TY - JOUR

T1 - An Equity-Based Optimization Model to Solve the Location Problem for Healthcare Centers Applied to Hospital Beds and COVID-19 Vaccination

AU - Delgado, Erwin J.

AU - Cabezas, Xavier

AU - Martin-Barreiro, Carlos

AU - Leiva, Víctor

AU - Rojas, Fernando

N1 - Funding Information:
Funding: This research was partially supported by Decanato de Investigación de la Escuela Superior Politécnica del Litoral ESPOL, Ecuador (E.J.D., X.C., C.M.-B); FONDECYT grant number 1200525 (V.L.) and FONDECYT grant number 11190004 (F.R.), both from the National Agency for Research and Development (ANID) of the Chilean government under the Ministry of Science, Technology, Knowledge, and Innovation.
Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - Governments must consider different issues when deciding on the location of healthcare centers. In addition to the costs of opening such centers, three further elements should be addressed: accessibility, demand, and equity. Such locations must be chosen to meet the corresponding demand, so that they guarantee a socially equitable distribution, and to ensure that they are accessible to a sufficient degree. The location of the centers must be chosen from a set of possible facilities to guarantee certain minimum standards for the operational viability of the centers. Since the set of potential locations does not necessarily cover the demand of all geographical zones, the efficiency criterion must be maximized. However, the efficient distribution of resources does not necessarily meet the equity criterion. Thus, decision-makers must consider the trade-off between these two criteria: efficiency and equity. The described problem corresponds to the challenge that governments face in seeking to minimize the impact of the pandemic on citizens, where healthcare centers may be either public hospitals that care for COVID-19 patients or vaccination points. In this paper, we focus on the problem of a zone-divided region requiring the localization of healthcare centers. We propose a non-linear programming model to solve this problem based on a coverage formula using the Gini index to measure equity and accessibility. Then, we consider an approach using epsilon constraints that makes this problem solvable with mixed integer linear computations at each iteration. A simulation algorithm is also considered to generate problem instances, while computational experiments are carried out to show the potential use of the proposed mathematical programming model. The results show that the spatial distribution influences the coverage level of the healthcare system. Nevertheless, this distribution does not reduce inequity at accessible healthcare centers, as the distribution of the supply of health centers must be incorporated into the decision-making process.

AB - Governments must consider different issues when deciding on the location of healthcare centers. In addition to the costs of opening such centers, three further elements should be addressed: accessibility, demand, and equity. Such locations must be chosen to meet the corresponding demand, so that they guarantee a socially equitable distribution, and to ensure that they are accessible to a sufficient degree. The location of the centers must be chosen from a set of possible facilities to guarantee certain minimum standards for the operational viability of the centers. Since the set of potential locations does not necessarily cover the demand of all geographical zones, the efficiency criterion must be maximized. However, the efficient distribution of resources does not necessarily meet the equity criterion. Thus, decision-makers must consider the trade-off between these two criteria: efficiency and equity. The described problem corresponds to the challenge that governments face in seeking to minimize the impact of the pandemic on citizens, where healthcare centers may be either public hospitals that care for COVID-19 patients or vaccination points. In this paper, we focus on the problem of a zone-divided region requiring the localization of healthcare centers. We propose a non-linear programming model to solve this problem based on a coverage formula using the Gini index to measure equity and accessibility. Then, we consider an approach using epsilon constraints that makes this problem solvable with mixed integer linear computations at each iteration. A simulation algorithm is also considered to generate problem instances, while computational experiments are carried out to show the potential use of the proposed mathematical programming model. The results show that the spatial distribution influences the coverage level of the healthcare system. Nevertheless, this distribution does not reduce inequity at accessible healthcare centers, as the distribution of the supply of health centers must be incorporated into the decision-making process.

KW - facility location problem

KW - Gini index

KW - linear programming

KW - multi-objective optimization

KW - SARS-CoV-2

KW - simulations

KW - spatial accessibility

KW - two-step floating catchment area method

UR - http://www.scopus.com/inward/record.url?scp=85131540791&partnerID=8YFLogxK

U2 - 10.3390/math10111825

DO - 10.3390/math10111825

M3 - Article

AN - SCOPUS:85131540791

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 11

M1 - 1825

ER -