Efficiency and welfare implications of managed public sector hospital waiting lists

A queuing model for public health service waiting lists is developed, and the implications for patient welfare of different systems for managing the waiting list are analysed. If patients are admitted to hospital on a first-come-first-served basis, a welfare gain is achieved by moving from a system of implicit to one of explicit rationing of access to the waiting list. If individual waiting times and hospital admissions are dependent on clinical priority, a further welfare gain is achievable without the use of explicit rationing, by reallocating the total waiting time from the more towards the less seriously ill. On efficiency and welfare criteria, a maximum waiting time guarantee does not appear to be a desirable development.     

Analysis via goal programming of the minimum achievable stay in surgical waiting lists

In this paper, a Goal Programming model is developed in order to study the possibility of decreasing the length of stay on the waiting list of a hospital that belongs to the Spanish Health Service. First, a problem is solved to determine the optimal planning for one year, so as to make the maximum waiting time decrease to six months (at present, some operations have a waiting list of more than a year). Afterwards, two other problems are solved in order to determine the impact that a further reduction of the waiting time (four months) would have on the requirements of extra resources for the hospital. The particular problem for the Trauma service is described in detail, but global results are shown and commented.     

Hospital Waiting List Management Models

This paper describes work carried out with hospital consultants in Lancaster District Health Authority to develop and use computerized waiting list management models. The ‘what if?’ models produced have been found to be a very useful tool in the constructive debate about problems faced by consultants and managers, and of the options available to them.     

Modeling the transplant waiting list: A queueing model with reneging

Motivated by the problem of organ allocation, we develop a queueing model with reneging that provides a stylistic representation of the transplant waiting list. The model assumes that there are several classes of patients, several classes of organs, and patient reneging due to death. We focus on randomized organ allocation policies and develop closed-form asymptotic expressions for the stationary waiting time, stationary waiting time until transplantation, and fraction of patients who receive transplantation for each patient class. Analysis of these expressions identifies the main factors that underlie the performance of the transplant waiting list and demonstrates that queueing models can prove useful when evaluating the organ allocation system. This revised version was published online in June 2006 with corrections to the Cover Date.     

Tolerance intervals for autoregressive models,with an application to hospital waiting lists

Long waiting lists are a symbol of inefficiencies of hospital services. The dynamics of waiting lists are complex, especially when trying to understand how the lists grow due to the demand of a particular treatment relative to a hospital's capacity. Understanding the uncertainty of forecasting growth/decline of waiting lists could help hospital managers with capacity planning. We address this uncertainty through the use of statistical tolerance intervals, which are intervals that contain a specified proportion of the sampled population at a given confidence level. Tolerance intervals are available for numerous settings, however, the approaches for autoregressive models are far more limited. This article fills that gap and establishes tolerance intervals for general AR(p) models, which may also have a mean or trend component present. A rigorous development of tolerance intervals in this setting is presented. Extensive simulation studies identify that good coverage properties are achieved when the AR process is stationary and the parameters of the AR model are well within the stationarity constraints. Otherwise, a bootstrap‐based correction can be applied to improve the coverage probabilities. Finally, the method is applied to the monthly number of patients on hospital waiting lists in England.     

Waiting list behaviour and the consequences for NHS targets

The United Kingdom's National Health Service (NHS) is investing considerable resources in reducing patient waiting times for elective treatment. This paper describes the development of a waiting list model and its use in a simulation to assess management options. Simulation usually assumes that waiting is adequately described by simple queuing disciplines, typically first-in-first-out. However, waiting in the United Kingdom's NHS is a more complex phenomenon. The waiting list behaviour is explored through an analysis of the changes in waiting time distributions for elective orthopaedics in one Scottish Health Board, NHS Fife. The evolving distributions suggest that there have been substantial changes in priorities in response to the various NHS targets. However, in the short or medium term, the form of the distribution appears reasonably stable, providing a basis for estimating future waiting times in different scenarios. A model of the waiting behaviour and prioritization in the appointment allocations was embedded in a simulation of the complete elective orthopaedic patient journey from referral, through outpatients and diagnostics to surgery. The model has been used to explore the consequences of various management options in the context of the NHS target that no patient should wait more than 18 weeks between referral and treatment.     

Modelling toolkit to assist with introducing a stepped care system design in mental health care

We describe a modelling toolkit that was developed with the aim of assisting those responsible for introducing stepped care systems to local mental health services in the UK. The toolkit was pre-populated with real patient flow data collected from four sites that piloted the stepped care system design. Two analytical models were developed and coded as part of the toolkit to provide insights concerning workload, patient throughput, and changes in waiting times and waiting list size. An interface was built to allow users to specify their own stepped care system and input their own estimates or data of service demands and capacities at different steps. Despite the challenges and limitations, the use of modelling to inform the design of new service configurations is an important step in the right direction and we would recommend this as a reasonable way forward.     

