A queuing model for ventilator capacity management during the COVID-19 pandemic.

We applied a queuing model to inform ventilator capacity planning during the first wave of the COVID-19 epidemic in the province of British Columbia (BC), Canada. The core of our framework is a multi-class Erlang loss model that represents ventilator use by both COVID-19 and non-COVID-19 patients. Input for the model includes COVID-19 case projections, and our analysis incorporates projections with different levels of transmission due to public health measures and social distancing. We incorporated data from the BC Intensive Care Unit Database to calibrate and validate the model. Using discrete event simulation, we projected ventilator access, including when capacity would be reached and how many patients would be unable to access a ventilator. Simulation results were compared with three numerical approximation methods, namely pointwise stationary approximation, modified offered load, and fixed point approximation. Using this comparison, we developed a hybrid optimization approach to efficiently identify required ventilator capacity to meet access targets. Model projections demonstrate that public health measures and social distancing potentially averted up to 50 deaths per day in BC, by ensuring that ventilator capacity was not reached during the first wave of COVID-19. Without these measures, an additional 173 ventilators would have been required to ensure that at least 95% of patients can access a ventilator immediately. Our model enables policy makers to estimate critical care utilization based on epidemic projections with different transmission levels, thereby providing a tool to quantify the interplay between public health measures, necessary critical care resources, and patient access indicators.

Evaluating a Covid-19 Vaccine Centre in the UK Using a DES Model

Efficient management of a Covid-19 vaccine centre (VC) is necessary for proper-functioning of a mass vaccination programme. This study reports on an evaluation of the operational performance of a VC. There are two key considerations: the VC capacity (patients per hour) and the patient flow-time (total time patients spent in the centre). In this paper, Witness Horizon a simulation model tool that can be used to enhance the effectiveness of vaccination facilities is introduced. The model is developed using discrete event simulation. The model utilises animation whilst dynamically displaying key performance indicators. The uniqueness of this approach is the ability to simulate and analyse VC scenarios stochastically by varying hourly arrivals, walk-ins to drive-in ratios, staffing levels, registration, immunization, and observation capacities. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

LOCATION AND CAPACITY PLANNING FOR PREVENTIVE HEALTHCARE FACILITIES WITH CONGESTION EFFECTS

A painful lesson got from pandemic COVID-19 is that preventive healthcare service is of utmost importance to governments since it can make massive savings on healthcare expenditure and promote the welfare of the society. Recognizing the importance of preventive healthcare, this research aims to present a methodology for designing a network of preventive healthcare facilities in order to prevent diseases early. The problem is formulated as a bilevel non-linear integer programming model. The upper level is a facility location and capacity planning problem under a limited budget, while the lower level is a user choice problem that determines the allocation of clients to facilities. A genetic algorithm (GA) is developed to solve the upper level problem and a method of successive averages (MSA) is adopted to solve the lower level problem. The model and algorithm is applied to analyze an illustrative case in the Sioux Falls transport network and a number of interesting results and managerial insights are provided. It shows that solutions to medium-scale instances can be obtained in a reasonable time and the marginal benefit of investment is decreasing. © 2023, Journal of Industrial and Management Optimization. All Rights Reserved.

Using DES to Improve the Efficiency of a Covid-19 Vaccination Centre

Many research and development teams around the world have developed and continue to improve Covid-19 vaccines. As vaccines are produced, preparedness and planning for mass vaccination and immunization has become an important aspect of the pandemic management. Mass vaccination has been used by public health agencies in the past and is a viable option for Covid-19 immunization. To be able to rapidly and safely immunize a large number of people against Covid-19, mass vaccination centres are accessible in the UK. Careful planning of these centres is a difficult and important job. Two key considerations are the capacity of each centre (measured as the number of patients served per hour) and the time (in minutes) spent by patients in the centre. This paper discusses a simulation study done to support this planning effort. In this paper, we explore the operations of a vaccination centre and use a simulation tool to enhance patient flow. The discrete event simulation (DES) tool outputs visually and numerically show the average and maximum patient flow times and the number of people that can be served (throughput values) under different number of patient arrivals (hourly). With some experimentation, the results show that marginally reducing the hourly arrival rate, patient congestion reduces enabling good patient service levels to be achieved. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

