Pooling of Samples to Increase Testing Capacity for COVID-19

Test, trace and isolate are the main pillars of the containment strategies promoted by epidemiologists in the COVID-19 pandemic. Equipment, material and labour required for testing is, however, limited, making it a challenge to adopt testing at a large scale. Pooling of samples has the potential to reduce the number of tests required for screening a population with a low infection prevalence. We provide a detailed analysis of a well-known pooling strategy called two-stage pooling which involves testing pools of a fixed size. We show that, while this approach can potentially reduce the number of tests, evaluating its cost effectiveness and configuring it optimally require existence of a reliable estimate of prevalence in the population. In the absence of such information, we propose inferring a prior distribution of the underlying prevalence using a combination of expert opinion and a limited exploratory testing of the population, and applying it with either a two-stage fixed pooling strategy, or a multi-stage adaptive pooling strategy. We explain how each of these strategies can be applied, propose algorithms for finding their corresponding optimal pool size, and identify the situations under which each of these strategies is preferred

Appointment Capacity Planning in Specialty Clinics: A Queueing Approach

Specialty clinics provide specialized care for patients referred by primary care physicians, emergency departments, or other specialists. Urgent patients must often be seen on the referral day, whereas nonurgent referrals are typically booked an appointment for the future. To deliver a balanced performance, the clinics must know how much “appointment capacity” is needed for achieving a reasonably quick access for nonurgent patients. To help identify the capacity that leads to the desired performance, we model the dynamics of appointment backlog as novel discrete-time bulk service queues and develop numerical methods for efficient computation of corresponding performance metrics. Realistic features such as arbitrary referral and clinic appointment cancellation distributions, delay-dependent no-show behaviour, and rescheduling of no-shows are explicitly captured in our models. The accuracy of the models in predicting performance as well as their usefulness in appointment capacity planning is demonstrated using real data. We also show the application of our models in capacity planning in clinics where patient panel size, rather than appointment capacity, is the major decision variable

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. A compact policy formulation is proposed that incorporates major operational levers suggested in the literature. It combines a slot publication policy, which specifies the pattern under which slots are released to the booking system, with an expediting policy that adjusts the daily workload of advance patients. Relying on a wide range of numerical experiments, a heuristic search method is developed for finding the joint publication and expediting policies, minimizing the cost of overtime slots whilst ensuring a waiting and an access constraint is met. Several managerial insights are derived using a combination of illustrative and real data, highlighting the importance of taking an integrated approach towards the operational levers captured by our policy formulation

Uniform fractional part: a simple fast method for generating continuous random variates

A known theorem in probability is adopted and through a probabilistic approach, it is generalized to develop a method for generating random deviates from the distribution of any continuous random variable. This method, which may be considered as an approximate version of the Inverse Transform algorithm, takes two random numbers to generate a random deviate, while maintaining all the other advantages of the Inverse Transform method, such as the possibility of generating ordered as well as correlated deviates and being applicable to all density functions, regardless of their parameter value

Reconfiguration of Inpatient Services to Reduce Bed Pressure in Hospitals

Healthcare systems around the world are facing an inpatient bed crisis. This was highlighted more than ever during the recent COVID-19 pandemic. The consequences of bed shortage are substantial for both patients and staff. Finding innovative ways to improve the utilization of the existing bed base is therefore of significant importance. We focus on reconfiguration of inpatient services as a cost-effective solution to bed pressure in hospitals, and propose a comprehensive methodology for finding a low-cost configuration given a total number of beds, a set of specialties, and a finite or infinite waiting time threshold for patients. This involves developing novel approximations for performance evaluation of overflow delay and abandonment systems, and embedding them within heuristic search algorithms. We apply our reconfiguration methodology on inpatient data from a large UK hospital. Simulation experiments show that the configurations proposed by our methodology can result in significant savings compared to the existing configuration, and that a clustered overflow configuration is likely to produce the best results in many scenarios

Approximate analysis of non-stationary loss queues and networks of loss queues with general service time distributions

A Fixed Point Approximation (FPA) method has recently been suggested for non-stationary analysis of loss queues and networks of loss queues with Exponential service times. Deriving exact equations relating time-dependent mean numbers of busy servers to blocking probabilities, we generalize the FPA method to loss systems with general service time distributions. These equations are combined with associated formulae for stationary analysis of loss systems in steady state through a carried load to offered load transformation. The accuracy and speed of the generalized methods are illustrated through a wide set of examples.Queueing Erlang loss model Time-dependent arrival rate Carried load

Approximate analysis of non-stationary loss queues and networks of loss queues with general service time distributions

A Fixed Point Approximation (FPA) method has recently been suggested for non-stationary analysis of loss queues and networks of loss queues with Exponential service times. Deriving exact equations relating time-dependent mean numbers of busy servers to blocking probabilities, we generalize the FPA method to loss systems with general service time distributions. These equations are combined with associated formulae for stationary analysis of loss systems in steady state through a carried load to offered load transformation. The accuracy and speed of the generalized methods are illustrated through a wide set of examples

A Framework for Optimal Recruitment of Temporary and Permanent Healthcare Workers in Highly Uncertain Environments

There has been a significant increase in the demand for temporary skilled workers in the health sector. They provide volume flexibility, but are generally more expensive than their permanent counterparts. In this paper, we propose a two-stage stochastic optimization framework to inform recruitment decision making for a period of highly uncertain demand in a setting where all patients must be served. The first stage identifies the number of permanent positions to advertise, and the second stage determines the number of temporary workers to recruit. Our framework accounts for the uncertainty in the permanent recruitment process, stochasticity of the service delivery, and asymmetry in demand information at the times of permanent and temporary recruitment. Under a general setting of the problem, we characterize the optimal first- and second-stage decisions analytically, propose fast numerical methods for finding their values, and prove some of their monotonicity properties. A case study based on data from a geriatric ward illustrates the application of our framework, and numerical experiments provide further managerial insights