster victims and vehicle capacity have significant impacts on the scheduling strategy.