Over the past 20 years, there has been an increase in simulation modeling applied in the health care industry to improve and optimize the various processes such as medical staff scheduling, resource allocation, patient admission, staff-patient ratio, and requirement of inpatient beds. The Covid-19 pandemic has put signification pressure on medical institutions to provide medical assistance to a high volume of patients with limited staff and resources.
Authors have presented discrete event simulation modeling before and during Covid-19 in various process flows, for example, laboratory saliva testing, hospital resource allocation between covid and non-covid patients, patient drive-through testing, and many more. Hospitals and other clinical testing institutions are complex and critical systems where real-time experimentations cannot be performed. Hence, the simulations models helped analyze their situation related to covid-19 and provided recommendations and improvement points, which helped provide quick services and reduced waiting time and queue lengths.
All research papers included in this study are related to discrete event simulation in healthcare during covid-19, except two. The research done by Qureshi, et al. (2019) on the nurse-patient ratio happened before the pandemic; however, it could also be related to the pandemic because of the shortage of nurses in hospitals and increased workload. Another research was conducted by Windeler, et al. (2021) and the team, which was based on converting an existing Ford Motor production line into an emergency ventilator manufacturing line. A shortage of ventilators was forecasted by research done at Imperial College London, for which a Ventilator Challenge UK consortium was formed.
Nurse to patient ratio is a crucial parameter in deciding the care quality and nurse workload; therefore, research was done before the pandemic itself to improve nurse conditions. Qureshi, et al. (2019) developed a simulation model using Rockwell ARENA to analyze the effect of the nurse-patient ratio on the nurse workload and patient care quality. The authors also used Microsoft Vision software to design the floor plan details of a caring unit, such as the nursing station and the number of beds. The data for simulation was obtained from a large urban academic health care center in Canada for a month. The data reports were generated from GRASP software (proprietary information processing software) used by the center. In the simulation model, task priorities, task schedules, and nurse priorities were fed, and simulated nurse agents had to complete those tasks based on the priorities. The nurse would check if there was any task pending in the queue. If there were more than one task, the nurse would complete them based on priority level. If there was more than one task on the same priority, the nearest distance task would be completed first. The model run for ten replications with each replication was of 12 hours. The task in queue time, task queue, missed care, and cumulative distance walked by the agent were the parameters recorded at the end of each simulation run. Nurse workload (tasks in queue: 2, 15, 33) increased with an increase in nurse-to-patient ratio (1:2, 1:4, 1:6). The increase also affected the missed care parameter (17, 24, 53) and task in queue time (0.3, 1, 1.2 hours).
Melman, et al. (2021) studied how different hospital resources are distributed between Covid-19 and non-Covid-19 patients in Addenbrooke’s hospital, UK. The authors developed a DES model in Arena software, v16, to implement patient flows and evaluate the impact of adopted resource allocation strategies on both groups. Patient flows were constructed based upon the data of 475 covid-19 patients and 28,831 non-covid patients in the hospital. Authors created three models based on ICU bed availability, opening/closing of operating theaters, and rejected patients. In the ICU bed model, the system would check the number of beds available on a daily basis, and if there is a shortage of beds (<15), the system would inform to open a new ward; otherwise, the ward should be closed if the availability was greater than 20 bed. The operating theatre model was based on ICU staff utilization rate. If the ICU staff utilization rate exceeded 95%, then operating theatre staff was moved to ICU; else, if ICU staff utilization were less than 90%, they would be delegated to theatre operations. The third model was for bed allocation to the patients. The model would check if a bed was available or not. If no bed were available, the model would put the patient in a waiting queue. A bed would be assigned to the patient if it became available before the maximum waiting time; else, the patient would exit the hospital. Authors found that covid-19 patients are more likely to need critical care, have a more extended stay, and have a significantly higher probability of dying in critical care than non-covid surgical patients.
