Allocating participants: a mathematical model for selection process

Selections, exams, and tests for knowledge assessment frequently require the participant be present on a facility to take a presential test. In 2017, 6.7 Million participants took the biggest Brazilian exam:  Exame Nacional do Ensino Medio (ENEM). Logistics is a fundamental key to the execution of these events, responsible to select the locations, allocate each participant in one of a list of possible preselect facilities, and hire temporary staff to apply the tests. Deciding the locations that will be used is a crucial step that determines the two major logistical costs (staff and rent), and a bad decision will directly impact the global costs of the event. Hence, the goal of this work is to elaborate mathematical models using Lingo 17.0 to assist the decision makers to decide which locations to use, including the designation where the participant will take the test, first to minimalize the costs and then maximize the participant service level. The resulting models include multiple complex and specific constraints solved extremely fast and focused on not only providing the best solution, but also automating a manual and time-consuming process. In addition, a trade-off curve between cost and participant service level assists the decision maker to select the best option for different scenarios.