B.ed Solved Assignment

[Dona Vansoest]

Assigninginpatients to hospital beds impacts patient satisfaction and the workload of nurses and doctors. The assignment is subject to unknown inpatient arrivals, in particular for emergency patients. Hospitals, therefore, need to deal with uncertainty on actual bed requirements and potential shortage situations as bed capacities are limited. This paper develops a model and solution approach for solving the patient bed-assignment problem that is based on a machine learning (ML) approach to forecasting emergency patients. First, it contributes by improving the anticipation of emergency patients using ML approaches, incorporating weather data, time and dates, important local and regional events, as well as current and historical occupancy levels. Drawing on real-life data from a large case hospital, we were able to improve forecasting accuracy for emergency inpatient arrivals. We achieved up to 17% better root mean square error (RMSE) when using ML methods compared to a baseline approach relying on averages for historical arrival rates. We further show that the ML methods outperform time series forecasts. Second, we develop a new hyper-heuristic for solving real-life problem instances based on the pilot method and a specialized greedy look-ahead (GLA) heuristic. When applying the hyper-heuristic in test sets we were able to increase the objective function by up to 5.3% in comparison to the benchmark approach in [40]. A benchmark with a Genetic Algorithm shows also the superiority of the hyper-heuristic. Third, the combination of ML for emergency patient admission forecasting with advanced optimization through the hyper-heuristic allowed us to obtain an improvement of up to 3.3% on a real-life problem.

Achieving an overall performance improvement of up to 3.3% in solving real-world patient bed-assignment data sets by synergizing machine learning for emergency patient admission forecasting with advanced optimization via the hyper-heuristic.

Rising life expectancy, higher morbidity, and a changed spectrum of illnesses, but also technical and medical progress, which increasingly makes it possible to treat more and more diseases, are causing demand to rise for hospital treatments and increasing healthcare spending. For example, in Germany, spending rose by 4% in 2018 compared to the previous year and healthcare spending accounted for almost 12% of Gross Domestic Product [43]. Contrary to the increased demand for healthcare services, existing resources were reduced at the hospital level to compensate for the higher spending. From 2000 to 2017, the median number of hospital beds in OECD countries decreased by 13% [37]. In Germany, where a longer data history is available, from 1991 to 2018, there is a reduction of 20% in the number of hospitals, 25% in the number of beds, and a 33% increase in patient numbers [44]. Higher demand needs to be serviced with the scarcity of resources. If this is not to be at the expense of the patients and the quality of medical care, this can only be achieved by optimizing the utilization of available resources.

Hospital beds are one of these scarce resources. To efficiently use hospital beds, they are not any more planned individually by each ward as in the past, but oftentimes for the entire hospital to obtain pooling effects (see e.g., [8, 20, 28]). When arriving at the hospital, patients are directly or after a treatment (e.g., in operating or emergency room) admitted to a ward bed. This operational problem of assigning inpatients to specific rooms and beds is defined as patient-bed assignment problem (PBA). Figure 1 illustrates the PBA and its dependencies.

Efficient real-time planning systems are required in order to guarantee patient satisfaction and trouble-free process flow (e.g., avoid waiting times until inpatient admission as well as blocking emergency departments). The complexity of the PBA results from different stakeholder needs, frequent changes in lengths of stay (LOS) and estimating the number of beds required. First of all, the PBA needs to bring together the interests of patients, doctors, and nurses. To facilitate doing rounds and patient visits, walking distances for doctors should be minimized. This can be achieved by grouping similar patients, i.e., patients associated with a specific department, into rooms. In contrast to doctors, nurses tend to a broader range of patients. However, they are typically dedicated to a specific ward, working in well-coordinated teams, and therefore cannot easily be transferred to other wards. Thus, balancing the workload between wards is a key objective for nurses when assigning patients to beds. Hence, the PBA affects patient satisfaction (e.g., immediately available bed, suitable room with adequate roommates), the workload of nurses (e.g., a mix of work-intensive and easy-to-handle patients), and workload of doctors (e.g., own patients located in proximity). These may comprise some trade-offs. For example, focusing only on patient satisfaction by putting optimal roommates together (i.e., patients of similar age or with similar illnesses) may be in conflict with the nurse workload. Second, deviations from expected medical conditions and treatment plans are normal, for example, if patients remain in intensive care units (ICU), LOS changes happen (e.g., earlier or later discharge, unforeseen surgical complications, newly detected medical conditions), elective inpatients do not arrive or different medical infrastructure becomes necessary. Whenever one of the events takes place, the PBA plan needs to be updated. This can easily affect 50% of all beds per day if, for example, 30% of the inpatients are discharged and admitted per day and 20% are affected by LOS updates. Finally, a further complication arouses from the inherent uncertainty of bed needs for emergency inpatients which may account for up to 90% of all inpatients. Appropriately predicting which kind of emergency patients and how many from each hospital department are likely to arrive is a fundamental input to the PBA. Several external effects like seasons, weather, or local events and different drivers for each discipline like snowy weather for trauma surgery may drive the volume of emergency patients.

