Logistics is a science and art that has been widely used by large commercial chains, whose main objectives focus on the distribution of products or services. This understanding has generated various logistics studies directed towards those businesses, without considering that science can also be applied to small or medium enterprises. The present study initially executes a bibliographic review of multiple works done by several authors that confirm that studies related to the field of logistics can be aimed at any organization. The theoretical investigation of this study is therefore widely supported. This work is focused on helping a small enterprise continue offering its services during the pandemic caused by the worldwide presence of COVID-19. Hence, the purpose of this research is to present a logistics model that will allow a small supermarket to continue its commercial activities in Quito, Ecuador, in compliance with diverse regulations issued by the Ecuadorian Government. The logistical model uses the methodology called savings method developed by Clarke and Wright. The designed model produces as a main outcome the establishment of short-distance home delivery routes of provision to customers by the supermarket, thereby achieving significant savings in time and money. Additionally, the design and implementation of the model can serve as an example to be replicated in similar businesses.