A Clustered Overflow Configuration of Inpatient Beds in Hospitals

Problem Definition: The shortage of inpatient beds is a major cause of delays and cancellations in many hospitals. It may also lead to patients being admitted to inappropriate wards, whereby resulting in a lower quality of care and a longer length of stay. Academic/Practical Relevance: Investment in additional beds is not always feasible. Instead, new and creative solutions for a more efficient use of existing resources must be sought. Methodology: We propose a new configuration of inpatient beds which we call the clustered overflow configuration. In this configuration, patients who are denied admission to their primary wards as a result of beds being fully occupied are admitted to overflow wards, with each designated to serve overflows from a certain subset of specialties and providing the same quality of care as in primary wards. We propose two different formulations for partitioning and bed allocation in the proposed configuration: one minimizing the sum of average daily costs of turning patients away and nursing teams, and another minimizing the numbers turned away subject to nursing cost falling below a given threshold. We heuristically solve instances from both formulations. Results: Applying the models to real data shows that the configurations obtained from our models compare very well with the other configurations proposed in the literature, provided that patients' willingness to wait is relatively short. Managerial Implications: The proposed configuration provides the combined advantages of the dedicated configuration, wherein patients are only admitted to their primary wards, and the exible configuration, in which all specialties share a single ward. On the other hand, it restricts the adverse impacts of pooling and minimizes cross-training costs through appropriate partitioning and bed allocation. As such, it serves as a viable alternative to existing inpatient configurations

Setting staffing requirements for time-dependent queueing networks: the case of accident and emergency departments

An incentive scheme aimed at reducing patients’ waiting times in accident and emergency departments was introduced by the UK government in 2000. It requires 98% of patients to be discharged, transferred, or admitted to inpatient care within 4 hours of arrival. Setting the minimal hour by hour medical staffing levels for achieving the government target, in the presence of complexities like time-varying demand, multiple types of patients, and resource sharing, is the subject of this paper. Building on extensive body of research on time dependent queues, we propose an iterative scheme which uses infinite server networks, the square root staffing law, and simulation to come up with a good solution. The implementation of this algorithm in a typical A&E department suggests that significant improvement on the target can be gained, even without increase in total staff hour

An integrated approach to demand and capacity planning in outpatient clinics

An outpatient clinic serving two independent demand streams, one representing advance booking requests and the other same-day requests, is considered. Advance requests book their appointments through an electronic booking system for a future day, and same-day requests are served on the day they arise. Taking an integrated approach to demand and capacity planning, a policy formulation compatible with electronic booking systems is proposed that incorporates major operational levers suggested in the literature. It combines a static slot publication policy, which specifies the pattern under which slots are released to the booking system, with an allocation policy that dynamically adjusts the daily workload of advance patients. The optimal policies are found numerically by developing a novel queueing model that e?fficiently evaluates major performance metrics. The application of the model with real data, obtained from one clinic with carve-out delivery and another with advanced access, demonstrates substantial savings

On queues with time-varying demand

The service sector lies at the heart of industrialized societies. Since the early decades of the twentieth century queueing theory has provided service managers with a mathematical framework to evaluate the operational service quality and service efficiency of their services, and to strive for a balance between the two aspects. Unlike most textbook queueing models, however, real service operations have time-varying arrival rates, usually with significant variations over a day. This non-stationarity of the arrival process, which often coincides with time-varying staffing levels; makes queueing models difficult to analyze. Two of the important problems arising when considering time-dependent queues concern service quality evaluation of queues with given parameters in terms of measures like customers' waiting times, and finding the minimal time-dependent staffing levels required for achieving a given service quality target. The former is addressed in the first part of the thesis, and the latter is addressed in the second part. In the first part of the thesis, we evaluate the potential and limitations of numerical methods and investigate approximation approaches proposed in the literature for service quality evaluation of time-dependent single and multiple facility queues. We also propose, implement, and test a novel approximation approach for service quality evaluation of a particular type of time-dependent queues, namely single-class, multi-class, and networks of loss queues. Combining an exact equation derived using infinite-server models with an approximate equation motivated by stationary loss models, the proposed approach produces close to exact results in very short times. The second part of the thesis is dedicated to the staffing problem of non-stationary service networks. In particular, we focus on complex services provided by English emergency departments where a Government set waiting time target must be achieved. Drawing upon infinite-server models' results and a square root staffing law as well as the strength and flexibility of simulation models, we propose a new heuristic approach for staffing emergency departments, based on the concept of time-stable performance. The approach accounts for complexities like multiple classes of customers and resource sharing, and is shown to achieve the desired target while saving some staff-hours in typical situations where staffing levels do not allow properly for the time lags in the workloads.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Developing a wide easy-to-generate class of bivariate copulas

As of late, copulas have drawn great attention in stochastic simulation, financial engineering, and risk management. Their power lies under their ability of modeling dependent random variables. Using a known theorem in probability which proves that the fractional part of the sum of a uniform and an arbitrary independent continuous random variable follows a uniform distribution, we construct a wide class of bivariate copulas in which bivariate random vector generation can be performed easily. Some important members of this new class and their properties together with two invariant correlation measures and some insights in their application are presente