Administrative days in acute care facilities: a queueing-analytic approach.

After acute care services are no longer required, a patient in an acute care hospital often must remain there while he or she awaits the provision of extended care services by a nursing home, through social support services, or by a home health care service. This waiting period is often referred to as "administrative days" because the time is spent in the acute facility not for medical reasons, but rather for administrative reasons. In this paper we use a queueing-analytic approach to describe the process by which patients await placement. We model the situation using a state-dependent placement rate for patients backed up in the acute care facility. We compare our model results with data collected from a convenience sample of 7 hospitals in New York State. We conclude with a discussion of the policy implications of our models.     

A queueing model for bed-occupancy management and planning of hospitals

The aim of this paper is, on the one hand, to describe the movement of patients through a hospital department by using classical queueing theory and, on the other hand, to present a way of optimising the use of hospital resources in order to improve hospital care. A queueing model is used to determine the main characteristics of the access of patients to hospital, such as mean bed occupancy and the probability that a demand for hospital care is lost because all beds are occupied. Moreover, we present a technique for optimising the number of beds in order to maintain an acceptable delay probability at a sufficiently low level and, finally, a way of optimising the average cost per day by balancing costs of empty beds against costs of delayed patients.     

Modelling the requirement for supplementary nurses in an intensive care unit

The intensive care unit (ICU) of a hospital is an essential yet costly resource. Consequently, intensive care modelling has become increasingly prevalent in recent years in attempts to increase efficiency and reduce costs. Previous models have usually assumed that the numbers of beds available are restricted; when all beds are occupied, any additional patients are referred elsewhere or elective surgeries are cancelled. In this study, activities at the ICU at a large teaching hospital were modelled using data relating to all admissions to the ICU during the year 2000—a total of 1084 admissions. The unit is unusual in that the majority of patients referred for intensive care therapy are admitted. Bed numbers are increased when necessary to cope with demand. However, nurses are a restricted resource. In order to maintain the required nurse:patient ratio of at least one:one, supplementary nurses are employed during busy periods. Supplementary nurse costs are substantial and so nurse utilization must be closely monitored. The development of a model that calculates the required number of supplementary nurses per shift, and also encapsulates the time-dependent nature of elective surgery admissions and complex duration-of-stay profiles, is presented in this paper. In particular, the model is used to determine the number of rostered nurses that are required to minimize overall nursing staff costs.     

Managing the overflow of intensive care patients

Many hospitals in the Netherlands are confronted with capacity problems at their intensive care units (ICUs) resulting in cancelling operations, overloading the staff with extra patients, or rejecting emergency patients. In practice, the last option is a common choice because for legal reasons, as well as for hospital logistics, rejecting emergency patients has minimal consequences for the hospital. As a result, emergency patients occasionally have to be transported to hospitals far away. In this work, we propose a cooperative solution for the ICU capacity problem. In our model, several hospitals in a region jointly reserve a small number of beds for regional emergency patients. We present a mathematical method for computing the number of regional beds for any given acceptance rate. The analytic approach is inspired by overflow models in telecommunication systems with multiple streams of telephone calls. Simulation studies show that our model is quite accurate. We conclude that cooperation between hospitals helps to achieve a high acceptance level with a smaller number of beds resulting in improved service for all patients.     

An integrated approach for scheduling health care activities in a hospital

To effectively utilise hospital beds, operating rooms (OR) and other treatment spaces, it is necessary to precisely plan patient admissions and treatments in advance. As patient treatment and recovery times are unequal and uncertain, this is not easy. In response, a sophisticated flexible job-shop scheduling (FJSS) model is introduced, whereby patients, beds, hospital wards and health care activities are respectively treated as jobs, single machines, parallel machines and operations. Our approach is novel because an entire hospital is describable and schedulable in one integrated approach. The scheduling model can be used to recompute timings after deviations, delays, postponements and cancellations. It also includes advanced conditions such as activity and machine setup times, transfer times between activities, blocking limitations and no wait conditions, timing and occupancy restrictions, buffering for robustness, fixed activities and sequences, release times and strict deadlines. To solve the FJSS problem, constructive algorithms and hybrid meta-heuristics have been developed. Our numerical testing shows that the proposed solution techniques are capable of solving problems of real world size. This outcome further highlights the value of the scheduling model and its potential for integration into actual hospital information systems.     

A Model to Assist Planning the Provision of Hospital Services

One of the most important health service issues concerns the level of provision of acute hospital beds. To assist resolution of this issue a model is proposed which simulates how hospital beds are used in terms of admission rates and lengths of stay for different categories of disease. The model can be used to predict the likely effects of changes in the provision of beds. Thus if it is proposed to increase the supply of beds, the model will estimate, by disease type, how much of an increase this will cause in admission rates and lengths of stay. The ability of the model to make reasonably accurate predictions is demonstrated by testing it with hospital data from Quebec Province, Canada. Some ways of improving the model's predictive power are discussed and possible future applications to hospital policy issues are outlined.     

