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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 .

 

Queueing models that are used to capture various service settings typically assume that customers require a single unit of resource (server) to be processed. However, there are many service settings where such an assumption may fail to capture the heterogeneity in resource requirements of different customers. We propose a multiserver queueing model with multiple customer classes in which customers from different classes may require different amounts of resources to be served. We study the optimal scheduling policy for such systems. To balance holding costs, service rates, resource requirement, and priority-induced idleness, we develop an index-based policy that we refer to as the idle-avoid [Formula: see text] rule. For a two-class two-server model, where policy-induced idleness can have a big impact on system performance, we characterize cases where the idle-avoid [Formula: see text] rule is optimal. In other cases, we establish a uniform performance bound on the amount of suboptimality incurred by the idle-avoid [Formula: see text] rule. For general multiclass multiserver queues, we establish the asymptotic optimality of the idle-avoid [Formula: see text] rule in the many-server regime. For long-time horizons, we show that the idle-avoid [Formula: see text] is throughput optimal. Our theoretical results, along with numerical experiments, provide support for the good and robust performance of the proposed policy.