A forecasting tool for a hospital to plan inbound transfers of COVID-19 patients from other regions.

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.

Impact of bi-directional electric vehicle and demand response on residential distributed PV capacity planning based on TOU pricing.

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.

Patient-to-nurse ratios: Balancing quality, nurse turnover, and cost.

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.

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.

Assessing needs-based supply of physicians: a criteria-led methodological review of international studies in high-resource settings.

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.

Research on outpatient capacity planning combining lean thinking and integer linear programming.

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.

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.

Leveraging multi-tier healthcare facility network simulations for capacity planning in a pandemic.

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.

Economies of scale and optimal size of maternity services in Belgium: A Data Envelopment Analysis.

This article uses a Data Envelopment Analysis to measure scale efficiency of maternity services in Belgium and estimate the minimum efficient scale in this context. Using administrative data for all maternity services in Belgium in 2016, the minimum efficient scale is estimated at 557 deliveries per year, which is above the currently prevailing norm of 400 deliveries per year. In particular, the closure of 17 small maternity services could improve efficiency without reducing accessibility. In addition to that, further efficiency gains could be attained by increasing the scale of maternity services up to at least 900 deliveries per year. Although most services are close to scale efficiency, the mean scale inefficiency level is 13% and low scores are mainly concentrated among the smallest services. These results are robust to changes in model specifications, bootstrapping and removal of outliers. In the current context of reform of the hospital and maternity landscape in Belgium, this study shows room for improvement and the possibility to generate substantial efficiency gains that could be reinvested in the healthcare system.

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.

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.

Managing capacity for virtual and office appointments in chronic care.

Patients living with a chronic disease often require regular appointments and treatments. Due to the constraints on the availability of office appointments and the capacity of physicians, access to chronic care can be limited; consequently, patients may fail to receive the recommended care suggested by clinical guidelines. Virtual appointments can provide a cost-effective alternative to traditional office appointments for managing chronic conditions. Advances in information technology infrastructure, communication, and connected medical devices are enabling providers to evaluate, diagnose, and treat patients remotely. In this study, we build a capacity allocation model to study the use of virtual appointments in a chronic care setting. We consider a cohort of patients receiving chronic care and model the flow of the patients between office and virtual appointments using an open migration network. We formulate the planning of capacity needed for office and virtual appointments with a newsvendor model to maximize long-run average earnings. We consider differences in treatment and diagnosis effectiveness for office and virtual appointments. We derive optimal capacity allocation policies and implement numerical experiments. With the model developed, capacity decisions for office and virtual appointments can be made more systematically with the consideration of patient disease progressions.

A robust optimization model for tactical capacity planning in an outpatient setting.

Tactical capacity planning is a key element of planning and control decisions in healthcare settings, focusing on the medium-term allocation of a clinic's resources to appointments of different types. One of the most scarce resources in healthcare is physician time. Due to uncertainty in demand for appointments, it is difficult to provide an exact match between the planned physician availability and appointment requests. Our study uses cardinality-constrained robust optimization to develop tactical capacity plans which are robust against uncertainty, providing a feasible allocation of capacity for all realizations of demand to the extent allowed by the budget of uncertainty. The outpatient setting we consider sees first-visit patients and re-visit patients, and both patient types have access time targets. We experimentally evaluate our robust model and its practical implications under different levels of conservatism. We show that we can guarantee 100% feasibility of the robust tactical capacity plan while not being fully conservative, which will lead to the clinic saving money while being able to meet demand despite uncertainty. We also show how the robust model helps us to identify the critical time periods leading to worst case physician peak load, which could be valuable to decision-makers. Throughout the experiments, we find that the step of translating available data into an uncertainty set can influence the true conservatism of a solution.

Markov chain analysis for the neonatal inpatient flow in a hospital.