A NOVEL SIMULATION-BASED TWO-STAGE OPTIMIZATION APPROACH FOR NURSE PLANNING

Maintaining the dynamism of the work scheduling of the nurses without causing them to lose their work motivation provides the sustainability of the effectiveness of health services. Thus, there is a need to develop patient-centred operational research approach applied to health services against new Covid19 waves or new pandemics. In this context, the aim of this study is to develop a novel simulation-based two-stage optimization approach to determine the required number of nurses and schedule the shifts of the nurse working in the Covid19 inpatient service in a Turkish State Hospital. We develop our model in three stages: 1) A simulation model is developed to specify the weekly required number of nurses and run for the scenarios based on demand increases and patient activity, 2) The first mathematical model is used to determine the weekly number of shifts, and 3) The second mathematical model is applied to prepare a fair nurse shift schedule in the pandemic service. This paper suggests a crucial study that will provide managers of healthcare services to plan ahead for personnel needs problems that may take place in the next waves of the Covid19 pandemic in advance. [ FROM AUTHOR]

A queueing Network approach for capacity planning and patient Scheduling: A case study for the COVID-19 vaccination process in Colombia.

This paper considers the problem of patient scheduling and capacity planning for the vaccination process during the COVID-19 pandemic. The proposed solution is based on a non-linear mathematical modeling approach representing the dynamics of an open Jackson Network and a Generalized Network. To test these models, we proposed three objective functions and analyzed different configurations of the process corresponding to various levels of the models' parameters as well as the conditions present in the case study. To assess the computational performance of the models, we also experimented with larger instances in terms of number of steps or stations used and number of patients scheduled. The computational results show how parameters such as the minimum percentage of patients served, the maximum occupation allowed per station and the objective functions used have an impact on the configuration of the process. The proposed approach can support the decision-making process in vaccination centers to efficiently assign human and material resources to maximize the number of patients vaccinated while ensuring reasonable waiting times, number of patients in queue and servers' utilization rates, which in turn are key to avoid overcrowding and other negative conditions in the system that could increase the risk of infections.

Predicting the LOS for Capacity Planning in the Covid-19 Era Using Machine Learning Algorithms

Due to the global pandemic of a novel coronavirus, many hospitals started running low on beds, ventilators, and staff. Therefore, it is extremely essential to predict the patient's Length of Stay (LOS) to observe a dynamic estimation for the hospital's capacity. In this work, different machine learning prediction algorithms were deployed for predicting the patients' LOS based on eleven classes. The prediction algorithm's performance was evaluated using the following performance parameters: accuracy, AUROC, sensitivity, and specificity. The maximum predicting accuracy was obtained using the CatBoost algorithm and it was found to be 0.46 while the corresponding sensitivity and specificity were 0.25 and 0.93, respectively. As an attempt for further accuracy boosting, the number of classes was reduced to five classes. This number of classes was derived from the elbow diagram. Two methods for combining the eleven classes into five classes were introduced. Finally, the predictivity of the different algorithms for the updated classes was investigated and feature selection was applied for reducing complexity and improving the models' accuracy. A considerable improvement was observed when reducing the number of classes where the highest accuracy was also achieved using the CatBoost algorithm and it was equal to 0.68. © 2022 IISE Annual Conference and Expo 2022. All rights reserved.

