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

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.

A Two-Stage Location Problem with Order Solved Using a Lagrangian Algorithm and Stochastic Programming for a Potential Use in COVID-19 Vaccination Based on Sensor-Related Data.

Healthcare service centers must be sited in strategic locations that meet the immediate needs of patients. The current situation due to the COVID-19 pandemic makes this problem particularly relevant. Assume that each center corresponds to an assigned place for vaccination and that each center uses one or more vaccine brands/laboratories. Then, each patient could choose a center instead of another, because she/he may prefer the vaccine from a more reliable laboratory. This defines an order of preference that might depend on each patient who may not want to be vaccinated in a center where there are only her/his non-preferred vaccine brands. In countries where the vaccination process is considered successful, the order assigned by each patient to the vaccination centers is defined by incentives that local governments give to their population. These same incentives for foreign citizens are seen as a strategic decision to generate income from tourism. The simple plant/center location problem (SPLP) is a combinatorial approach that has been extensively studied. However, a less-known natural extension of it with order (SPLPO) has not been explored in the same depth. In this case, the size of the instances that can be solved is limited. The SPLPO considers an order of preference that patients have over a set of facilities to meet their demands. This order adds a new set of constraints in its formulation that increases the complexity of the problem to obtain an optimal solution. In this paper, we propose a new two-stage stochastic formulation for the SPLPO (2S-SPLPO) that mimics the mentioned pandemic situation, where the order of preference is treated as a random vector. We carry out computational experiments on simulated 2S-SPLPO instances to evaluate the performance of the new proposal. We apply an algorithm based on Lagrangian relaxation that has been shown to be efficient for large instances of the SPLPO. A potential application of this new algorithm to COVID-19 vaccination is discussed and explored based on sensor-related data. Two further algorithms are proposed to store the patient's records in a data warehouse and generate 2S-SPLPO instances using sensors.

Disjoint and Functional Principal Component Analysis for Infected Cases and Deaths Due to COVID-19 in South American Countries with Sensor-Related Data.

In this paper, we group South American countries based on the number of infected cases and deaths due to COVID-19. The countries considered are: Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Peru, Paraguay, Uruguay, and Venezuela. The data used are collected from a database of Johns Hopkins University, an institution that is dedicated to sensing and monitoring the evolution of the COVID-19 pandemic. A statistical analysis, based on principal components with modern and recent techniques, is conducted. Initially, utilizing the correlation matrix, standard components and varimax rotations are calculated. Then, by using disjoint components and functional components, the countries are grouped. An algorithm that allows us to keep the principal component analysis updated with a sensor in the data warehouse is designed. As reported in the conclusions, this grouping changes depending on the number of components considered, the type of principal component (standard, disjoint or functional) and the variable to be considered (infected cases or deaths). The results obtained are compared to the k-means technique. The COVID-19 cases and their deaths vary in the different countries due to diverse reasons, as reported in the conclusions.