Emergency Patient Arrivals Research Articles

Multi-objective stochastic scheduling of inpatient and outpatient surgeries

AbstractWith the advancement of surgery and anesthesiology in recent years, surgical clinical pathways have changed significantly, with an increase in outpatient surgeries. However, the surgical scheduling problem is particularly challenging when inpatients and outpatients share the same operating room blocks, due to their different characteristics in terms of variability and preferences. In this paper, we present a two-phase stochastic optimization approach that takes into account such characteristics, considering multiple objectives and dealing with uncertainty in surgery duration, arrival of emergency patients, and no-shows. Chance Constrained Integer Programming and Stochastic Mixed Integer Programming are used to deal with the advance scheduling and the allocation scheduling, respectively. Since Monte Carlo sampling is inefficient for solving the allocation scheduling problem for large size instances, a genetic algorithm is proposed for sequencing and timing procedures. Finally, a quantitative analysis is performed to analyze the trade-off between schedule robustness and average performance under the selection of different patient mixes, providing general insights for operating room scheduling when dealing with inpatients, outpatient, and emergencies.

Multiple operation theatre scheduling for mitigating the disturbance caused by emergency patients

Scheduling emergency patients is a problem that most hospitals struggle to solve without disturbing elective surgery patients' schedules. The present work undertakes this problem and considers scheduling elective patients surgeries in multiple operation theatres to mitigate the possible disturbance caused by emergency patient arrivals. The resultant problem has been termed as multiple operation theatre problems with total expected disturbance (MOTED). The number of elective surgeries and their corresponding surgery times are known and given in advance. However, emergency patient arrivals are stochastic in nature, which is tackled through scenario-generation techniques. The model assumes that emergency case scenarios can be predicted from historical data, and determines the sequence of elective patients in a multiple operation theatre such that the sum of the total expected disturbance (TED) caused by emergency patients and the total completion time of elective surgeries is minimized. The disturbance minimization increases the satisfaction level of patients, physicians and other medical staff, and indirectly reduces the overtime costs. The work provides an optimal algorithm for the MOTED problem with a single-operation theatre. Three heuristics and two metaheuristics have been proposed to solve the complete MOTED problem. The metaheuristic involves particle swarm optimization (PSO) and ant colony optimization (ACO). An extensive numerical experiment is performed using 48 randomly generated problem instances.

Presented a Framework of Computational Modeling to Identify the Patient Admission Scheduling Problem in the Healthcare System.

Operating room scheduling is a prominent study topic due to its complexity and significance. The increasing number of technical operating room scheduling articles produced each year calls for another evaluation of the literature to enable academics to respond to new trends more quickly. The mathematical application of a model for the patient admission scheduling issue with stochastic arrivals and departures is the subject of this study. The approach for applying our model to real-world issues is discussed here. We present a solution technique for efficient computing, a numerical model analysis, and examples to demonstrate the methodology. This study looked at the challenge of assigning procedures to operate rooms in the face of ambiguity regarding surgery length and the arrival of emergency patients based on a flexible policy (capacity reservation). We demonstrate that the proposed methods derived from deterministic models are inadequate compared to the answers produced from our stochastic model using simple numerical examples. We also use heuristics to estimate the objective function to build more complicated numerical examples for large-scale issues, demonstrating that our methodology can be applied quickly to real-world situations that often include big information sets.

Stochastic programming for outpatient scheduling with flexible inpatient exam accommodation.

