The imperative to deploy Deep Neural Network (DNN) models on resource-constrained edge devices, spurred by privacy concerns, has become increasingly apparent. To facilitate the transition from cloud to edge computing, this paper introduces a technique that effectively reduces the memory footprint of DNNs, accommodating the limitations of resource-constrained edge devices while preserving model accuracy. Our proposed technique, named Post-Training Intra-Layer Multi-Precision Quantization (PTILMPQ), employs a post-training quantization approach, eliminating the need for extensive training data. By estimating the importance of layers and channels within the network, the proposed method enables precise bit allocation throughout the quantization process. Experimental results demonstrate that PTILMPQ offers a promising solution for deploying DNNs on edge devices with restricted memory resources. For instance, in the case of ResNet50, it achieves an accuracy of 74.57% with a memory footprint of 9.5 MB, representing a 25.49\% reduction compared to previous similar methods, with only a minor 1.08% decrease in accuracy.