The purpose of this work is to apply a strategy for reducing the inventory replenishment cycle time for a Mexican Convenience Store Supply Chain. This strategy is structured with the aim of reducing the store inventory level from about 30 days on average. This work describes the efforts of the company to decrease the delivery cycle time by increasing the inventory replenishment frequency in the Metropolitan area of Monterrey city. The methodology used is based on the application of a waste elimination scheme complemented with mathematical models for determining delivery frequencies. Results of simulation and pilot studies of implementing the suggested initiatives are provided.