Open Access
A GRASP-based algorithm for solving the emergency room physician scheduling problem
(Elsevier, 2021) Cildoz Esquíroz, Marta; Mallor Giménez, Fermín; Mateo, Pedro; Institute of Smart Cities - ISC
This paper addresses a physician scheduling problem in an Emergency Room (ER) requiring a long-term work calendar to allocate work days and types of shift among all the doctors. The mathematical model is created without simplifications, using the real calendar, including holidays. This precludes the possibility of cyclic-type solutions, and involves numerous and varied constraints (demand, workload, ergonomics, fairness, etc.). An effective solution to this very difficult practical problem cannot be obtained, for large instances, with exact solution methods. We formulate a mathematical representation of a real-world ER physician scheduling problem featuring a hybrid algorithm combining continuous linear programming with a greedy randomized adaptive search procedure (GRASP). Linear programming is used to model a general physician-demand covering problem, where the solution is used to guide the construction phase of the GRASP, to obtain initial full schedules for subsequent improvement by iterative application of Variable Neighborhood Descent Search (VNDS) and Network Flow Optimization (NFO). A computational study shows the superiority of our approach over the Integer Linear Programming method in a set of instances of varying size and difficulty inspired by a real setting. The methodology is embedded in a software tool for generating one-year-ahead physician schedules for a local ER. These solutions, which are now in use, outperform the manually-created schedules used previously. © 2021 Elsevier B.V.
Open Access
The optimal container selection problem for parts transportation in the automotive sector
(Elsevier, 2024) Cildoz Esquíroz, Marta; Mateo, Pedro; Alonso, María Teresa; Parreño, Francisco; Alvarez-Valdes, Ramon; Mallor Giménez, Fermín; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Today's automotive factories are essentially assembly plants that receive parts from a vast network of suppliers around the world. Transporting thousands of part types over very long distances is a major logistic problem whose solution is a critical factor in the factory management. In this study we have developed a statistical and optimization methodology implemented in a software tool to help the decision makers select the most appropriate container for each part. A key element is to determine the number of parts that fit in a given container. Two optimization procedures have been developed, depending on the type of part, and used to calculate costs of each container. These costs include not only transporting parts from supplier to factory, but also the costs of handling parts within the factory and returning the empty containers to the supplier.
Open Access
Police as first reponders improve out-of-hospital cardiac arrest survival
(BMC, 2023) Jean Louis, Clint; Cildoz Esquíroz, Marta; Echarri Sucunza, Alfredo; Beaumont, Carlos; Mallor Giménez, Fermín; Greif, Robert; Baigorri Iguzquiaguirre, Miguel; Reyero Díez, Diego; Ciencias de la Salud; Osasun Zientziak; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Background: Police forces are abundant circulating and might arrive before the emergency services to Out-of-Hospital-Cardiac-Arrest victims. If properly trained, they can provide basic life support and early defibrillation within minutes, probably increasing the survival of the victims. We evaluated the impact of local police as first responders on the survival rates of out-of-hospital cardiac arrest victims in Navarra, Spain, over 7 years. Methods: A retrospective analysis of an ongoing Out-of-Hospital Cardiac registry to compare the characteristics and survival of Out-of-Hospital-Cardiac-Arrest victims attended to in first place by local police, other first responders, and emergency ambulance services between 2014 and 2020. Results: Of 628 cases, 73.7% were men (aged 68.9 ± 15.8), and 26.3% were women (aged 65,0 ± 14,7 years, p < 0.01). Overall survival of patients attended to by police in the first place was 17.8%, other first responders 17.4% and emergency services 13.5% with no significant differences (p > 0.1). Time to initiating cardiopulmonary resuscitation is significant for survival. When police arrived first and started CPR before the emergency services, they arrived at a mean of 5.4 ± 3 min earlier (SD = 3.10). This early police intervention showed an increase in the probability of survival by 10.1%. Conclusions: The privileged location and the sole amount of personnel of local police forces trained in life support and their fast delivery of defibrillators as first responders can improve the survival of out-of-hospital cardiac arrest victims.
Open Access
Estimation of patient flow in hospitals using up-to-date data: application to bed demand prediction during pandemic waves
(Public Library of Science, 2023) García de Vicuña Bilbao, Daniel; López-Cheda, Ana; Jácome, María Amalia; Mallor Giménez, Fermín; Institute of Smart Cities - ISC
Hospital bed demand forecast is a first-order concern for public health action to avoid healthcare systems to be overwhelmed. Predictions are usually performed by estimating patients flow, that is, lengths of stay and branching probabilities. In most approaches in the literature, estimations rely on not updated published information or historical data. This may lead to unreliable estimates and biased forecasts during new or non-stationary situations. In this paper, we introduce a flexible adaptive procedure using only near-real-time information. Such method requires handling censored information from patients still in hospital. This approach allows the efficient estimation of the distributions of lengths of stay and probabilities used to represent the patient pathways. This is very relevant at the first stages of a pandemic, when there is much uncertainty and too few patients have completely observed pathways. Furthermore, the performance of the proposed method is assessed in an extensive simulation study in which the patient flow in a hospital during a pandemic wave is modelled. We further discuss the advantages and limitations of the method, as well as potential extensions.
