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PURPOSE: Tactical capacity planning is crucial when hospitals must cope with substantial changes in patient requirements, as recently experienced during the Covid-19 pandemic. However, there is only little understanding of the nature of capacity limitations in a hospital, which is essential for effective tactical capacity planning. DESIGN/METHODOLOGY/APPROACH: We report a detailed analysis of capacity limitations at a Norwegian tertiary public hospital and conducted 22 in-depth interviews. The informants participated in capacity planning and decision-making during the Covid-19 pandemic. Data are clustered into categories of capacity limitations and a correspondence analysis provides additional insights. FINDINGS: Personnel and information were the most mentioned types of capacity limitations, and middle management and organizational functions providing specialized treatment felt most exposed to capacity limitations. Further analysis reveals that capacity limitations are dynamic and vary across hierarchical levels and organizational functions. RESEARCH LIMITATIONS/IMPLICATIONS: Future research on tactical capacity planning should take interdisciplinary patient pathways better into account as capacity limitations are dynamic and systematically different for organizational functions and hierarchical levels. PRACTICAL IMPLICATIONS: We argue that our study possesses common characteristics of tertiary public hospitals, including professional silos and fragmentation of responsibilities along patient pathways. Therefore, we recommend operations managers in hospitals to focus more on intra-organizational information flows to increase the agility of their organization. ORIGINALITY/VALUE: Our detailed capacity limitation analysis at a tertiary public hospital in Norway during the Covid-19 pandemic provides novel insights into the nature of capacity limitations, which may enhance tactical capacity planning.

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BACKGROUND: The COVID-19 pandemic has highlighted the critical importance of robust healthcare capacity planning and preparedness for emerging crises. However, healthcare systems must also adapt to more gradual temporal changes in disease prevalence and demographic composition over time. To support proactive healthcare planning, statistical capacity forecasting models can provide valuable information to healthcare planners. This systematic literature review and evidence mapping aims to identify and describe studies that have used statistical forecasting models to estimate healthcare capacity needs within hospital settings. METHOD: Studies were identified in the databases MEDLINE and Embase and screened for relevance before items were defined and extracted within the following categories: forecast methodology, measure of capacity, forecast horizon, healthcare setting, target diagnosis, validation methods, and implementation. RESULTS: 84 studies were selected, all focusing on various capacity outcomes, including number of hospital beds/ patients, staffing, and length of stay. The selected studies employed different analytical models grouped in six items; discrete event simulation (N = 13, 15 %), generalized linear models (N = 21, 25 %), rate multiplication (N = 15, 18 %), compartmental models (N = 14, 17 %), time series analysis (N = 22, 26 %), and machine learning not otherwise categorizable (N = 12, 14 %). The review further provides insights into disease areas with infectious diseases (N = 24, 29 %) and cancer (N = 12, 14 %) being predominant, though several studies forecasted healthcare capacity needs in general (N = 24, 29 %). Only about half of the models were validated using either temporal validation (N = 39, 46 %), cross-validation (N = 2, 2 %) or/and geographical validation (N = 4, 5 %). CONCLUSION: The forecasting models' applicability can serve as a resource for healthcare stakeholders involved in designing future healthcare capacity estimation. The lack of routine performance validation of the used algorithms is concerning. There is very little information on implementation and follow-up validation of capacity planning models.

