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Abstract When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how the perturbation of MCMC affects the convergence speed and approximation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has fast convergence speed and high approximation accuracy as well. Our convergence analysis is conducted under either the Wasserstein metric or the$$\chi^2$$metric, both are widely used in the literature. The results can be extended to obtain non-asymptotic error bounds for MCMC estimators. We demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis, Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally, we present some simple numerical examples to verify our theoretical claims. 

Queue scheduling, in which limited resources must be allocated to incoming customers, has numerous applications in service operations management. With increasing data availability and advances in predictive models, personalized scheduling—which leverages individual information about underlying stochastic processes beyond just probability distributions—has gained significant attention. A new study reveals that, even with noisy service-time predictions, the (predicted) shortest-job-first (SJF) policy can effectively optimize performance in many-server systems with inpatient customers. The study also characterizes the impact of prediction errors on the policy’s effectiveness. Additionally, the study shows that a two-class priority rule, in which customers with shorter predicted service times (below a carefully designed threshold) are prioritized, can asymptotically match the performance of SJF, offering a simpler policy for implementation in practice. 

Abstract IntroductionIn order to be positioned to address the increasing strain of burnout and worsening nurse shortage, a better understanding of factors that contribute to nursing workload is required. This study aims to examine the difference between order‐based and clinically perceived nursing workloads and to quantify factors that contribute to a higher clinically perceived workload. DesignA retrospective cohort study was used on an observational dataset. MethodsWe combined patient flow, nurse staffing and assignment, and workload intensity data and used multivariate linear regression to analyze how various shift, patient, and nurse‐level factors, beyond order‐based workload, affect nurses' clinically perceived workload. ResultsAmong 53% of our samples, the clinically perceived workload is higher than the order‐based workload. Factors associated with a higher clinically perceived workload include weekend or night shifts, shifts with a higher census, patients within the first 24 h of admission, and male patients. ConclusionsThe order‐based workload measures tended to underestimate nurses' clinically perceived workload. We identified and quantified factors that contribute to a higher clinically perceived workload, discussed the potential mechanisms as to how these factors affect the clinically perceived workload, and proposed targeted interventions to better manage nursing workload. Clinical RelevanceBy identifying factors associated with a high clinically perceived workload, the nurse manager can provide appropriate interventions to lighten nursing workload, which may further reduce the risk of nurse burnout and shortage. 

Determining emergency department (ED) nurse staffing decisions to balance quality of service and staffing costs can be extremely challenging, especially when there is a high level of uncertainty in patient demand. Increasing data availability and continuing advancements in predictive analytics provide an opportunity to mitigate demand uncertainty by using demand forecasts. In this work, we study a two-stage prediction-driven staffing framework where the prediction models are integrated with the base (made weeks in advance) and surge (made nearly real-time) nurse staffing decisions in the ED. We quantify the benefit of having the ability to use the more expensive surge staffing and identify the importance of balancing demand uncertainty versus system stochasticity. We also propose a near-optimal two-stage staffing policy that is straightforward to interpret and implement. Last, we develop a unified framework that combines parameter estimation, real-time demand forecasts, and nurse staffing in the ED. High-fidelity simulation experiments for the ED demonstrate that the proposed framework has the potential to reduce annual staffing costs by 10%–16% ($2 M–$3 M) while guaranteeing timely access to care. This paper was accepted by David Simchi-Levi, healthcare management. Funding: J. Dong was partially supported by the Division of Civil, Mechanical and Manufacturing Innovation [Grant CMMI-1944209]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2021.02781 . 

Problem definition: Delays in admission to rehabilitation care can adversely impact patient outcomes. In addition, delayed patients keep occupying their acute care beds, making them unavailable for incoming patients. Admission delays are mainly caused by a lack of rehabilitation bed capacity and the time required to plan for rehabilitation activities, which we refer to as processing times. Because of non-standard bed allocation decisions and data limitations in practice, quantifying the magnitude of the two sources of delays can be technically challenging yet critical to the design of evidence-based interventions to reduce delays. We propose an empirical approach to understanding the contributions of the two sources of delays when only a single (combined) measure of admission delay is available. Methodology/results: We propose a hidden Markov model (HMM) to estimate the unobserved processing times and the status-quo bed allocation policy. Our estimation results quantify the magnitude of processing times versus capacity-driven delays and provide insights into factors impacting the bed allocation decision. We validate our estimated policy using a queueing model of patient flow and find that ignoring processing times or using simple bed allocation policies can lead to highly inaccurate delay estimates. In contrast, our estimated policy allows for accurate evaluation of different operational interventions. We find that reducing processing times can be highly effective in reducing admission delays and bed-blocking costs. In addition, allowing early transfer—whereby patients can complete some of their processing requirements in the rehabilitation unit—can significantly reduce admission delays, with only a small increase in rehab LOS. Managerial implications: Our study demonstrates the importance of quantifying different sources of delays in the design of effective operational interventions for reducing delays in admission to rehabilitation care. The proposed estimation framework can be applied in other transition-of-care settings with personalized capacity allocation decisions and hidden processing delays. History: This paper was selected for Fast Track in the M&SOM journal from the 2022 MSOM Healthcare SIG Conference. Funding: J. Dong was supported in part by the National Science Foundation [Grant CMMI-1762544]. V. Sarhangian was supported in part by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2018-04518] and the Connaught Fund. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.0377 . 

When having access to demand forecasts, a crucial question is how to effectively use this information to make better resource allocation decisions, especially during demand surges like the COVID-19 pandemic. Despite the emergence of various advanced prediction models for hospital resources, there has been a lack of prescriptive solutions for hospital managers seeking concrete decision support, for example, guidance on whether to allocate beds from other specialties to meet the surge demand from COVID-19 patients by postponing elective surgeries. In their paper “Optimal Routing under Demand Surge: the Value of Future Arrival Rate,” the authors present a systematic framework to incorporate future demand into routing decisions in parallel server systems with partial flexibility and quantify the benefits of doing so. They propose a simple and interpretable two-stage index-based policy that explicitly incorporates demand forecasts into real-time routing decisions. Their analytical and numerical results demonstrate the policy’s effectiveness, even in the presence of large prediction errors.