Kuncová, et al. (2021) simulated the drive-in Covid-19 sample collection operation in one of Prague’s hospitals. Patients arriving by car used drive-in collection points; therefore, the aim of the study was to find the doctors and medics required to reduce the waiting time in queue, and the length of the queue should not exceed 30. The authors collected data from the hospital and interviewed a few doctors and patients, and, based upon that, developed the DES model on SIMUL8. In the model, a patient would enter the drive-in facility and wait in a queue. A doctor/staff member would check the order of the queue, and if there were any problems with a patient (4% probability), the patient would exit the system. The correctly ordered patients would fill out a service form which the medic would check. If there was an issue with the service form, the patient would call the practitioner for verification; else, they would go for sampling. The collected sample would be stored, and the patient would exist in the model. It was found the queue time with only one doctor, and no medic was 83.53 minutes, whereas adding one medic had a huge impact on queuing time, reducing it to 5.78 minutes.
(Hage, et al., 2021) developed a discrete event simulation model in SIMIO package to represent the Covid-19 testing process in the University of Maryland testing center. The model focused on testing operations (such as barcode scanning, uncapping, deswabbing, etc.) being carried out in the laboratory after the arrival of collected samples. The input data was represented based on historical data, onsite observations, and stakeholders’ estimates. Three KPIs (total number of tests conducted per week, average turnaround time from sample collection to return results, percent utilization of resources) were used to measure the performance of the testing systems and evaluate “what-if” scenarios. One hundred runs were performed for each scenario (for example, a longer work shift, increasing technician in uncapping and deswabbing process) to computer distribution and summary statistics for the KPIs. Among different bottlenecks, the deswabbing process had maximum queuing time due to 100% machine utilization. Reducing the need for deswabbing by 70% doubled the entire laboratory capacity, from 33,000 to 63,000 per week. Another key challenge was variation in samples collected at the testing station ranging from 15,000 to 44,000 collected weekly. These variations affect the overall process since the operators and machines would be overloaded during peak season, whereas they would sit idle in low demands.
During the pandemic, it was essential to perform testing at a very high rate to identify and stop the spread of the virus. Saidani, et al. (2021) built a discrete event simulation model using Anylogic software to determine the required number of equipment, machines, and operators and their allocation at different workstations at the University of Illinois Urbana-Champaign campus. The goal was to test 10,000 Covid-19 samples daily and provide the results within 24 hours timeframe. The modeling involved the steps taken after a saliva sample arrives in the laboratory, such as preparing samples, collecting samples into test tubes, followed by pre-testing and testing. Machines and human operators performed 21 different operations. For some sequences of operations, the same operator was assigned to perform the whole sequence of operations before the operator was released. Time distribution for each task was provided by the “Covid-19 Shield” team. One simulation run corresponded to one working day at an actual testing facility that started between 6–8 A.M and stopped between 6–8 P.M. Ten different configurations varying the number of operators in the preparation, transfer, and testing machines were simulated, resulting in the identification of three bottlenecks in the whole process that took maximum time and slowed down the overall testing process. Simulation test #7 out of 10 tests (with 13 operators in preparation, 12 operators in transfer, and four machines in testing) had the optimal resource allocation. It met the goal of testing 10,000 testing vials in the provided time window.
Bartenschlager, et al. (2022) analyzed admission processes of a German maximum care university hospital, the University Hospital of Augsburg, and built a simulation model in Anylogic to replicate the process. The staff arrival and patient arrival flow involved only one step in their process, whereas visitor admission involved several queues, starting with waiting in an initial sitting space. Later, visitors were segregated based on online registration and walk-in, and a separate queue was maintained for individual groups. The study provided recommendations on digitalization, average waiting time in queue, and staff and space utilization for visitor admission flow. Four different processes were constructed based on resource utilization, infection prevention strategies, and visitor restrictions. Data was gathered from the hospital entrance area, and several assumptions were made based on an interview with managers. For instance, only 60% of patients had visitors on weekdays in pandemic lockdown. One hundred simulation runs were performed with a running period of one week for each process configuration. The model performance was measured on mean waiting, service, and utilization time. It was found that the digitalization of the visitor admission process by QR code fast-tracked the flow and reduced the total time of visitors up to 90%. Another important finding was that unlimited admission of visitors was not possible from a management perspective; therefore, there should be a limit on the patient-visitor ratio.