Computer Simulation Models for a Multi-Specialty Ward

This paper describes computer simulation models of the utilization of shared resources by two E.N.T. consultants and two ophthalmology consultants in an English hospital. The resources in question are the hospital beds used by their patients, which are in the same wards, and the operating theatre, whose use they share.The validity of the models in relation to the actual system studied is assessed and experiments are described which evaluate alternative arrangements for the use of these resources.The models are discussed both as part of a continuing programme of research into hospital decision-making and as tools aiding the evaluation of the options open to hospital staff faced with a specific problem.     

Improving operational effectiveness of tactical master plans for emergency and elective patients under stochastic demand and capacitated resources

This paper develops a two-stage planning procedure for master planning of elective and emergency patients while allocating at best the available hospital resources. Four types of resources are considered: operating theatre, beds in the medium and in the intensive care units, and nursing hours in the intensive care unit. A tactical plan is obtained by minimizing the deviations of the resources consumption to the target levels of resources utilization, following a goal programming approach. The MIP formulation to get this tactical plan is specifically designed to account for emergency care since it allows for the reservation of some capacity for emergency patients and possible capacity excess. To deal with the deviation between actually arriving elective patients and the average number of patients on which the tactical plan is based, we consider the possibility of planning a higher number of patients than the average to create operating slots in the tactical plan (slack planning). These operating slots are then filled in the operational plan following several flexibility rules. We consider three options for slack planning that lead to three different tactical plans on which we apply three flexibility rules to get finally nine alternative weekly schedules of elective patients. We then develop an algorithm to modify this schedule on a daily basis so as to account for emergency patients’ arrivals. Scheduled elective patients may be cancelled and emergency patients may be sent to other hospitals. Cancellation rules for both types of patients rely on the possibility to exceed the available capacities. Several performance indicators are defined to assess patient service and hospital efficiency. Simulation results show a trade-off between hospital efficiency and patient service.     

Dimensioning hospital wards using the Erlang loss model

How many beds must be allocated to a specific clinical ward to meet production targets? When budgets get tight, what are the effects of downsizing a nursing unit? These questions are often discussed by medical professionals, hospital consultants, and managers. In these discussions the occupancy rate is of great importance and often used as an input parameter. Most hospitals use the same target occupancy rate for all wards, often 85%. Sometimes an exception is made for critical care and intensive care units. In this paper we demonstrate that this equity assumption is unrealistic and that it might result in an excessive number of refused admissions, particularly for smaller units. Queuing theory is used to quantify this impact. We developed a decision support system, based on the Erlang loss model, which can be used to evaluate the current size of nursing units. We validated this model with hospital data over the years 2004–2006. Finally, we demonstrate the efficiency of merging departments.     

A multi-objective model to determine efficient resource levels in a medical assessment unit

This paper details models that determine the efficient allocation of resources on a medical assessment unit (MAU) of a general hospital belonging to the National Health Service (NHS) UK. The MAU was established to improve the quality of care given to acute medical patients on admission, and also provide the organizational means of rapid assessment and investigation in order to avoid unnecessary admissions. To analyse the performance of the MAU, doctors, nurses and beds are considered as the three main resources. Then a model is developed using the goal programming approach in multiobjective decision making and solved to deal with MAU performance. The developed model is solved under three different sets of patient admissions with the same resource levels using past data from the MAU. The results of the model are used to analyse the needed resource levels. Conclusions as to the appropriate staffing levels and functions of the MAU are drawn.     

Patient mix optimization in tactical cardiothoracic surgery planning: a case study

Cardiothoracic surgery planning involves different resourcessuch as operating theatre (OT) time, medium care beds, intensivecare beds and nursing staff. Within cardiothoracic surgery differentcategories of patients can be distinguished with respect totheir requirements of resources. The mix of patients is, therefore,an important aspect of decision making for the hospital to managethe use of these resources. A master OT schedule is used atthe tactical level of planning for deriving the weekly OT plan.It defines for each day of a week the number of OT hours availableand the number of patients operated from each patient category.We develop a model for this tactical level planning problem,the core of which is a mixed integer linear program. The modelis used to evaluate scenarios for surgery planning at tacticalas well as strategic levels, demonstrating the potential ofinteger programming for providing recommendations for change.     

Nursing care demand prediction based on a decomposed semi-markov population model

The semi-markovian population model introduced by Kao for the planning of progressive care hospitals is adapted to the prediction of nursing care demand at the level of a care unit in a general hospital. Assuming a feedback admission policy which refills the unit as soon as discharges occur, it is shown that the care unit can be decomposed into B independent subsystems corresponding to each of the B beds in the unit.For each bed the semi-Markov model permits the computation of the expected care demand and its variance for each of the seven forthcoming days. The model permits also the prediction of admissions of new patients. A prediction formula can thus be obtained where the expected care demand is expressed as a linear function of the expected number of admissions in the forthcoming days.Finally this methodology is illustrated on real data obtained in the gynaecology department of the Montreal Jewish General Hospital.     