Discrete-time Markov chain and queueing-theoretic models are used to quantitatively formulate the flow of neonatal inpatients over several wards in a hospital. Parameters of the models are determined from the operational analysis of the record of the numbers of admission/departure for each ward every day and the order log of patient movement from ward to ward for two years provided by the Medical Information Department of the University of Tsukuba Hospital in Japan. Our formulation is based on the analysis of the precise routes (the route of an inpatient is defined as a sequence of the wards in which he/she stays from admission to discharge) and their length-of-stay (LoS) in days in each ward on their routes for all neonatal inpatients. Our theoretical model calculates the probability distribution for the number of patients staying in each ward per day which agrees well with the corresponding histogram observed for each ward as well as for the whole hospital. The proposed method can be used for the long-term capacity planning of hospital wards with respect to the probabilistic bed utilization.

Interactive Multiobjective Procedure for Mixed Problems and Its Application to Capacity Planning.

A problem that appears in many decision models is that of the simultaneous occurrence of deterministic, stochastic, and fuzzy values in the set of multidimensional evaluations. Such problems will be called mixed problems. They lead to the formulation of optimization problems in ordered structures and their scalarization. The aim of the paper is to present an interactive procedure with trade-offs for mixed problems, which helps the decision-maker to make a final decision. Its basic advantage consists of simplicity: after having obtained the solution proposed, the decision-maker should determine whether it is satisfactory and if not, how it should be improved by indicating the criteria whose values should be improved, the criteria whose values cannot be made worse, and the criteria whose values can be made worse. The procedure is applied in solving capacity planning treated as a mixed dynamic programming problem.

Resource optimization for cancer pathways with aggregate diagnostic demand: a perishable inventory approach.

This work proposes a novel framework for planning the capacity of diagnostic tests in cancer pathways that considers the aggregate demand of referrals from multiple cancer specialties (sites). The framework includes an analytic tool that recursively assesses the overall daily demand for each diagnostic test and considers general distributions for both the incoming cancer referrals and the number of required specific tests for any given patient. By disaggregating the problem with respect to each diagnostic test, we are able to model the system as a perishable inventory problem that can be solved by means of generalized G/D/C queuing models, where the capacity [Formula: see text] is allowed to vary and can be seen as a random variable that is adjusted according to prescribed performance measures. The approach aims to provide public health and cancer services with recommendations to align capacity and demand for cancer diagnostic tests effectively and efficiently. Our case study illustrates the applicability of our methods on lung cancer referrals from UK's National Health Service.

Development and cohort study of an audit approach to evaluate patient management in family practice in the UK: the 7S tool.

BACKGROUND: In the UK, there is increased pressure on general practitioners' time due to an increase in (elderly) population and a shortage of general practitioners. This means that time has to be used efficiently, whilst optimizing adherence to consistent, appropriate and timely provision of care. OBJECTIVE(S): Create an audit tool that assists general practitioners and family practice staff to evaluate if patients are managed as effectively as possible, and to test the usefulness of this tool in a family practice. METHODS: The '7S' audit tool has seven outcome elements; these broadly stand for what the actual and desired patient contact outcome was, or should have been. Terms include 'surgery', 'speak' and 'specific other' for an appointment at the practice, by telephone or with a dedicated specialist such as a practice nurse or phlebotomist, respectively. RESULTS: A very small, rural, general practice in the UK was audited using the 7S tool. Five hundred patient contacts were reviewed by an independent general practitioner and the decision made if the mode of contact was appropriate or not for each case; in one of the three cases, the choice of care provision was inappropriate and chronic disease cases contributed most to this. General practitioners instigated the majority of poor patient management choices, and chronic disease patients were frequently seen in suboptimal settings. CONCLUSIONS: Inefficiencies in the management of patients in family practice can be identified with the 7S audit tool, thereby producing evidence for staff education and service reconfiguration.

Multi-objective admission planning problem: a two-stage stochastic approach.

