Profit maximization and patient distribution in strategic pharmacy network models

This paper addresses the problem of optimizing the spatial distribution of pharmacies within a regional healthcare system, with the aim of improving accessibility and equity in pharmaceutical services.We propose a nonlinear programming model based on the theory of variational inequalities, which captures the equilibrium behavior of users in choosing pharmacies, considering travel costs, service attractiveness, and territorial constraints.Unlike classical discrete location models, our approach allows for a realistic representation of users' decentralized decisions.A numerical example is presented to illustrate the applicability of the proposed framework and its potential to guide strategic decisions in pharmaceutical supply chain management.It is an illustrative setting designed to validate the internal consistency of the model.Its goal is to highlight how the theoretical formulation can be effectively implemented and to show the model's ability to capture the complex interactions among stakeholders in the pharmaceutical distribution network.