Variability Scaling and Capacity Planning in Covid-19 Pandemic

Capacity planning is a very important global challenge in the face of Covid-19 pandemic. In order to hedge against the fluctuations in the random demand and to take advantage of risk pooling effect, one needs to have a good understanding of the variabilities in the demand of resources. However, Covid-19 predictive models that are widely used in capacity planning typically often predict the mean values of the demands (often through the predictions of the mean values of the confirmed cases and deaths) in both the temporal and spatial dimensions. They seldom provide trustworthy prediction or estimation of demand variabilities, and therefore, are insufficient for proper capacity planning. Motivated by the literature on variability scaling in the areas of physics and biology, we discovered that in the Covid-19 pandemic, both the confirmed cases and deaths exhibit a common variability scaling law between the average of the demand μ and its standard deviation σ, that is, σ∝μβ, where the scaling parameter β is typically in the range of 0.65 to 1, and the scaling law exists in both the temporal and spatial dimensions. Based on the mechanism of contagious diseases, we further build a stylized network model to explain the variability scaling phenomena. We finally provide simple models that may be used for capacity planning in both temporal and spatial dimensions, with only the predicted mean demand values from typical Covid-19 predictive models and the standard deviations of the demands derived from the variability scaling law.

A pragmatic method to compare international critical care beds: Implications to pandemic preparedness and non-pandemic planning.

BACKGROUND: The current method for assessing critical care (CCU) bed numbers between countries is unreliable. METHODS: A pragmatic method is presented using a logarithmic relationship between CCU beds per 1000 deaths and deaths per 1000 population, both of which are readily available. The method relies on the importance of the nearness to death effect, and on the effect of population size. RESULTS: The method was tested using CCU bed numbers from 65 countries. A series of logarithmic relationships can be seen. High versus low countries can be distinguished by adjusting all countries to a common crude mortality rate. Hence at 9.5 deaths per 1000 population 'high' CCU bed countries average of around 30 CCU beds per 1000 deaths, while 'very low' countries only average 3 CCU beds per 1000 deaths. The United Kingdom falls among countries with low critical care provision with an average of 8 CCU beds per 1000 deaths, and during the COVID-19 epidemic UK industry intervened to rapidly manufacture various types of ventilators to avoid a catastrophe. CCU bed numbers in India are around 8.1 per 1000 deaths, which places it in the low category. However, such beds are inequitably distributed with the poorest states all in the 'very low' category. In India only around 50% of CCU beds have a ventilator. CONCLUSION: A feasible region is defined for the optimum number of CCU beds.

Managing medical equipment capacity with early spread of infection in a region.

We develop a model for a regional decision-maker to analyze the requirement of medical equipment capacity in the early stages of a spread of infections. We use the model to propose and evaluate ways to manage limited equipment capacity. Early-stage infection growth is captured by a stochastic differential equation (SDE) and is part of a two-period community spread and shutdown model. We use the running-maximum process of a geometric Brownian motion to develop a performance metric, probability of breach, for a given capacity level. Decision-maker estimates costs of economy versus health and the time till the availability of a cure; we develop a heuristic rule and an optimal formulation that use these estimates to determine the required medical equipment capacity. We connect the level of capacity to a menu of actions, including the level and timing of shutdown, shutdown effectiveness, and enforcement. Our results show how these actions can compensate for the limited medical equipment capacity in a region. We next address the sharing of medical equipment capacity across regions and its impact on the breach probability. In addition to traditional risk-pooling, we identify a peak-timing effect depending on when infections peak in different regions. We show that equipment sharing may not benefit the regions when capacity is tight. A coupled SDE model captures the messaging coordination and movement across regional borders. Numerical experiments on this model show that under certain conditions, such movement and coordination can synchronize the infection trajectories and bring the peaks closer, reducing the benefit of sharing capacity.

A Machine Learning Approach to Daily Capacity Planning in E-Commerce Logistics

Due to the accelerated activity in e-commerce especially since the COVID-19 outbreak, the congestion in the transportation systems is continually increasing, which affects on-time delivery of regular parcels and groceries. An important constraint is the fact that a given number of delivery drivers have a limited amount of time and daily capacity, leading to the need for effective capacity planning. In this paper, we employ a Gaussian Process Regression (GPR) approach to predict the daily delivery capacity of a fleet starting their routes from a cross-dock depot and for a specific time slot. Each prediction specifies how many deliveries in total the drivers in a given cross-dock can make for a certain time-slot of the day. Our results show that the GPR model outperforms other state-of-the-art regression methods. We also improve our model by updating it daily using shipments delivered within the day, in response to unexpected events during the day, as well as accounting for special occasions like Black Friday or Christmas. © 2022, Springer Nature Switzerland AG.