Zemaitis, et al. (2021) used discrete event simulation modeling for an outpatient laboratory clinic, the University of Michigan Canton Health Center, to maintain covid-19 rules and guidelines in the laboratory. Many services were provided in the clinic (diagnostic, curative, consultative). The study’s primary goal was to analyze the blood draw process and reduce the number of patients in the waiting area and the average and maximum queuing time. Simio software was used to create the model using observational data from the clinic. The authors also used Stat::Fit statistical package to fit the observed data and verified the collected data against the electronic health records maintained by the clinic. The blood draw process in the clinic started with a patient entering the premises and performing a check-in. Afterward, the patient waited in the waiting room and differentiated based on being a pediatric or non-pediatric patient. A pediatric patient (five-year-old child or younger) required two technicians to complete a blood draw, unlike a non-pediatric patient (adult) who required only one technician. The authors created three experiments based on (a) the number of staff and staff scheduling, (b) utilization of blood draw stations between pediatric and non-pediatric patients, and © adopting an appointment-based system for patients. The authors found that a minimum of six technicians should be available in the clinic to have minimum waiting time and queue length. Also, allowing the use of resources by all patients would be best for the clinic, helping in reducing the queue length.
Windeler, et al. (2021) and Powertrain Operations Manufacturing Engineering (PTME) team built a simulation model to facilitate the conversion of their Ford Motor Dagenham plant into a ventilator production facility. The team used Lanner’s Witness Horizon simulation software for the simulation purpose. The model was divided into two main areas: Assembly of ventilators, and testing, with five and three subcategories in respective areas. Due to the lack of stable system descriptions and cycle times of each process, the initial model was built on assumptions for cycle time and rejection rate, based on past experiences of the team and discussions held with key stakeholders. As the production progressed, the collected data was fed into the simulation to identify the bottlenecks and speed up the process. Completed Jobs per hour (JPH) of every process was recorded; the “regulator and control assembly” process in the assembly area was performing minimum jobs per hour, constraining the whole assembly flow. Sensitivity analysis of process cycle time, reject rate, and repair time also helped optimize the labor resource between production and repair. With the help of a simulation model, the team was able to predict the throughput of the ventilator production line, including waiting time at each process station.
Nurses interact maximum with the patients, providing them medicine, food, and other support. Therefore, it is crucial to understand the nurse-patient ratio and maintain nurses’ workload to provide high care quality. It is impossible to fine-tune the parameters (nurse-patient ratio, workload, number of tasks) manually because it would increase the number of missed cases and increase injuries. Hence DES has been a promising strategy shown by Qureshi, et al. (2019) to test different nurse-patient ratios and visualize the impact on nurses and patients.
In Melman, et al. (2021) research, three strategies were formulated based on hospital resource allocation: proactive cancellation, reactive cancellation, and ring-fencing capacity. These were tested based on aggregated hospital performance. It was found that a proactive cancellation had fewer surgeries of patients than reactive surgeries but there was no decrease in deaths or acute care rejections. The ring-fencing strategy had increased surgical capacity, but the critical care did not accommodate the increased number of covid-19 patients in a worst-case scenario. According to the simulation results, no best resource allocation strategy could perform well in both base and worst-case scenarios. Nevertheless, the simulation showed the implication of prioritization between covid and non-covid patients and gave recommendations on resolving bottlenecks in worst-case scenarios.
Hage, et al. (2021) worked on scaling the Covid-19 RT-PCR testing facility and provided a few recommendations to decrease the turnaround time inside the lab, such as eliminating the deswabbing step. The lab investigated the different strategies possible for the deswabbing step: hiring additional personnel to remove swabs from samples that arrived or asking the collection sites to discard swabs rather than leaving them inside the test tubes. The lab adopted the latter, which was cheaper and avoided the collection of waste in the testing area. Likewise, the lab also worked on machine utilization rates and upgraded the instruments, which resulted in a high testing capacity. Another important finding was that high variability in demand for testing directly impacted the lab’s performance; the lab could perform much better if the incoming sample rate were stable.
