Testing facility location with constrained queue time problem: A case study on Brazilian capital cities

This paper addresses the Testing Facility Location with Constrained Queue Time Problem. This optimization problem was designed to determine the best places to deploy testing facilities for contagious diseases and the number of testers in each facility, while constraining the maximum waiting time in the queue, with a given probability. An integer programming model was formulated, presented and applied to the 27 capital cities of Brazil. In addition, the results achieved by the model were validated using a Monte Carlo simulation, to verify if the constrained queue time was being satisfied. Through several experiments, testing plans can be determined for various scenarios, comprising different parameters. When evaluating its similarities and differences, this provides interesting insights to the decision-maker. The results indicate that the model successfully produces valuable information to support the creation of testing plans, as every outcome respected the constrained maximum waiting time in the queue in all executions. In addition to pointing out the minimum investment necessary to execute a testing plan in all the capital cities, they also show that a small increase (less than 4%) in the total costs could allow both a decrease in waiting time and an increase in service level, allowing the decision-maker to apply the best combination of parameters, based on the current situation.