Multiclass Queue Scheduling Under Slowdown: An Approximate Dynamic Programming Approach with Evidence from Rehabilitation Care

Information Systems and Operations Management 

Intervenant: Berk Görgülü (McMaster University)

Salle Bernard Ramanantsoa

Abstract:

In many service systems, especially those in healthcare, waiting times can result in increased service requirements. Such service slowdowns can significantly impact system performance through propagating congestion in the system. Therefore, it is important to properly account for their impact when designing scheduling policies. Scheduling under wait-dependent service times is challenging, especially when multiple customer classes are heterogeneously affected by waiting. Motivated by the problem of patient flow from acute care to rehabilitation, in this work, we study scheduling policies in multiclass, multiserver queues with wait-dependent service slowdowns. We propose a novel simulation-based Approximate Dynamic Programming (ADP) algorithm to find near-optimal scheduling policies. Through extensive numerical experiments, we illustrate that the ADP algorithm generates policies that outperform well-known benchmarks. We also provide insights into the structure of the optimal policy, which reveals an important trade-off between instantaneous cost reduction and preventing the system from reaching high-cost equilibria. Lastly, we conduct a case study on scheduling admissions into rehabilitation care to illustrate the effectiveness of the ADP algorithm in practice.