Cyclic shift scheduling with on-call duties for emergency medical services

Abstract

In workforce scheduling for emergency medical services, it is important to ensure sufficient coverage at all time. Thus, planning has to consider unpredictable employee absences. To hedge against this type of uncertainty, on-call duties can be assigned to employees. In practice, these are often assigned ex-post based on the regular schedule. Little literature on workforce scheduling for ambulances or the planning of on-call duties exists. We present new set covering based integer programming formulations for cyclic stint-based staff scheduling with on-call duties. It is desirable for employees to work on consecutive days, called a stint, with a subsequent recovery period. On-call duties can be individually scheduled in-between two stints. Our model formulations integrate different cycle times for regular and on-call duties. A simple schedule that repeats quickly is devised for regular duties, while the on-call duty schedule rotates after each cycle to ensure fairness. The proposed models are applied to a local German emergency medical services provider. Using our stint-based model formulations, the planning complexity has been greatly reduced and reasonably large problem instances can be solved to optimality. Employee preferences, such as fairness, less work on weekends and longer recovery times, were taken into account to a high degree.

Patient scheduling based on a service-time prediction model: a data-driven study for a radiotherapy center

Abstract

With the growth of the population, access to medical care is in high demand, and queues are becoming longer. The situation is more critical when it concerns serious diseases such as cancer. The primary problem is inefficient management of patients rather than a lack of resources. In this work, we collaborate with the Centre Intégré de Cancérologie de Laval (CICL). We present a data-driven study based on a nonblock approach to patient appointment scheduling. We use data mining and regression methods to develop a prediction model for radiotherapy treatment duration. The best model is constructed by a classification and regression tree; its accuracy is 84%. Based on the predicted duration, we design new workday divisions, which are evaluated with various patient sequencing rules. The results show that with our approach, 40 additional patients are treated daily in the cancer center, and a considerable improvement is noticed in patient waiting times and technologist overtime.

A review on ambulance offload delay literature

Abstract

Ambulance offload delay (AOD) occurs when care of incoming ambulance patients cannot be transferred immediately from paramedics to staff in a hospital emergency department (ED). This is typically due to emergency department congestion. This problem has become a significant concern for many health care providers and has attracted the attention of many researchers and practitioners. This article reviews literature which addresses the ambulance offload delay problem. The review is organized by the following topics: improved understanding and assessment of the problem, analysis of the root causes and impacts of the problem, and development and evaluation of interventions. The review found that many researchers have investigated areas of emergency department crowding and ambulance diversion; however, research focused solely on the ambulance offload delay problem is limited. Of the 137 articles reviewed, 28 articles were identified which studied the causes of ambulance offload delay, 14 articles studied its effects, and 89 articles studied proposed solutions (of which, 58 articles studied ambulance diversion and 31 articles studied other interventions). A common theme found throughout the reviewed articles was that this problem includes clinical, operational, and administrative perspectives, and therefore must be addressed in a system-wide manner to be mitigated. The most common intervention type was ambulance diversion. Yet, it yields controversial results. A number of recommendations are made with respect to future research in this area. These include conducting system-wide mitigation intervention, addressing root causes of ED crowding and access block, and providing more operations research models to evaluate AOD mitigation interventions prior implementations. In addition, measurements of AOD should be improved to assess the size and magnitude of this problem more accurately.

A study on the impact of prioritising emergency department arrivals on the patient waiting time

Abstract

In the past decade, the crowding of the emergency department has gained considerable attention of researchers as the number of medical service providers is typically insufficient to fulfil the demand for emergency care. In this paper, we solve the stochastic emergency department workforce planning problem and consider the planning of nurses and physicians simultaneously for a real-life case study in Belgium. We study the patient arrival pattern of the emergency department in depth and consider different patient acuity classes by disaggregating the arrival pattern. We determine the personnel staffing requirements and the design of the shifts based on the patient arrival rates per acuity class such that the resource staffing cost and the weighted patient waiting time are minimised. In order to solve this multi-objective optimisation problem, we construct a Pareto set of optimal solutions via the 𝜖-constraints method. For a particular staffing composition, the proposed model minimises the patient waiting time subject to upper bounds on the staffing size using the Sample Average Approximation Method. In our computational experiments, we discern the impact of prioritising the emergency department arrivals. Triaging results in lower patient waiting times for higher priority acuity classes and to a higher waiting time for the lowest priority class, which does not require immediate care. Moreover, we perform a sensitivity analysis to verify the impact of the arrival and service pattern characteristics, the prioritisation weights between different acuity classes and the incorporated shift flexibility in the model.

