Food supply chain demands accessible technologies for real-time freshness monitoring; however, current solutions lack efficient olfactory assessment capabilities. This paper presents a lightweight transformer for odor classification system designed for low-power food detection on edge devices. Specifically, the model processes gas resistance signals from a Bosch BME688 sensor. Evaluated through a case study involving coffee powders, a proxy for perishable goods, the proposed approach is rigorously benchmarked against off-the-shelf solutions under identical conditions. Our model improves classification accuracy and F1 score by 8%, while reducing the false positive rate by 9% compared to the baseline. Thus, the architectural simplifications reduce the complexity of the model while preserving temporal pattern recognition. Finally, this approach paves the way for integrating olfactory analysis into circular food infrastructures aimed at minimizing waste.