Retail location models have traditionally relied on scalar formulations, such as Huff's (Huff, 1963) and Reilly's (Reilly, 1931) gravity models, which capture store attractiveness and distance but ignore directionality in competitive forces. This study introduces a novel vector-based model that represents store influence as a two-dimensional field, integrating both magnitude and direction of attraction. A distinctive feature of the model is the incorporation of store age as a proxy for attractiveness, reflecting consumer trust and familiarity with established retailers. Using georeferenced data from 6928 pharmacy openings and closures in São Paulo over more than a decade, we compute competitive pressure fields and assess their relationship with firm survival. Results show that stores entering high-intensity competitive zones face significantly lower survival probabilities, as evidenced by density estimations, t-tests, and Kaplan–Meier survival curves. Illustrative cases highlight how saturation effects undermine early entrants, while peripheral areas provide conditions for longer lifespans. The findings advance the state of the art by extending classical gravity models into a directional, vector-based framework that better reflects urban retail competition. This model can be used for strategic planning in urban retail environments, helping to identify optimal locations and predict firm survival in competitive zones. Managerially, the model provides a transparent and generalizable tool for location planning, supporting strategic decisions on expansion, repositioning, and urban retail policy.
Uchida et al. (2026) studied this question.