Open Access
Coping with stress in emergency department physicians through improved patient-flow management
(Elsevier, 2020) Cildoz Esquíroz, Marta; Ibarra, Amaia; Mallor Giménez, Fermín; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
This paper provides a method for the real-time monitoring of job stress in emergency department (ED) physicians. It is implemented in a Decision Support System (DSS) designed for patient-to-physician assignment after triage. Our concept of job stress includes not only the workload but also time pressure and uncertainty. A job stress function is estimated based on the consensus views of ED physicians obtained through a novel methodology involving stress factor analysis, questionnaire design, and the statistical analysis of expert opinions. The resulting stress score enables the assessment of job stress using workload data from the ED physicians’ whiteboard. These data can be used for the real-time measurement and monitoring of ED physician job stress in a stochastic and dynamic environment, which is the main novelty of this method as compared to previous workload and stress measurement proposals. A further advantage of this methodology is that it is general enough to be adapted to physician job stress monitoring in any ED. The use of the DSS for ED patient-flow management reduces job stress and spreads it more evenly among the whole team of physicians, while also improving other important ED performance measures such as arrival-to-provider time and the percentage of compliance with patient waiting time targets. A case study illustrates the application of the methodology for the construction of a stress-score, the monitoring of physician stress levels, and ED patient-flow management.
Open Access
Acuity-based rotational patient-to-physician assignment in an emergency department using electronic health records in triage
(SAGE, 2023) Cildoz Esquíroz, Marta; Ibarra Bolt, Amaya; Mallor Giménez, Fermín; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Emergency department (ED) operational metrics generated by a new acuity-based rotational patient-to-physician assignment (ARPA) algorithm are compared with those obtained with a simple rotational patient assignment (SRPA) system aimed only at an equitable patient distribution. The new ARPA method theoretically guarantees that no two physicians’ assigned patient loads can differ by more than one, either partially (by acuity levels) or in total; whereas SRPA guarantees only the latter. The performance of the ARPA method was assessed in practice in the ED of the main public hospital (Hospital Compound of Navarra) in the region of Navarre in Spain. This ED attends over 140 000 patients every year. Data analysis was conducted on 9,063 ED patients in the SRPA cohort, and 8,892 ED patients in the ARPA cohort. The metrics of interest are related both to patient access to healthcare and physician workload distribution: patient length of stay; arrival-to-provider time; ratio of patients exceeding the APT target threshold; and range of assigned patients across physicians by priority levels. The transition from SRPA to ARPA is associated with improvements in all ED operational metrics. This research demonstrates that ARPA is a simple and useful strategy for redesigning front-end ED processes.
Open Access
Hospital preparedness during epidemics using simulation: the case of COVID-19
(Springer, 2021) García de Vicuña Bilbao, Daniel; Esparza, Laida; Mallor Giménez, Fermín; Institute of Smart Cities - ISC; Gobierno de Navarra / Nafarroako Gobernua
This paper presents a discrete event simulation model to support decision-making for the short-term planning of hospital resource needs, especially Intensive Care Unit (ICU) beds, to cope with outbreaks, such as the COVID-19 pandemic. Given its purpose as a short-term forecasting tool, the simulation model requires an accurate representation of the current system state and high fidelity in mimicking the system dynamics from that state. The two main components of the simulation model are the stochastic modeling of patient admission and patient flow processes. The patient arrival process is modelled using a Gompertz growth model, which enables the representation of the exponential growth caused by the initial spread of the virus, followed by a period of maximum arrival rate and then a decreasing phase until the wave subsides. We conducted an empirical study concluding that the Gompertz model provides a better fit to pandemic-related data (positive cases and hospitalization numbers) and has superior prediction capacity than other sigmoid models based on Richards, Logistic, and Stannard functions. Patient flow modelling considers different pathways and dynamic length of stay estimation in several healthcare stages using patient-level data. We report on the application of the simulation model in two Autonomous Regions of Spain (Navarre and La Rioja) during the two COVID-19 waves experienced in 2020. The simulation model was employed on a daily basis to inform the regional logistic health care planning team, who programmed the ward and ICU beds based on the resulting predictions.