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Currently, the development of HRESs (hybrid renewable energy systems) in remote areas is of great importance and popularity. However, measuring and optimizing the capacity of these systems faces a difficult challenge. Multiple works had been reported in the literature to optimize such systems, all of which aim to achieve an optimal configuration with minimum annual net cost. Therefore, the significance of providing off-grid electrification to remote areas through HRESs can be highlighted as a crucial case for sustainable growth. Accordingly, the study proposes a modified metaheuristic approach, known as the Hybrid Golden Search Algorithm (HGSA), for long-term application planning and optimization of the off-grid HRES. The aim of this algorithm is to minimize the amount of net cost which is used annually; to reduce the probability of power supply interruption. In order to assess the effectiveness of the proposed algorithm, a simulation study over a long period on a remote area was conducted. From the results, increasing the reliability level from 1 % to 3 % causes a decrease in the total net annual cost by around 7.3 % under the proposed HGSA and also results in a reduction in component size (around 6 % and 21 % reductions for the wind turbine area and storage tanks, respectively). Further, the HGSA technique obtains the lowest value of fitness function for the hybrid system at a reliability level of 3 %, which is 31,539,810$. This result demonstrates that the efficiency of HGSA outperforms Fuzzy Logic and Optimization, Artificial Bee Colony (ABC), and GSA techniques. Based on this, the proposed HGSA could lead to more promising results than the other comparative algorithms. Hence, the proposed HGSA can be a valuable tool for long-term application planning and optimization of off-grid HRES, which can contribute significantly to achieving sustainable development goals.

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The widespread deployment of residential distributed photovoltaic (RDPV) remains complex and challenging due to photovoltaic output intermittency, fluctuating electricity demand, and rising electric vehicle (EV) adoption. Simultaneously, the energy storage capabilities of EVs and residential demand response (DR) offer solutions for optimizing RDPV applications. This study proposes an integrated RDPV capacity planning model by encompassing EV charging, vehicle-to-home, and flexible load DR. Five scenarios are established to reveal the impact of various factors on the optimal photovoltaic installation capacity, electricity cost, self-consumption and self-sufficiency rate. A case study of three typical residential electricity demand patterns indicates that DR and vehicle-to-home significantly reduce the optimal photovoltaic installation capacity and total electricity cost. When the feed-in tariff during photovoltaic generation periods is higher than the off-peak pricing, DR results in a reduction in photovoltaic self-sufficiency rate and an increase in photovoltaic self-consumption rate. EV charging and vehicle-to-home have minimal impact on photovoltaic self-consumption rate, while EV charging significantly decreases self-sufficiency rate and vehicle-to-home exacerbates this effect.

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BACKGROUND: In April 2021, the province of Ontario, Canada, was at the peak of its third wave of the COVID-19 pandemic. Intensive Care Unit (ICU) capacity in the Toronto metropolitan area was insufficient to handle local COVID patients. As a result, some patients from the Toronto metropolitan area were transferred to other regions. METHODS: A spreadsheet-based Monte Carlo simulation tool was built to help a large tertiary hospital plan and make informed decisions about the number of transfer patients it could accept from other hospitals. The model was implemented in Microsoft Excel to enable it to be widely distributed and easily used. The model estimates the probability that each ward will be overcapacity and percentiles of utilization daily for a one-week planning horizon. RESULTS: The model was used from May 2021 to February 2022 to support decisions about the ability to accept transfers from other hospitals. The model was also used to ensure adequate inpatient bed capacity and human resources in response to various COVID-related scenarios, such as changes in hospital admission rates, managing the impact of intra-hospital outbreaks and balancing the COVID response with planned hospital activity. CONCLUSIONS: Coordination between hospitals was necessary due to the high stress on the health care system. A simple planning tool can help to understand the impact of patient transfers on capacity utilization and improve the confidence of hospital leaders when making transfer decisions. The model was also helpful in investigating other operational scenarios and may be helpful when preparing for future outbreaks or public health emergencies.

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This study examines how staff pooling can be used to create a higher service level at a predetermined total capacity in the healthcare sector. We develop new empirical knowledge through a systematic empirical study, using a mixed-methods approach, with a preliminary interview study followed by a principal quantitative survey study, with data from a multihospital system. The purpose was to explore practical barriers for a staff pooling strategy in healthcare systems. Three barriers were identified:recruitment difficulties, community view, and specialisation. Significant differences in perceived height among these barriers were found. The results from this study have important managerial implications for healthcare systems when implementing a staff pooling approach. This study contributes to the existing literature since, to the best of our knowledge, no previous research has been done where barriers to staff pools are systematically identified using a holistic approach that includes all healthcare professions in a multihospital system.

