As the population grows and demand increases, cities have seen a rise in the number of chain stores. To remain competitive, these companies must reduce costs and attract more customers. A key factor in achieving this is the strategic placement of store branches, which reduces the distance between stores and customers, instilling trust and increasing their appeal while also cutting costs by reducing the need for employees to navigate longer distances. In this study, an integer linear programming model is presented with the goal of dividing a zone in Ahvaz city into several scenarios to determine the optimal number of stores while maintaining control over the distance between active stores. This research is the first to include this specific limitation in the mathematical model of the problem. The results of the study demonstrate a significant reduction in the distance between customers and stores.