A Bi-Level Vaccination Points Location Problem That Aims at Social Distancing and Equity for the Inhabitants

Abstract

Designing efficient vaccination programs that consider the needs of the population is very relevant to prevent reoccurrence of the COVID-19 pandemic. The government needs to provide vaccination points to give out vaccine doses to the population. In this paper, the authors analyze the location of vaccination points whilst addressing the inhabitants’ preferences. Two objectives that prevent crowding of inhabitants are considered. The government aims for the minimum distance between located vaccination points is maximized, and for the number of inhabitants that attend the different vaccination points to be equitable. One of the key aspects of this problem is the assumption that inhabitants freely choose the located vaccination point to go. That decision affects the objectives of the government, since crowding at vaccination points may appear due to the inhabitants’ decisions. This problem is modeled as a bi-objective, bi-level program, in which the upper level is associated to the government and the lower level to the inhabitants. To approximate the Pareto front of this problem, a cross-entropy metaheuristic is proposed. The algorithm incorporates criteria to handle two objective functions in a simultaneous manner, and optimally solve the lower-level problem for each government decision. The proposed algorithm is tested over an adapted set of benchmark instances and pertinent analysis of the results is included. An important managerial insight is that locating far vaccination points does not lead us to a more equitable allocation of inhabitants.

Keywords

• bi-level programming
• COVID-19
• public facility location
• vaccination system
• cross-entropy metaheuristic