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Aiming at the accuracy of modeling in existing integrated energy system planning methods, a comprehensive energy system p lanning method that takes into account the actual operating efficiency of the system is proposed. First, the output model of various equipment units based on the basic structure of the integrated energy system is established. Then, based on the traditional energy hub model, a correction model for the work efficiency of energy equipment to construct an improved dynamic efficiency model of energy equipment is established. With the goal of minimizing the comprehensive cost of the integrated energy system, an integrated energy system planning operation model that takes into account the operating characteristics of the equipment is proposed. Finally, the planning method proposed in this paper is verified through simulation. The results show that: compared with the traditional planning method based on energy hubs, the method proposed in this paper improves the actual part-load performance of the system by improving the accuracy of energy coupling equipment, making the proposed planning model more reasonable and economical.

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We consider the problem of setting appropriate patient-to-nurse ratios in a hospital, an issue that is both complex and widely debated. There has been only limited effort to take advantage of the extensive empirical results from the medical literature to help construct analytical decision models for developing upper limits on patient-to-nurse ratios that are more patient- and nurse-oriented. For example, empirical studies have shown that each additional patient assigned per nurse in a hospital is associated with increases in mortality rates, length-of-stay, and nurse burnout. Failure to consider these effects leads to disregarded potential cost savings resulting from providing higher quality of care and fewer nurse turnovers. Thus, we present a nurse staffing model that incorporates patient length-of-stay, nurse turnover, and costs related to patient-to-nurse ratios. We present results based on data collected from three participating hospitals, the American Hospital Association (AHA), and the California Office of Statewide Health Planning and Development (OSHPD). By incorporating patient and nurse outcomes, we show that lower patient-to-nurse ratios can potentially provide hospitals with financial benefits in addition to improving the quality of care. Furthermore, our results show that higher policy patient-to-nurse ratio upper limits may not be as harmful in smaller hospitals, but lower policy patient-to-nurse ratios may be necessary for larger hospitals. These results suggest that a "one ratio fits all" patient-to-nurse ratio is not optimal. A preferable policy would be to allow the ratio to be hospital-dependent.

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This paper presents a three-step conceptual framework that can be used to structure the care-related capacity planning process in a nursing home context. The proposed framework provides a sound practical vehicle to organise client-centred care without overstretching available capacity. Within this framework, an MILP for shift scheduling and a Genetic Algorithm (GA) for task-scheduling are proposed. To investigate the performance of the proposed framework, it is benchmarked against the current situation. The results show that considerable improvements can be achieved in terms of efficiency and waiting time. More specifically, it is shown that very modest waiting times can be achieved without exceeding available capacity, despite the fluctuations in care demand across the day.

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INTRODUCTION: Algorithm-enabled remote patient monitoring (RPM) programs pose novel operational challenges. For clinics developing and deploying such programs, no standardized model is available to ensure capacity sufficient for timely access to care. We developed a flexible model and interactive dashboard of capacity planning for whole-population RPM-based care for T1D. METHODS: Data were gathered from a weekly RPM program for 277 paediatric patients with T1D at a paediatric academic medical centre. Through the analysis of 2 years of observational operational data and iterative interviews with the care team, we identified the primary operational, population, and workforce metrics that drive demand for care providers. Based on these metrics, an interactive model was designed to facilitate capacity planning and deployed as a dashboard. RESULTS: The primary population-level drivers of demand are the number of patients in the program, the rate at which patients enrol and graduate from the program, and the average frequency at which patients require a review of their data. The primary modifiable clinic-level drivers of capacity are the number of care providers, the time required to review patient data and contact a patient, and the number of hours each provider allocates to the program each week. At the institution studied, the model identified a variety of practical operational approaches to better match the demand for patient care. CONCLUSION: We designed a generalizable, systematic model for capacity planning for a paediatric endocrinology clinic providing RPM for T1D. We deployed this model as an interactive dashboard and used it to facilitate expansion of a novel care program (4 T Study) for newly diagnosed patients with T1D. This model may facilitate the systematic design of RPM-based care programs.