This study is concerned with the determination of an optimal appointment schedule in an outpatient-inpatient hospital system where the inpatient exams can be cancelled based on certain rules while the outpatient exams cannot be cancelled. Stochastic programming models were formulated and solved to tackle the stochasticity in the procedure durations and patient arrival patterns. The first model, a two-stage stochastic programming model, is formulated to optimize the slot size. The second model further optimizes the inpatient block (IPB) placement and slot size simultaneously. A computational method is developed to solve the second optimization problem. A case study is conducted using the data from Magnetic Resonance Imaging (MRI) centers of Lahey Hospital and Medical Center (LHMC). The current schedule and the schedules obtained from the optimization models are evaluated and compared using simulation based on FlexSim Healthcare. Results indicate that the overall weighted cost can be reduced by 11.6% by optimizing the slot size and can be further reduced by an additional 12.6% by optimizing slot size and IPB placement simultaneously. Three commonly used sequencing rules (IPBEG, OPBEG, and a variant of ALTER rule) were also evaluated. The results showed that when optimization tools are not available, ALTER variant which evenly distributes the IPBs across the day has the best performance. Sensitivity analysis of weights for patient waiting time, machine idle time and exam cancellations further supports the superiority of ALTER variant sequencing rules compared to the other sequencing methods. A Pareto frontier was also developed and presented between patient waiting time and machine idle time to enable medical centers with different priorities to obtain solutions that accurately reflect their respective optimal tradeoffs. An extended optimization model was also developed to incorporate the emergency patient arrivals. The optimal schedules from the extended model show only minor differences compared to those from the original model, thus proving the robustness of the scheduling solutions obtained from our optimal models against the impacts of emergency patient arrivals.

Stochastic surgery selection and sequencing under dynamic emergency break-ins

Anticipating the impact of urgent emergency arrivals on operating room schedules remains methodologically and computationally challenging. This paper investigates a model for surgery scheduling, in which both surgery durations and emergency patient arrivals are stochastic. When an emergency patient arrives he enters the first available room. Given the sets of surgeries available to each operating room for that day, as well as the distributions of the main stochastic variables, we aim to find the per-room surgery sequences that minimise a joint objective, which includes over- and under-utilisation, the amount of cancelled patients, as well as the risk that emergencies suffer an excessively long waiting time. We show that a detailed analysis of emergency break-ins and their disruption of the schedule leads to a lower total cost compared to less sophisticated models. We also map the trade-off between the threshold for excessive waiting time, and the set of other objectives. Finally, an efficient heuristic is proposed to accurately estimate the value of a solution with significantly less computational effort.

Adaptive operating rooms planning and scheduling: A rolling horizon approach

Accounting for a large portion of the hospital’s total revenue and cost, better management of the operating rooms is extremely important in improving healthcare resource utilization. This paper investigates the Operating Rooms (ORs) Planning and Scheduling Problem in a hospital with a modified block scheduling policy. Thus, the candidate patients have to be assigned a date and an operating room/block as well as being sequenced in the assigned operating rooms/blocks. A reserved slack policy is considered to take care of the arrival of emergency patients. Surgery durations are considered to be randomly distributed. In this regard, a stochastic mixed integer linear programming model is proposed that includes different patient, staff and surgeon preferences: minimization of the total patient waiting time, the tardiness, the number of cancellations, the patient surgery start times, the block overtime, the number of surgeon’s surgery days within the planning horizon and the sum of the idle times of the surgeons. Two different 2-phase heuristic solution approaches are developed in a rolling horizon framework in order to solve the Adaptive ORs Planning and Scheduling Problem. The efficiency of the solution framework is surveyed by applying real data obtained from hospital records through numerical experiments. The results show that the developed solution framework significantly outperforms the commercial solver CPLEX in terms of solution quality and CPU time, in medium- as well as in large-sized problems. Furthermore, the results show that the assumptions and features made to the formulation (i.e. the modified block scheduling policy, the reserved slack policy, and the stochastic surgery durations) will result in more efficient solutions.