Developing a platform for comparison of hospital admission systems: An illustration

There is an increasing need to develop a platform for comparing hospital admission planning systems due to a shift in the service paradigm in the health sector. The current service concept of hospital admission planning aims at optimising the use of scarce hospital resources without paying much attention to the level of service offered to patients. As patients nowadays do not accept long waiting times for hospital admission, it becomes necessary to consider alternative admission service concepts. Waiting lists have also become a political issue, and alternative concepts have been advocated such as giving all patients an appointment for admission. A simulation model was built to examine the impacts of extreme admission service concepts in a simplified hospital setting. The alternative concepts considered are based on the ‘zero waiting time’ principle (immediate treatment), and the ‘booked admissions’ principle (using an appointment for admission). The results of these admission service concepts are compared with the results of the current concept, based on the ‘maximising resource use’ principle. The paper deals with the development of a framework and tool that allows evaluating different, somehow conflicting, hospital admission planning concepts and the usefulness of such framework and tool for more refined/real-life approaches to hospital admission planning.     

A heuristic algorithm for the hospital health examination scheduling problem

This study considers the problem of health examination scheduling. Depending on their gender, age, and special requirements, health examinees select one of the health examination packages offered by a health examination center. The health examination center must schedule all the examinees, working to minimize examinee/doctor waiting time and respect time and resource constraints, while also taking other limitations, such as the sequence and continuity of the examination procedures, into consideration. The Binary integer programming (BIP) model is one popular way to solve this health examination scheduling problem. However, as the number of examinees and health examination procedures increase, solving BIP models becomes more and more difficult, if not impossible. This study proposes health examination scheduling algorithm (HESA), a heuristic algorithm designed to solve the health examination scheduling problem efficiently and effectively. HESA has two primary objectives: minimizing examinee waiting time and minimizing doctor waiting time. To minimize examinee waiting time, HESA schedules the various parts of each examinee’s checkup for times when the examinee is available, taking the sequence of the examination procedures and the availability of the resources required into account. To minimize doctor waiting time, HESA focuses on doctors instead of examinees, assigning waiting examinees to a doctor as soon as one becomes available. Both complexity analysis and computational analyses have shown that HESA is very efficient in solving the health examination scheduling problem. In addition to the theoretical results, the results of HESA’s application to the concrete health examination scheduling problems of two large hospitals in Taiwan are also reported.     

A novel ant colony optimization approach for on-line scheduling and due date determination

This paper aims to develop an on-line Ant Colony Optimization (ACO) framework, where jobs arrive over time, and at any time we lack knowledge concerning future jobs. A due date is determined upon job arrival, and jobs are sequenced on the machine to optimize the sum of weighted lead times with all due dates met. We propose that each ant is associated with a sequence of waiting jobs with quoted due dates. This waiting sequence is constantly updated over time (whenever a job is selected to be processed or a new job arrives). The on-line schedule is constructed by selecting the first job in the waiting list of the “best” ant to process (along with its due date) as the machine becomes available. However, for the ant where this job is not the first one in the list, processing it pushes back the waiting jobs positioned before it. If such push back results in a due date violation, this ant will be eliminated. Further, our ACO framework does not include the iterative procedure due to the characteristics of the on-line problem; this is one difference from the traditional ACO framework besides ant elimination. The computational testing on generated instances shows that our ACO algorithm outperforms an existing effective on-line algorithm in the literature. Also, with local search incorporated using the EDD (Earliest Due Date) rule, improvements can be obtained in both computational outcome and time.     

Queueing models for appointment-driven systems

Many service systems are appointment-driven. In such systems, customers make an appointment and join an external queue (also referred to as the “waiting list”). At the appointed date, the customer arrives at the service facility, joins an internal queue and receives service during a service session. After service, the customer leaves the system. Important measures of interest include the size of the waiting list, the waiting time at the service facility and server overtime. These performance measures may support strategic decision making concerning server capacity (e.g. how often, when and for how long should a server be online). We develop a new model to assess these performance measures. The model is a combination of a vacation queueing system and an appointment system.     

On waiting time distributions associated with compound patterns in a sequence of multi-state trials

In this article, waiting time distributions of compound patterns are considered in terms of the generating function of the numbers of occurrences of the compound patterns. Formulae for the evaluation of the generating functions of waiting time are given, which are very effective computational tools. We provide several viewpoints on waiting time problems associated with compound patterns and develop a general workable framework for the study of the corresponding distributions. The general theory is employed for the investigation of some examples in order to illustrate how the distributions of waiting time can be derived through our theoretical results. This research was partially supported by the ISM Cooperative Research Program (2006-ISM·CRP-2007).     