The main body of related literature considers elective patients only (see e.g., [6, 16, 32]). In these applications, assignment is done for a known set of patients to a given set of empty beds. Some extensions deal with dynamically arriving elective patients (see e.g., [13]) and uncertainty in LOS (see e.g., [36]). The present paper builds upon the extended model introduced by [40] that copes with patient-, nurse- and doctor-specific criteria, and accounts for dynamically arriving elective and emergency patients as well as dynamic changes of LOS. They apply an average emergency inpatient arrival rate. However, simply predicting emergency patients based on historical averages will be suboptimal, as it seems highly probable that the actual number of emergency admissions is dependent on a plethora of internal and external factors in each medical specialty. We extend this approach by proposing a ML approach to anticipate future emergency inpatient arrivals. The analysis is based on a comprehensive empirical data collection (e.g., patient data, weather, regional events). This allows us to investigate factors that can predict emergency admissions for each medical specialty and analyze the impact of improving the forecasts on bed planning employing numerical studies with actual data from a maximum-care hospital. ML will continue to revolutionizing healthcare management due to the exponential increase of data and computing power (see, e.g., [3]). Predictive analytics will be entering the space of operational management in hospitals and improve decision making (see, e.g., [27]). We develop insights in the use of ML on emergency patient admission forecasting. We further contribute with an advanced solution approach by tailoring a hyper-heuristic framework to the PBA. We combine the forecasts obtained with ML with a hyper-heuristic framework for solving the PBA efficiently for large problem instances within a real-life application.

The remainder of this paper is organized as follows. We review related literature in Section 2. The underlying mathematical model of our decision problem and advanced optimization approach is summarized in Section 3. Section 4 provides several numerical examples based on actual hospital data. Finally, Section 5 presents a summary of the main results and outlines potential avenues for further research.

We contribute to the PBA literature and the related forecasting of emergency patients. The literature can be structured along (i) static and (ii) dynamic models for PBA and (iii) forecasting models for bed requirements.

The static PBA was first introduced by [16]. They consider a situation in which a hospital is initially empty and all future patient arrivals within a given time horizon are deterministically known as well as their respective parameters, e.g., actual LOS, gender, department adherence, and individual infrastructural needs. Patients are assigned to rooms such that an overall objective function based on violating patient-specific requirements is minimized. Capacity is assumed to be sufficient to accommodate all inpatients. As such, it does not allow for shortage situations. Furthermore, they do not distinguish between emergency and elective patients. Several authors like [6, 9, 13, 17, 23, 32, 47] have since built on the model of [16] by providing alternative solution approaches like matheuristics such as the Genetic Algorithm (GA). For details, we refer to Table 1. To summarize, the static models assign elective patients to beds. However, whenever a patient is admitted to or discharged from wards, patients are reassigned from the overflow, no-shows of elective patients occur, sudden changes in medical infrastructural requirements, an unexpected need for medical isolation or changes in the LOS become necessary, the static plan is no longer valid. The PBA need to be updated. Therefore, the static models provide only a starting point for solving the PBA.

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