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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.

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BACKGROUND: Many health systems embrace the normative principle that the supply of health services ought to be based on the need for healthcare. However, a theoretically grounded framework to operationalize needs-based supply of healthcare remains elusive. The aim of this paper is to critically assess current methodologies that quantify needs-based supply of physicians and identify potential gaps in approaches for physician planning. To this end, we propose a set of criteria for consideration when estimating needs-based supply. METHODS: We conducted searches in three electronic bibliographic databases until March 2020 supplemented by targeted manual searches on national and international websites to identify studies in high-resource settings that quantify needs-based supply of physicians. Studies that exclusively focused on forecasting methods of physician supply, on inpatient care or on healthcare professionals other than physicians were excluded. Additionally, records that were not available in English or German were excluded to avoid translation errors. The results were synthesized using a framework of study characteristics in addition to the proposed criteria for estimating needs-based physician supply. RESULTS: 18 quantitative studies estimating population need for physicians were assessed against our criteria. No study met all criteria. Only six studies sought to examine the conceptual dependency between need, utilization and supply. Apart from extrapolations, simulation models were applied most frequently to estimate needs-based supply. 12 studies referred to the translation of need for services with respect to a physician's productivity, while the rest adapted existing population-provider-ratios. Prospective models for estimating future care needs were largely based on demographic predictions rather than estimated trends in morbidity and new forms of care delivery. CONCLUSIONS: The methodological review shows distinct heterogeneity in the conceptual frameworks, validity of data basis and modeling approaches of current studies in high-resource settings on needs-based supply of physicians. To support future estimates of needs-based supply, this review provides a workable framework for policymakers in charge of health workforce capacity planning.

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BACKGROUND: The size and cost of outpatient capacity directly affect the operational efficiency of a whole hospital. Many scholars have faced the study of outpatient capacity planning from an operations management perspective. OBJECTIVE: The outpatient service is refined, and the quantity allocation problem of each type of outpatient service is modeled as an integer linear programming problem. Thus, doctors' work efficiency can be improved, patients' waiting time can be effectively reduced, and patients can be provided with more satisfactory medical services. METHODS: Outpatient service is divided into examination and diagnosis service according to lean thinking. CPLEX is used to solve the integer linear programming problem of outpatient service allocation, and the maximum working time is minimized by constraint solution. RESULTS: A variety of values are taken for the relevant parameters of the outpatient service, using CPLEX to obtain the minimum and maximum working time corresponding to each situation. Compared with no refinement stratification, the work efficiency of senior doctors has increased by an average of 25%. In comparison, the patient flow of associate senior doctors has increased by an average of 50%. CONCLUSION: In this paper, the method of outpatient capacity planning improves the work efficiency of senior doctors and provides outpatient services for more patients in need; At the same time, it indirectly reduces the waiting time of patients receiving outpatient services from senior doctors. And the patient flow of the associate senior doctors is improved, which helps to improve doctors' technical level and solve the problem of shortage of medical resources.

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The goals for increased patient access and fast fulfillment have motivated considerable interest in autologous cell therapy manufacturing networks having multiple and geographically distributed manufacturing facilities. However, the cost of safety manufacturing capacity to mitigate supplier disruption risk-a significant risk in the emerging cell manufacturing industry-would be lower if manufacturing is centralized. In this paper, we analyze a decentralized network that has as its objective to minimize the cost of network resilience for mitigating supplier disruption by making use of the fact that bioreactors for autologous therapy manufacturing are small enough to be relocatable. We model this problem as a Markov decision process and develop efficient algorithms that are based on real-time demand data to minimize safety manufacturing capacity and determine how relocatable capacity should be distributed while satisfying resilience constraints. In case studies, based in part on data collected from a Chimeric antigen receptor T cell therapy manufacturing facility at the University of Pennsylvania, we compare decentralized network models with different heuristic algorithms. Results indicate that transshipment in a decentralized network can result in a significant reduction of required safety capacity, reducing the cost of network resilience.