An integrated queuing and multi-objective bed allocation model with application to a hospital in China

In this paper, a multi-objective decision aiding model is introduced for allocation of beds in a hospital. The model is based on queuing theory and goal programming (GP). Queuing theory is used to obtain some essential characteristics of access to various departments (or specialities) within the hospital. Results from the queuing models are used to construct a multi-objective decision aiding model within a GP framework, taking account of targets and objectives related to customer service and profits from the hospital manager and all department heads. The paper describes an application of the model, dealing with a public hospital in China that had serious problems with loss of potential patients in some departments and a waste of hospital beds in others. The performance of the model and implications for hospital management are presented.     

Time-dependent analysis for refused admissions in clinical wards

For capacity planning issues in health care, such as the allocation of hospital beds, the admissions rate of patients is commonly assumed to be constant over time. In addition to the purely random fluctuations, there is also typically a predictable pattern in the number of arriving patients. For example, roughly 2/3 of the admitted patients at an Intensive Care Unit arrives during office hours. Also, most of the scheduled admissions occur during weekdays instead of during the weekend.     

Using a Markov reward model to estimate spend-down costs for a geriatric department

A Markov model is used to describe movements of geriatric patients within a hospital system where the states of the Markov chain are acute/rehabilitative, long-stay care, discharge or death. By assigning costs to the states of this model, we can estimate the spend-down costs of running down services given that there are no more admissions and different costs are assigned to acute/rehabilitative and long-stay care. The model is used to estimate the spend-down costs using data previously validated for three Departments of Geriatric Medicine in the South West Thames Region of England. Our approach allows hospital planners to identify cost-effective strategies which take into account the fact that some geriatric patients remain in long-stay care for very long periods of time.     

Modelling hospital costs to produce evidence for policies that promote equity and efficiency

Third party payers for health care, when introducing policies to promote equity, through formulas for resource allocation by capitation, and efficiency, through prospective payment by case-mix, have sought to make adjustments for “unavoidable” hospital costs, which are caused by structural characteristics and are beyond the scope of local hospital management. To date, however, most published studies of such estimates have been inadequate. This paper reports the development of a generalisable model that aims to produce sound estimates of “unavoidable” hospital costs and shows how this stochastic multilevel model can be used to estimate unavoidable costs per unit of measurable output, identify sources of allocative inefficiency, and capture systematic variations in costs between different types of hospitals, through prospective payment by case-mix or formulas for resource allocation by capitation The application of the model to Portuguese hospitals has identified various causes of allocative inefficiencies: centrally-determined distributions of beds and doctors, a lack of local flexibility, systems with perverse incentives, and the existence of diseconomies of scale.     

Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds

In this paper we establish an SIR model with a standard incidence rate and a nonlinear recovery rate, formulated to consider the impact of available resource of the public health system especially the number of hospital beds. For the three dimensional model with total population regulated by both demographics and diseases incidence, we prove that the model can undergo backward bifurcation, saddle-node bifurcation, Hopf bifurcation and cusp type of Bogdanov–Takens bifurcation of codimension 3. We present the bifurcation diagram near the cusp type of Bogdanov–Takens bifurcation point of codimension 3 and give epidemiological interpretation of the complex dynamical behaviors of endemic due to the variation of the number of hospital beds. This study suggests that maintaining enough number of hospital beds is crucial for the control of the infectious diseases.     

Improving the Use of Hospital Maternity Beds

Two studies are described dealing with the problem of hospital admission and duration of stay for maternity care. Maternity admissions and deliveries are shown to be strongly influenced by the general availability of hospital beds; duration of stay is not affected by bed scarcity. A statistical method of assessing the perinatal mortality risk of individual cases and selecting women for hospital care is outlined.     

Patient flow-based allocation of inpatient resources: A case study

The paper considers the allocation of inpatient resources such as beds, operating theatres and nursing staff to specialties within a hospital setting. It describes an allocation procedure that takes patient flows as its starting point and enables an evaluation of combined impacts on the different resources involved. The paper is written in the format of a case study, dealing with a hospital that had serious problems with the utilization of beds and was faced with many admission-stops. However, the method can be used to a wide range of resource management problems in hospitals and can contribute to improving flexibility in the use of hospital resources.     

医疗资源影响下具有潜伏期的一类传染病模型建立及性态分析

建立了医疗资源影响下的考虑疾病具有潜伏期的一类传染病模型,并分析了模型的动力学性态.发现疾病流行与否由基本再生数和医院病床数共同决定,并得到了病床数的阈值条件.当基本再生数R_0大于1时,系统只存在惟一正平衡点,且通过构造Dulac函数证明了正平衡点只要存在一定是全局渐近稳定的;当R_01,我们得到系统存在两个正平衡点及无正平衡点的条件,且只有当医院的病床数小于阈值时,系统会经历后向分支.因此,可根据实际情况使医院病床的投入量不低于阈值条件,不仅有利于疾病的控制而且不会出现医疗资源过剩的现象.