Open Access
Including learning and forgetting processes in agent-based simulation models: application to police intervention in out-of-hospital cardiac arrests
(Elsevier, 2025-01-01) Baigorri Iguzquiaguirre, Miguel; Mallor Giménez, Fermín; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Agent-based modeling has become increasingly popular in recent decades; however, defining agents that accurately depict human behavior remains a significant challenge. This paper contributes to the precise definition of human-like agents by incorporating learning and forgetting processes from the medical and psychological literature into agent-based simulation models. Specifically, the mathematical model for forgetting is developed to be compatible with empirical findings. The empirical evidence also supports the decomposition of the learning process into training sessions and the application of skills in real situations, as followed in this model. The resulting model of learning agents is then applied to study police intervention in out-of-hospital cardiac arrests. In numerous urban areas, there's ongoing discussion regarding the provision of defibrillators in patrol cars and CPR training for police officers. The results demonstrate that including learning and forgetting processes in simulation models provide a more accurate understanding of the benefits of using local police to attend cardiac arrests.
Open Access
Gestión de camas hospitalarias durante la pandemia en Navarra con el apoyo de métodos matemáticos de predicción
(Departamento de Salud del Gobierno de Navarra, 2023) Rodrigo Rincón, Isabel; García de Vicuña Bilbao, Daniel; Esparza Artanga, Laida; Santana-Domínguez, Sergio; Martínez-Larrea, Jesús Alfredo; Mallor Giménez, Fermín; Institute of Smart Cities - ISC
Durante la pandemia por coronavirus, en Navarra se utilizaron modelos matemáticos de predicción para estimar las camas necesarias, convencionales y de críticos, para atender a los pacientes COVID-19. Las seis ondas pandémicas presentaron distinta incidencia en la población, ocasionando variabilidad en los ingresos hospitalarios y en la ocupación hospitalaria. La respuesta a la enfermedad de los pacientes no fue constante en cada onda, por lo que, para la predicción de cada una, se utilizaron los datos correspondientes de esa onda. El método de predicción constó de dos partes: una describió la entrada de pacientes al hospital y la otra su estancia dentro del mismo. El modelo requirió de la alimentación a tiempo real de los datos actualizados. Los resultados de los modelos de predicción fueron posteriormente volcados al sistema de información corporativo tipo Business Intelligence. Esta información fue utilizada para planificar el recurso cama y las necesidades de profesionales asociadas a la atención de estos pacientes en el ámbito hospitalario. En la cuarta onda se realizó un análisis para cuantificar el grado de acierto de los modelos predictivos. Los modelos predijeron adecuadamente el pico, la meseta y el cambio de tendencia, pero sobreestimaron los recursos necesarios para la atención de los pacientes en la parte descendente de la curva. El principal punto fuerte de la sistemática utilizada para la construcción de modelos predictivos fue proporcionar modelos en tiempo real con datos recogidos con precisión por los sistemas de información que consiguieron un grado de acierto aceptable permitiendo una utilización inmediata.
Open Access
Early detection of new pandemic waves: control chart and a new surveillance index
(Public Library of Science, 2024) Cildoz Esquíroz, Marta; Gastón Romeo, Martín; Frías Paredes, Laura; García de Vicuña Bilbao, Daniel; Azcárate Camio, Cristina; Mallor Giménez, Fermín; Institute of Smart Cities - ISC
The COVID-19 pandemic highlights the pressing need for constant surveillance, updating of the response plan in post-peak periods and readiness for the possibility of new waves of the pandemic. A short initial period of steady rise in the number of new cases is sometimes followed by one of exponential growth. Systematic public health surveillance of the pandemic should signal an alert in the event of change in epidemic activity within the community to inform public health policy makers of the need to control a potential outbreak. The goal of this study is to improve infectious disease surveillance by complementing standardized metrics with a new surveillance metric to overcome some of their difficulties in capturing the changing dynamics of the pandemic. At statistically-founded threshold values, the new measure will trigger alert signals giving early warning of the onset of a new pandemic wave. We define a new index, the weighted cumulative incidence index, based on the daily new-case count. We model the infection spread rate at two levels, inside and outside homes, which explains the overdispersion observed in the data. The seasonal component of real data, due to the public surveillance system, is incorporated into the statistical analysis. Probabilistic analysis enables the construction of a Control Chart for monitoring index variability and setting automatic alert thresholds for new pandemic waves. Both the new index and the control chart have been implemented with the aid of a computational tool developed in R, and used daily by the Navarre Government (Spain) for virus propagation surveillance during post-peak periods. Automated monitoring generates daily reports showing the areas whose control charts issue an alert. The new index reacts sooner to data trend changes preluding new pandemic waves, than the standard surveillance index based on the 14-day notification rate of reported COVID-19 cases per 100,000 population.