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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.

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The COVID-19 pandemic has placed severe demands on healthcare facilities across the world, and in several countries, makeshift COVID-19 centres have been operationalised to handle patient overflow. In developing countries such as India, the public healthcare system (PHS) is organised as a hierarchical network with patient flows from lower-tier primary health centres (PHC) to mid-tier community health centres (CHC) and downstream to district hospitals (DH). In this study, we demonstrate how a network-based modelling and simulation approach utilising generic modelling principles can (a) quantify the extent to which the existing facilities in the PHS can effectively cope with the forecasted COVID-19 caseload; and (b) inform decisions on capacity at makeshift COVID-19 Care Centres (CCC) to handle patient overflows. We apply the approach to an empirical study of a local PHS comprising ten PHCs, three CHCs, one DH and one makeshift CCC. Our work demonstrates how the generic modelling approach finds extensive use in the development of simulations of multi-tier facility networks that may contain multiple instances of generic simulation models of facilities at each network tier. Further, our work demonstrates how multi-tier healthcare facility network simulations can be leveraged for capacity planning in health crises.

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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.

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Comparing international or regional hospital bed numbers is not an easy matter, and a pragmatic method has been proposed that plots the number of beds per 1000 deaths versus the log of deaths per 1000 population. This method relies on the fact that 55% of a person's lifetime hospital bed utilization occurs in the last year of life-irrespective of the age at death. This is called the nearness to death effect. The slope and intercept of the logarithmic relationship between the two are highly correlated. This study demonstrates how lines of equivalent bed provision can be constructed based on the value of the intercept. Sweden looks to be the most bed-efficient country due to long-term investment in integrated care. The potential limitations of the method are illustrated using data from English Clinical Commissioning Groups. The main limitation is that maternity, paediatric, and mental health care do not conform to the nearness to death effect, and hence, the method mainly applies to adult acute care, especially medical and critical care bed numbers. It is also suggested that sensible comparison can only be made by comparing levels of occupied beds rather than available beds. Occupied beds measure the expressed bed demand (although often constrained by access to care issues), while available beds measure supply. The issue of bed supply is made complex by the role of hospital size on the average occupancy margin. Smaller hospitals are forced to operate at a lower average occupancy; hence, countries with many smaller hospitals such as Germany and the USA appear to have very high numbers of available beds. The so-called 85% occupancy rule is an "urban myth" and has no fundamental basis whatsoever. The very high number of "hospital" beds in Japan is simply an artefact arising from "nursing home" beds being counted as a "hospital" bed in this country. Finally, the new method is applied to the expressed demand for occupied acute beds in Australian states. Using data specific to acute care, i.e., excluding mental health and maternity, a long-standing deficit of beds was identified in Tasmania, while an unusually high level of occupied beds in the Northern Territory (NT) was revealed. The high level of demand for beds in the NT appears due to an exceptionally large population of indigenous people in this state, who are recognized to have elevated health care needs relative to non-indigenous Australians. In this respect, indigenous Australians use 3.5 times more occupied bed days per 1000 deaths (1509 versus 429 beds per 1000 deaths) and 6 times more occupied bed days per 1000 population (90 versus 15 beds per 1000 population) than their non-indigenous counterparts. The figure of 1509 beds per 1000 deaths (or 4.13 occupied beds per 1000 deaths) for indigenous Australians is indicative of a high level of "acute" nursing care in the last months of life, probably because nursing home care is not readily available due to remoteness. A lack of acute beds in the NT then results in an extremely high average bed occupancy rate with contingent efficiency and delayed access implications.

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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.

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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.

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