Edge computing in person re-identification (ReID) is crucial for reducing the load on central cloud servers and ensuring user privacy. Conventional methods for obtaining compact models require computations for each individual student model. When multiple models of varying sizes are needed to accommodate different resource conditions, this leads to repetitive and cumbersome calculations.To address this challenge, we propose a novel knowledge inheritance approach named OSKT (One-Shot Knowledge Transfer), which consolidates the knowledge of the teacher model into an intermediate carrier called a weight chain. When a downstream scenario demands a model that meets specific resource constraints, this weight chain can be expanded to the target model size without additional computation.OSKT significantly outperforms state-of-the-art compression methods, with the added advantage of one-time knowledge transfer that eliminates the need for frequent computations for each target model.On the Market1501 benchmark, using pre-trained ResNet50 or ViT-S as the teacher model, OSKT generates smaller student models (1/64th and 1/10th the parameters respectively) achieving accuracies of 89.4\% and 87.1\%, outperforming pruning (80.7\%, 74.1\%) and knowledge distillation (65.7\%, 38.7\%).