Using system dynamics principles for conceptual modelling of publicly funded hospitals

This paper examines the long-standing operational issue of patients boarding in the emergency department (ED), who have been admitted to hospital (inpatient ‘boarders’). From this analysis we design a conceptual model that provides a roadmap to create sustainable improvements in ED waiting times. The conceptual model is built using system dynamics methodology, and illustrates the use of system archetypes, a set of common causal feedback loops that illustrate how well-intended decisions have unintentional side effects. This paper outlines the journey taken by one large academic health centre to address these issues, and highlights the larger implications and recommendations that are applicable to other publicly funded hospitals.     

基于仿真优化算法的医院关键资源能力分派研究

图像检查设备是医院的瓶颈资源。医院管理者通常追求瓶颈资源的高利用率,导致患者需长时间等待才能进行检查。长时间的等待加剧了患者的焦虑情绪,也会给患者造成病情加重等隐患。考虑患者具有不同的目标等待时间,本文针对医疗关键资源能力分派问题,提出了双层嵌套的阈值策略。非紧急患者预约时,双层嵌套阈值考虑为将来到达的紧急患者预留一定量的能力。如果患者在目标等待时间内预约不成功,则离开医院,并对医院造成患者流失惩罚。目标函数是使患者总流失惩罚最小。本文用目标函数对嵌套阈值的偏导数作为最速梯度法下降方向,基于样本路径对该偏导数进行估计,并通过不断迭代得到最优阈值。数值实验中,与医院应用的传统阈值策略比较,结果显示,本文所提嵌套阈值策略能够有效降低因超过目标等待时间而流失的患者给医院带来的损失。     

On Waiting Time Problems Associated with Runs in Markov Dependent Trials

A general technique is developed to study the waiting time distribution for the r-th occurrence of a success run of length k in a sequence of Markov dependent trials. Sooner and later waiting time problems are also discussed.     

On waiting time distributions for patterns in a sequence of multistate trials

In this paper, we consider the waiting time distributions for patterns in a sequence of multistate trials. A simple and general framework, using the Markov chain imbedding method, is developed to study the waiting time distributions of both simple and compound patterns. Algorithms for the computation of these are given. The general theory is employed for the investigation of some examples in order to illustrate the theoretical results.     

Utilizing buffer management to improve performance in a healthcare environment

For over 50 years, the United Kingdom’s National Health Service has aspired to provide universal access to quality health care. However, as evidenced by huge backlogs and lengthy waiting times for many services, the NHS is showing the strain of accommodating rising contemporary expectations within a constrained budget. This paper describes the concept of buffer management, its origins in manufacturing applications, and how it can be applied to generate improvements in health care systems. The successful implementation of buffer management is illustrated with recent applications in the Accident and Emergency departments and the hospital admissions process of three NHS facilities.     

Non-block scheduling with priority for radiotherapy treatments

In this paper, a quite challenging operational problem within health care delivery has been considered: the optimal management of patients waiting for radiotherapy treatments. Long waiting times for radiotherapy treatments of several cancers are largely documented all over the world. This problem is mainly due to an imbalance between supply and demand of radiotherapy services, which negatively affects the effectiveness and the efficiency of the health care delivered. Within this context, the paper presents an innovative solution approach for effectively scheduling a set of patients waiting to start the radiotherapy plan. The proposed approach is based on a well tailored integer linear optimization program, modelling a non-block scheduling strategy, with the aim to minimize the mean waiting time or maximize the number of new scheduled patients. The model has been tested and evaluated by carrying out some numerical experiments on suitable use-case scenarios, and the obtained results demonstrate the effectiveness and reliability of the proposed approach.     

Modelling resource availability in general hospitals design and implementation of a decision support model

Admission planning in general hospitals means selecting elective patients from a waiting list in order to obtain optimal utilisation of the available beds, nursing staff and operating theatre facilities while taking into account emergency admissions. Also, a wide variety of other factors, often situational and not explicitly stated, play a part in this decision process. As such, it is a complex problem which is difficult to handle for any decision maker. In this paper a statistical model for the prediction of resource availability is presented. The model is first tested on empirical data. On the basis of the model a DSS was designed which is now in daily use in several hospitals. Problems encountered in that implementation process will be stated. The results obtained with the model show that such an approach based on statistical data provides sufficiently accurate results to be useful.