Operational patient-bed assignment problem in large hospital settings including overflow and uncertainty management

Managing patient to bed allocations is an everyday task in hospitals which in recent years has moved into focus due to a general rise in occupancy levels and the resulting need to efficiently manage tight hospital bed-capacities. This holds true especially when being faced with high volatility and uncertainty regarding patient arrivals and lengths of stay. In our work with a large German hospital we identified three main stakeholders, namely patients, nurses, and doctors, whose individual objectives and constraints regarding patient-bed allocation (PBA) lead to a potential trade-off situation. We developed a decision support model that tackles the PBA problem considering this trade-off, while also being capable of handling overflow situations. In addition, we anticipate emergency patient arrivals based on historical probability distributions and account for uncertainty regarding patient arrival and discharge dates. We develop a greedy look-ahead heuristic which allows for generating solutions for large real-life operational planning situations involving high ratios of emergency patients. We demonstrate the performance of our heuristic approach by comparison with the results of a near-optimal solution achieved by Gurobi’s MIP solver. Finally, we tested our approach using data sets from the literature as well as actual clinic data from our case study hospital, for which we were able to reduce overflow by over 96% while increasing overall utilization by 5%.

A hybrid ARIMA-SVR approach for forecasting emergency patient flow

The goal of this study is to explore and evaluate the use of a hybrid ARIMA-SVR approach to forecast daily radiology emergency patient flow. Owing to the fact that emergency patient flow is highly uncertain and dynamic, the forecasting problem is regarded as a complicated task. As the emergency patient flow may have both linear and nonlinear patterns, this paper presents a hybrid ARIMA-SVR approach, which hybridizes autoregressive integrated moving average (ARIMA) model and support vector regression (SVR) model to predict emergency patient arrivals. The proposed model is applied to 4 years of daily emergency visits data in the radiology department of a large hospital to justify the performance of the hybrid model against single models. The MAPE, RMSE and MAE of the hybrid model are 7.02%, 19.20 and 14.97, respectively. Furthermore, the hybrid model achieves better prediction performance than its competitors because it can capture the linear and nonlinear patterns simultaneously. Experimental results indicate that the proposed hybrid ARIMA-SVR approach is a promising alternative for forecasting emergency patient flow. These findings are beneficial for efficient patient flow management and scheduling decisions optimization.

Planning and scheduling operating rooms for elective and emergency surgeries with uncertain duration

In this paper we investigate the planning of operating rooms at Rigshospitalet, a large Danish hospital. Each operation must be assigned to a specific operating room and also be scheduled for a specific time while taking into account clinical guidelines. Both elective and emergency operations are included, such that the elective operations are planned while still taking potential emergency operations into consideration. Furthermore, the duration of each operation is uncertain. The aim is to construct robust operating room schedules that minimise overtime work and release unused capacity.Due to the uncertainty associated with arrival of emergency patients and also the duration of each operation, a deterministic model is not suitable for this problem. Therefore, we develop a stochastic model where operation duration can vary and where the arrivals of emergency patients are unknown. The stochastic model is computationally heavy, so two mixed integer programming based heuristics denoted 2-Step Relax-and-Fix and All Open Relax-and-Fix are developed to solve the problem.The computational study is based on an extensive dataset compromising 304 days. The heuristics give good results with half of the operating rooms having less than 8 min of overtime work. To test the robustness of the solutions we carry out a simulated implementation of the operation plans. The simulation shows that the heuristic solutions are fairly robust. In general, results show a clear potential for implementing the method for planning and scheduling of operating rooms at Rigshospitalet.

Predictive / Reactive Planning and Scheduling of a Surgical Suite with Emergency Patient Arrival.

This paper surveys the problem of predictive / reactive scheduling of an integrated operating theatre with two types of demand for surgery: 1) elective or known demand; 2) emergency or uncertain demand. The stochastic arrival of emergency patients with uncertain surgery time enforces the scheduler to react to disruption and modify scheduling plan of elective patients. We focus on this predictive / reactive scheduling problem which has not been investigated in such way before. As in hospitals, at the time of occurrence a disruption in a surgical suite, the scheduler has not enough time to make the best decision; we propose a new approach based on two-stage stochastic programming model with recourse which determines the best recourse strategy in advance of any disruption occurrence. Using the proposed approach, the primary schedule is generated in such a way that it can absorb disruption with minimum effect on planned elective surgeries. For the first time in operating theatre planning, two new significant sets of performance measures comprising "robustness" and "stability" measures are considered in generation of primary schedule which will be shown to be of great importance in efficiency of surgical suite planning. Computational experiments performed on sets of generated problem based on the data obtained from a non-profit hospital. In order to demonstrate efficiency of the proposed method, computational results of the proposed approach are compared with classic approach.

