A Queueing Model to Evaluate the Impact of Patient “Batching” on Throughput and Flow Time in a Medical Teaching Facility

Abstract

We consider the work flow in a medical teaching facility, examining the process that involves an initial patient exam by a resident physician, a subsequent conference between the resident and the attending physician, and the attending physician's visit with the patient. We create an analytical model of a tandem queue with finite buffer space to analyze the impact of different work prioritization policies on the throughput and the flow time of patients in the facility—measures that influence both the facility's finances and patients' satisfaction. We derive throughput-optimal policies and show that these policies involve dynamic batching. This finding is interesting because our model does not include any setup times, and setup times normally imply batching; rather it is the uncertain service times and the requirement for simultaneous service in the conference step that make batching optimal. The optimal dynamic batching policy is complex, so we consider a simpler static batching policy. We show that, in systems with limited buffer space, large batches can sometimes degrade efficiency by simultaneously increasing flow time and decreasing throughput. However, in general, both flow time and throughput increase with batch size. Flow time increases at a faster rate than throughput, so hospital management may want to consider what batch size is optimal given the value it places on the two measures.

On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking

“…Dai and Lin (2005) consider throughput maximization in processing networks (see specifically section 7 therein for indivisible resources). Dobson et al (2012) consider a tandem queueing network with two distinct resources and three stages and derive control policies that maximize throughput by using MDP techniques. They are motivated by physician scheduling in emergency departments.…”

A Review of the Healthcare-Management (Modeling) Literature Published in Manufacturing & Service Operations Management

“…They develop time-varying fluid and diffusion approximations to come up with staffing policies that are shown to perform well. Dobson et al (2012) examine the interaction between junior (resident) physicians who may batch patients before seeking the input of a senior (attending) physician in the context of the ED at a teaching hospital. More specifically, the authors develop a (tandem) queueing model to examine the impact of batching on throughput.…”

Front-office multitasking between service encounters and back-office tasks

“…Collaboration is also modeled in Gurvich and Van Mieghem (2014), who study networks where some activities require the simultaneous processing by multiple types of multitasking human resources. Dobson et al (2012) consider a system with three tandem stations and two servers. Each server serves at one station, however a third station in the middle represents a collaborative task where both servers have to be simultaneously present.…”