Optimization and Adaptation of a Resource Planning Tool for Hospitals Under Special Consideration of the COVID-19 Pandemic

Hospitals and health-care institutions need to plan the resources required for handling the increased load, i.e., beds and ventilators during the COVID-19 pandemic. BaBSim.Hospital, an open-source tool for capacity planning based on discrete event simulation, was developed over the last year to support doctors, administrations, health authorities, and crisis teams in Germany. To obtain reliable results, 29 simulation parameters such as durations and probabilities must be specified. While reasonable default values were obtained in detailed discussions with medical professionals, the parameters have to be regularly and automatically optimized based on current data. We investigate how a set of parameters that is tailored to the German health system can be transferred to other regions. Therefore, we use data from the UK. Our study demonstrates the flexibility of the discrete event simulation approach. However, transferring the optimal German parameter settings to the UK situation does not work-parameter ranges must be modified. The adaptation has been shown to reduce simulation error by nearly 70%. The simulation-via-optimization approach is not restricted to health-care institutions, it is applicable to many other real-world problems, e.g., the development of new elevator systems to cover the last mile or simulation of student flow in academic study periods. © 2021 European Union

Staffing and Capacity Planning for SARS-CoV-2 Monoclonal Antibody Infusion Facilities: A Performance Estimation Calculator Based on Discrete-Event Simulations.

Background: The COVID-19 pandemic has significantly stressed healthcare systems. The addition of monoclonal antibody (mAb) infusions, which prevent severe disease and reduce hospitalizations, to the repertoire of COVID-19 countermeasures offers the opportunity to reduce system stress but requires strategic planning and use of novel approaches. Our objective was to develop a web-based decision-support tool to help existing and future mAb infusion facilities make better and more informed staffing and capacity decisions. Materials and Methods: Using real-world observations from three medical centers operating with federal field team support, we developed a discrete-event simulation model and performed simulation experiments to assess performance of mAb infusion sites under different conditions. Results: 162,000 scenarios were evaluated by simulations. Our analyses revealed that it was more effective to add check-in staff than to add additional nurses for middle-to-large size sites with ≥2 infusion nurses; that scheduled appointments performed better than walk-ins when patient load was not high; and that reducing infusion time was particularly impactful when load on resources was only slightly above manageable levels. Discussion: Physical capacity, check-in staff, and infusion time were as important as nurses for mAb sites. Health systems can effectively operate an infusion center under different conditions to provide mAb therapeutics even with relatively low investments in physical resources and staff. Conclusion: Simulations of mAb infusion sites were used to create a capacity planning tool to optimize resource utility and allocation in constrained pandemic conditions, and more efficiently treat COVID-19 patients at existing and future mAb infusion sites.

Testing facility location and dynamic capacity planning for pandemics with demand uncertainty.

The outbreak of coronavirus disease 2019 (COVID-19) has seriously affected the whole world, and epidemic research has attracted increasing amounts of scholarly attention. Critical facilities such as warehouses to store emergency supplies and testing or vaccination sites could help to control the spread of COVID-19. This paper focuses on how to locate the testing facilities to satisfy the varying demand, i.e., test kits, caused by pandemics. We propose a two-phase optimization framework to locate facilities and adjust capacity during large-scale emergencies. During the first phase, the initial prepositioning strategies are determined to meet predetermined fill-rate requirements using the sample average approximation formulation. We develop an online convex optimization-based Lagrangian relaxation approach to solve the problem. Specifically, to overcome the difficulty that all scenarios should be addressed simultaneously in each iteration, we adopt an online gradient descent algorithm, in which a near-optimal approximation for a given Lagrangian dual multiplier is constructed. During the second phase, the capacity to deal with varying demand is adjusted dynamically. To overcome the inaccuracy of long-term prediction, we design a dynamic allocation policy and adaptive dynamic allocation policy to adjust the policy to meet the varying demand with only one day's prediction. A comprehensive case study with the threat of COVID-19 is conducted. Numerical results have verified that the proposed two-phase framework is effective in meeting the varying demand caused by pandemics. Specifically, our adaptive policy can achieve a solution with only a 3.3% gap from the optimal solution with perfect information.