A Multi-Fidelity Rollout Algorithm for Dynamic Resource Allocation in Population Disease Management

Abstract

Dynamic resource allocation for prevention, screening, and treatment interventions in population disease management has received much attention in recent years due to excessive healthcare costs. In this paper, our goal is to design a model and an efficient algorithm to optimize sequential intervention policies under resource constraints to improve population health outcomes. We consider a discrete-time finite-horizon budget allocation problem with disease progression within a closed birth-cohort population. To address the computational challenges associated with large-state and multiple-period dynamic decision-making problems, we propose a low-fidelity approximation that preserves the population dynamics under a stationary policy. To improve the healthcare interventions in terms of population health outcomes, we then embed the low-fidelity approximation into a high-fidelity optimization model to efficiently identify a good non-stationary sequential intervention policy. Our approach is illustrated by a numerical example of screening and treatment policy implementation for chronic hepatitis C virus (HCV) infection over a budget planning period. We numerically compare our Multi-Fidelity Rollout Algorithm (MF-RA) to a grid search approach and demonstrate the similarity of sequential policy trends and closeness of overall health outcomes measured by quality-adjusted life-years (QALYs) and the total number of individuals that undergo screening and treatment for different annual budgets and birth-cohorts. We also show how our approach scales well to problems with high dimensionality due to many decision periods by studying time to elimination of HCV.

Improving the efficiency of the operating room environment with an optimization and machine learning model

Abstract

The operating room is a major cost and revenue center for most hospitals. Thus, more effective operating room management and scheduling can provide significant benefits. In many hospitals, the post-anesthesia care unit (PACU), where patients recover after their surgical procedures, is a bottleneck. If the PACU reaches capacity, patients must wait in the operating room until the PACU has available space, leading to delays and possible cancellations for subsequent operating room procedures. We develop a generalizable optimization and machine learning approach to sequence operating room procedures to minimize delays caused by PACU unavailability. Specifically, we use machine learning to estimate the required PACU time for each type of surgical procedure, we develop and solve two integer programming models to schedule procedures in the operating rooms to minimize maximum PACU occupancy, and we use discrete event simulation to compare our optimized schedule to the existing schedule. Using data from Lucile Packard Children’s Hospital Stanford, we show that the scheduling system can significantly reduce operating room delays caused by PACU congestion while still keeping operating room utilization high: simulation of the second half of 2016 shows that our model could have reduced total PACU holds by 76% without decreasing operating room utilization. We are currently working on implementing the scheduling system at the hospital.

Hospital physicians can’t get no long-term satisfaction – an indicator for fairness in preference fulfillment on duty schedules

Abstract

Physicians are a scarce resource in hospitals. In order to minimize physician attrition, schedulers incorporate individual physician preferences when creating the physicians’ duty roster. The manual creation of a roster is very time-consuming and often produces suboptimal results. Many schedulers therefore use model-based software to assist in planning. The planning horizon for duty schedules is usually a single month. Many models optimize the plan for the current planning horizon, without taking into account data on preference fulfillment and work load distribution from previous months. It is therefore possible that, when looking at a longer time horizon, some physicians are disadvantaged in terms of preference fulfillment more often than their peers, simply because this generates better results for the individual months. This may be perceived as unfair by the disadvantaged physicians. In order to eliminate this imbalance, we introduce a satisfaction indicator for preference fulfillment in physician scheduling. This indicator is computed for each physician on each monthly plan and is then used to inform decisions regarding preference fulfillment on the current and future plans. As a result, a more equal distribution of preference fulfillment among physicians is achieved. We run a computational study with three different update strategies for our satisfaction indicator. Our study uses 24 months of data from a German university hospital and derives additional generated data from it. Results indicate that our satisfaction indicator, combined with the right update strategy, can achieve an equal distribution of satisfaction over all physicians within a peer group, as well as stable satisfaction levels for each individual physician over a longer time horizon. As our main contribution, we identify that our satisfaction indicator is more effective in creating equal distribution of long-term satisfaction the higher the rate of conflicting preferences is.

The self-regulating nature of occupancy in ICUs: stochastic homoeostasis

Abstract

As pressure on the health system grows, intensive care units (ICUs) are increasingly operating close to their capacity. This has led a number of authors to describe a link between admission and discharge behaviours, labelled variously as: ‘bumping’, ‘demand-driven discharge’, ‘premature discharge’ etc. These labels all describe the situation that arises when a patient is discharged to make room for the more acute arriving patient. This link between the admission and discharge behaviours, and other potential occupancy-management behaviours, can create a correlation between the arrival process and LOS distribution. In this paper, we demonstrate the considerable problems that this correlation structure can cause capacity models built on queueing theory, including discrete event simulation (DES) models; and provide a simple and robust solution to this modelling problem. This paper provides an indication of the scope of this problem, by showing that this correlation structure is present in most of the 37 ICUs in Australia. An indication of the size of the problem is provided using one ICU in Australia. By incorrectly assuming that the arrival process and LOS distribution are independent (i.e. that the correlation structure does not exist) for an occupancy DES model, we show that the crucial turn-away rates are markedly inaccurate, whilst the mean occupancy remains unaffected. For the scenarios tested, the turn-away rates were over-estimated by up to 46 days per year. Finally, we present simple and robust methods to: test for this correlation, and account for this correlation structure when simulating the occupancy of an ICU.