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.

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.

Terminals are key components of intermodal transport networks, as they are the facilities where freight is transferred between transport modes. The efficiency of such facilities crucially depends on their locations (and sizes), which are typically chosen considering two levels of analysis: local/urban and regional/country. Our focus in this presentation is the regional/country level. At this level, the problems involved in the locational (and sizing) decisions at stake are a particular variety of hub locations problems—a class of problems that has been widely studied through optimization approaches. However, they typically assume that decisions are made in a centralized management context: decision-makers not only choose the locations of intermodal terminals (or hubs), but also fully control their utilization (i.e., which terminal each user will patronize). This signifies that such approaches are not applicable when users–potentially, any companies that move freight–behave according to their own individual interests; that is, they are not applicable in a decentralized management context. In this presentation, we describe an ongoing study where (regional) intermodal terminal location problems are dealt with in this type of context considering terminals of different types and respective capacity and operation ranges. In particular, we present the complex optimization model we have developed to handle such problems, and the (sometimes counterintuitive) results it led to when applied to a case study inspired by the Portuguese reality.

La respuesta efectiva a las crisis humanitarias y emergencias originadas por desastres de diversa índole representa una tarea desafiante. Los aspectos logísticos inherentes a la planeación y ejecución de acciones de respuesta se orientan a minimizar los costos y las pérdidas humanas de una forma eficaz. En este estudio, se propone un modelo matemático que apoye la toma de decisiones de las organizaciones involucradas en brindar apoyo ante un evento emergente. Esa asistencia variada puede ir desde sugerir la ubicación de centros de transferencia temporales; la distribución de recursos a través de rutas secundarias desde los centros hacia las zonas afectadas por el desastre, y reducir el riesgo de que se entreguen en forma tardía. El aspecto innovador de este trabajo es que se incorpora en la función objetivo una medida que cuantifica monetariamente el tiempo en que una persona vulnerable se encuentra privada de un recurso, es decir, la diferencia de tiempo entre el momento en que la persona recibe la ayuda y el momento en que esta demanda es generada. Finalmente, se aplica el modelo propuesto en una instancia derivada de los efectos causados por el terremoto en Ecuador en 2016.

This paper explores strategies to enhance the convergence of Newton and Trust Region methods, which are employed to obtain optimal solutions for the optimization problems underlying the Logistic Regression technique. The optimization problems consist of maximizing the likelihood function and minimizing the sum of squared errors. These are addressed using the mentioned gradient-based algorithms. Improvements include using a local search heuristic to find a good initial solution and determining the optimal learning rate at each iteration. The heuristic-generated initial points significantly improve the convergence rate of these gradient-based methods. Additionally, instead of using a fixed learning rate or step size, the optimization process dynamically computes these parameters using the Golden Search method, ensuring a more adaptive and efficient search strategy. Extensive numerical experiments and a detailed case study validate the effectiveness of this approach.