A stochastic programming approach for operating theatre scheduling under uncertainty

Operating theatre scheduling is a critical task that directly impacts the efficient delivery of surgical care. In this context, we propose a comprehensive stochastic programming modelling framework which handles the inherent uncertainty characterizing the arrival of emergency patients and the duration of surgery. In particular, three recourse strategies are presented with the aim of modelling different reactive scheduling policies actually adopted by hospital managers. In order to solve realistic-sized instances in a reasonable amount of time, we develop tailored heuristic solution strategies that exploit the problem structure. Computational results obtained on a set of randomly generated problems show the effective impact of the stochastic programming approach and the efficiency of the proposed heuristics.

Delays in Service for Non-Emergent Patients Due to Arrival of Emergent Patients in the Emergency Department: A Case Study in Hong Kong

BackgroundIn Hong Kong Emergency Departments (EDs), the timeliness of providing high-quality services has been compromised by the increasing attendance of non-emergent patients in addition to the unpredictable arrival of emergency patients. ObjectivesWe sought to quantify the impact of the presence of emergent patients and other related factors on the delay in service for non-emergent patients. MethodsWe conducted a retrospective study in patients who visited the ED of a large hospital in Hong Kong from July 1, 2009 to June 30, 2010. We estimated waiting and length of stay (LOS) for individual non-emergent patients registered during day and evening shifts. Using multiple linear regression, we estimated waiting time and LOS as a function of the presence of emergent patients and other related factors such as patient demographics and clinical factors. In particular, we evaluated the influence of the arrival or presence of emergent patients on the odds of violating the 120-min waiting time target for semi-urgent patients. ResultsThe arrival of a new emergent patient prolonged the waiting time and LOS of a non-emergent patient by 14.9% (95% confidence interval [CI] 14.2–15.5) and 10.8% (95% CI 10.6–11.0), respectively. An additional patient-hour needed for an emergent patient increased the probability of violating the waiting time target for non-emergent patients (odds ratio 2.3, 95% CI 2.2–2.4). ConclusionsThe arrival of an emergent patient significantly prolonged the waiting time and LOS for non-emergent patients. Discouraging non-urgent ED utilization and building a real-time decision-support system are critical methods needed to relieve staff pressure and guide contingent resource reallocation when emergent patients arrive.

Rescheduling of elective patients upon the arrival of emergency patients

In this study, a mixed integer linear programming (MILP) model is developed for rescheduling elective patients upon the arrival of emergency patients by considering two types of clinical units, namely operating rooms and post-anesthesia care units (PACUs). The model considers the overtime cost of the operating rooms and/or the PACUs, the cost of postponing or preponing elective surgeries, and the cost of turning down the emergency patients. The results indicate that a mainstream commercial solver can efficiently find an optimal solution in a particular scenario with light elective surgery load, but becomes very inefficient in searching optimal solutions in all other scenarios. As such, a genetic algorithm is developed to efficiently obtain the approximately optimal solutions in those scenarios that are difficult for the commercial solver. In the genetic algorithm, a novel chromosome structure is proposed and applied to represent the feasible solutions to the MILP model. It is shown that for the scenarios with heavy load of elective surgeries, the genetic algorithm can find approximate optimal solutions significantly faster than the commercial solver. In practice, the two solution methodologies should be used jointly to provide hospitals a solid tool for making sound and timely decisions in admitting emergency patients and rescheduling elective patients.