  The optimal placement of healthcare facilities, including the placement of
diagnostic test centers, plays a pivotal role in ensuring efficient and
equitable access to healthcare services. However, the emergence of unique
complexities in the context of a pandemic, exemplified by the COVID-19 crisis,
has necessitated the development of customized solutions. This paper introduces
a bi-objective integer linear programming model designed to achieve two key
objectives: minimizing average travel time for individuals visiting testing
centers and maximizing an equitable workload distribution among testing
centers. To address this problem, we propose a customized local search
algorithm based on the Voronoi diagram. Additionally, we employ an
$\epsilon$-constraint approach, which leverages the Gurobi solver. We
rigorously examine the effectiveness of the model and the algorithms through
numerical experiments and demonstrate their capability to identify
Pareto-optimal solutions. We show that while the Gurobi performs efficiently in
small-size instances, our proposed algorithm outperforms it in large-size
instances of the problem.