Effective admission planning can improve inpatient throughput and waiting times, resulting in better quality of service. The uncertainty in the patient arrival and the availability of resources makes the patient's allocation difficult to manage. Thus, in the admission process hospitals aim to accomplish targets of resource utilization and to lower the cost of service. Both objectives are related and in conflict. In this paper, we present a bi-objective stochastic optimization model to study the trade-off between the resource utilization and the cost of service, taking into account demand and capacity uncertainties. Real data from the surgery and medical areas of a Chilean public hospital are used to illustrate the approach. The results show that the solutions of our approach outperform the actual practice in the Chilean hospital.

The impact of new cancer drug therapies on site specialised cancer treatment activity in a UK cancer network 2014-2018.

INTRODUCTION: Drug treatment for cancer has changed dramatically over the past decade with many new drugs often with multiple applications. More recently, the detailed pathway for approval from the National Institute for Health and Care Excellence (NICE) in the UK has been simplified. To explore how these changes have impacted on systemic anti-cancer therapy tumour site-specific prescribing and workload activities, we have reviewed the prescribing records for 2014-2018 in a UK cancer network. METHODS: Information about the numbers of new systemic anti-cancer therapy drugs and NICE approvals were obtained from print editions of the British National Formulary (BNF) and the NICE website. Data on the numbers of new chemotherapy courses and individual treatment-related attendances were obtained from the cancer network Chemocare electronic prescribing system. RESULTS: During the five-year study period, there were 49 new systemic anti-cancer therapy drugs for all tumour types, and a total of 65 NICE technology approvals for solid tumour indications. Overall numbers of treatment courses increased by 40.7% and total treatment-related visits by 80.6%. There was a wide variation across tumour types with the highest number of increased visits seen for melanoma (349.3%) and prostate cancer (242.3%), but in contrast, no appreciable increases were seen for lower gastrointestinal cancers or small cell lung cancer. CONCLUSION: The study confirms the major impact of the arrival of new drug technology and positive NICE appraisals on increasing systemic anti-cancer therapy prescribing and chemotherapy unit activity. The data in this study may be of help in planning for future service delivery planning and workforce configurations.

Capacity and patient flow planning in post-term pregnancy outpatient clinics: a computer simulation modelling study.

BACKGROUND: The demand for a large Norwegian hospital's post-term pregnancy outpatient clinic has increased substantially over the last 10 years due to changes in the hospital's catchment area and to clinical guidelines. Planning the clinic is further complicated due to the high did not attend rates as a result of women giving birth. The aim of this study is to determine the maximum number of women specified clinic configurations, combination of specified clinic resources, can feasibly serve within clinic opening times. METHODS: A hybrid agent based discrete event simulation model of the clinic was used to evaluate alternative configurations to gain insight into clinic planning and to support decision making. Clinic configurations consisted of six factors: X0: Arrivals. X1: Arrival pattern. X2: Order of midwife and doctor consultations. X3: Number of midwives. X4: Number of doctors. X5: Number of cardiotocography (CTGs) machines. A full factorial experimental design of the six factors generated 608 configurations. RESULTS: Each configuration was evaluated using the following measures: Y1: Arrivals. Y2: Time last woman checks out. Y3: Women's length of stay (LoS). Y4: Clinic overrun time. Y5: Midwife waiting time (WT). Y6: Doctor WT. Y7: CTG connection WT. Optimisation was used to maximise X0 with respect to the 32 combinations of X1-X5. Configuration 0a, the base case Y1 = 7 women and Y3 = 102.97 [0.21] mins. Changing the arrival pattern (X1) and the order of the midwife and doctor consultations (X2) configuration 0d, where X3, X4, X5 = 0a, Y1 = 8 woman and Y3 86.06 [0.10] mins. CONCLUSIONS: The simulation model identified the availability of CTG machines as a bottleneck in the clinic, indicated by the WT for CTG connection effect on LoS. One additional CTG machine improved clinic performance to the same degree as an extra midwife and an extra doctor. The simulation model demonstrated significant reductions to LoS can be achieved without additional resources, by changing the clinic pathway and scheduling of appointments. A more general finding is that a simulation model can be used to identify bottlenecks, and efficient ways of restructuring an outpatient clinic.