Cope with the COVID-19 pandemic: Dynamic bed allocation and patient subsidization in a public healthcare system.

In many countries and territories, public hospitals play a major role in coping with the COVID-19 pandemic. For public hospital managers, on the one hand, they must best utilize their hospital beds to serve the COVID-19 patients immediately. On the other hand, they need to consider the need of bed resources from non-COVID-19 patients, including emergency and elective patients. In this work, we consider two control mechanisms for public hospital managers to maximize the overall utility of patients. One is the dynamic allocation of bed resources according to the evolution process of the COVID-19 pandemic. The other is the usage of a subsidy scheme to move elective patients from the public to private hospitals. We develop a dynamic programming model to study the allocation of isolation and ordinary beds and the effect of the subsidy policy in serving three types of patients, COVID-19, emergency, and elective-care. We first show that the dynamic allocation between isolation and ordinary beds can provide a better utilization of bed resources, by cutting down at least 33.5% of the total cost compared with the static policy (i.e., keeping a fixed number of isolation beds) when facing a medium pandemic alert. Our results further show that subsidizing elective patients and referring them to private hospitals is an efficient way to ease the overcrowded situation in public hospitals. Our results demonstrate that, by dynamically conducting bed allocation and subsidy scheme in different phases of the COVID-19 pandemic, patient overall utility can be greatly improved.

COVID-19 Pandemic Planning: Simulation Models to Predict Biochemistry Test Capacity for Patient Surges.

BACKGROUND: Patient surges beyond hospital capacity during the initial phase of the COVID-19 pandemic emphasized a need for clinical laboratories to prepare test processes to support future patient care. The objective of this study was to determine if current instrumentation in local hospital laboratories can accommodate the anticipated workload from COVID-19 infected patients in hospitals and a proposed field hospital in addition to testing for non-infected patients. METHODS: Simulation models predicted instrument throughput and turn-around-time for chemistry, ion-selective-electrode, and immunoassay tests using vendor-developed software with different workload scenarios. The expanded workload included tests from anticipated COVID patients in 2 local hospitals and a proposed field hospital with a COVID-specific test menu in addition to the pre-pandemic workload. RESULTS: Instrumentation throughput and turn-around time at each site was predicted. With additional COVID-patient beds in each hospital, the maximum throughput was approached with no impact on turnaround time. Addition of the field hospital workload led to significantly increased test turnaround times at each site. CONCLUSIONS: Simulation models depicted the analytic capacity and turn-around times for laboratory tests at each site and identified the laboratory best suited for field hospital laboratory support during the pandemic.

Measure what matters: Counts of hospitalized patients are a better metric for health system capacity planning for a reopening.

OBJECTIVE: Responding to the COVID-19 pandemic requires accurate forecasting of health system capacity requirements using readily available inputs. We examined whether testing and hospitalization data could help quantify the anticipated burden on the health system given shelter-in-place (SIP) order. MATERIALS AND METHODS: 16,103 SARS-CoV-2 RT-PCR tests were performed on 15,807 patients at Stanford facilities between March 2 and April 11, 2020. We analyzed the fraction of tested patients that were confirmed positive for COVID-19, the fraction of those needing hospitalization, and the fraction requiring ICU admission over the 40 days between March 2nd and April 11th 2020. RESULTS: We find a marked slowdown in the hospitalization rate within ten days of SIP even as cases continued to rise. We also find a shift towards younger patients in the age distribution of those testing positive for COVID-19 over the four weeks of SIP. The impact of this shift is a divergence between increasing positive case confirmations and slowing new hospitalizations, both of which affects the demand on health systems. CONCLUSION: Without using local hospitalization rates and the age distribution of positive patients, current models are likely to overestimate the resource burden of COVID-19. It is imperative that health systems start using these data to quantify effects of SIP and aid reopening planning.