Kuncová, et al. (2021) showed that constructing a simple simulation model and adding one extra resource to the system could highly impact the waiting queue time of the system and reduce the workload of doctors. In the drive-through base model, one resource (doctor) was performing all the operations and was over-utilized. The operator worked at a 97% utilization rate and even during the lunch break provided at the hospital. With the addition of one medical staff, the utilization rate of operator one (doctor) decreased to 68%, which also reduced the average queuing time. Additional two staff members lowered the utilization rate even further, but it would not be an optimal solution.
Many performance indicators were used in Bartenschlager, et al., (2022) research work, such as waiting area space utilization until noon and in the evening, the maximum length of queue (persons), total patients in a queue, total visitors in QR code queue, and resource utilization. Out of four processes modeled by the authors, no single model performed well for all the indicators. Process one was better in staff hours per weekday, but it increased in process two because of separate admission and temperature control. Process three had the minimum number of persons in the queue because of the no visitor policy for an admitted patient; hence, mostly staff and patients (and visitors with those patients) were present in the queue. According to their research, most hospitals in Germany follow the manual registration process. They should move to an online/QR registration process because it would result in a shorter queue and lower waiting times.
In (Saidani, et al., 2021) research work, the authors had a predefined output target of achieving 10,000 sample testing within 11–12 hours every day, rather than just optimizing the existing process. Therefore, with the help of DES, they demonstrated how the resources of the testing facility could be allocated and utilized to achieve the goal. After analyzing the input data gathered by an expert from “COVID-19 Shield: Target, Test, Tell”, it was found that the number of samples collected was maximum in the early days of weeks and on weekends, whereas minimum samples were tested on Wednesday. The developed DES model could provide optimal resource allocation (minimum number of operators and machines) of any testing facility, given the accuracy of input data and the number of samples collected per day.
All the premises and public gathering areas, not restricted to hospitals, had to follow Covid-19 safety rules and regulations (such as maximum people in an area, social distancing, people in a queue) to help reduce the spread of the virus. Zemaitis, et al., (2021) the research was related to a clinical atmosphere that was not directly related to treating covid-19 patients. Implementation of the recommendation (minimum of six technicians in the clinic daily) provided by the authors resulted in enhanced patient experience and improved KPIs. The simulation model helped reduce the queue waiting time and number of people in an area that was crucial to follow the guidelines.
Windeler, et al. (2021) research work was related to the manufacturing assembly process, but it was also indirectly related to the covid-19 healthcare. The use of discrete event modeling in case of emergency showed how important and beneficial it is to do simulation modeling of a new process. Without simulation modeling, it would not be possible to change the existing Ford assembly line into a ventilator production line cost-efficiently and promptly. The authors successfully demonstrated how a new process could be modeled without the availability of any actual data and purely based on the assumptions and expertise of stakeholders. Authors applied DES modeling in all phases: planning, commissioning, production, and decommissioning phase.
It is nearly impossible to change any hospital or clinical process for experimental purposes because it would disturb the whole system and might lead to a fatal injury or death. Therefore, discrete event modeling provides a feasible option to modify and optimize the existing processes. DES also helps identify the utilization rate of different operators involved in the healthcare domain, such as nurses, doctors, medical assistants, and lab technicians. Covid-19 was an unpredictable time, with an exponential increase in patients and a shortage in hospital ICU beds, ventilators, oxygen cylinders, PPE kits, and medical staff. It has been a catalyst that increased simulation modeling in healthcare. DES allows the evaluation of different “what if” scenarios that could arise during brainstorming of new process flows and helps in making data-driven decisions. The existing hospital and clinical processes can be altered based on past data and stakeholders, as seen in most research papers in this study; nevertheless, new processes can also be initiated with the help of discrete event simulation.