Introduction

Effective and efficient delivery of healthcare is a major societal concern in the US and throughout the world and the paradigm of coordinated care delivery has gained increasing visibility in recent years. Because the entire healthcare system in the US (and in other countries as well) is coming under increasing cost pressure to increase efficiency, there is also a financial incentive to transition to larger more coordinated network care models such as those found at the Mayo Clinic.

This chapter develops innovative stochastic modeling methods to forecast the workload across the network of outpatient care resources for any given patient sched- ule. This stochastic location model serves as the mechanism for linking admission de- cisions to outpatient service workload. Combining the stochastic location model with

a controlled arrival stream yields what we call a controlled-arrival-location model (CALM). In this chapter, we develop the CALM model in such a way as to allow for optimization methods that can determine improved patient schedules in a tractable manner.

Though large providers enjoy many benefits, there are also great operational and management challenges of coordinating the complex network of resources that com- prise these healthcare organizations. A primary controllable driver of efficiency in these complex systems is patient scheduling. The way in which patients are scheduled has a major effect on the workload experienced in an organization’s various network resources. As an example, consider the workload in the breast diagnostic clinic for three different schedules that generate three different workload profiles. The output based on historical data from the Mayo Clinic is shown in Figure 4.1.

0 5 10 15 20 25

Mon Tue Wed Thu Fri

#  M.D . C o nsul t  Appoi tnm ent s Mean 75% Quantile 0 5 10 15 20 25

Mon Tue Wed Thu Fri

#  M.D . C o nsul t  Appoi tnm ent s Mean 75% Quantile 0 5 10 15 20 25

Mon Tue Wed Thu Fri

#  M.D . C o nsul t  Appoi tnm ent s Mean 75% Quantile

(a) Unbalanced (b) Partially unbalanced (c) Completely Balanced

Figure 4.1: The effect of the patient schedule on the workload at the breast diagnostic clinic.

The schedule that generates an unbalanced workload profile (Fig 4.1 (a)) requires over 33% more resources on average in the middle of the week than the schedule that generates a balanced schedule. This causes the organization to adopt an un- balanced staffing profile (which requires more resources in aggregate and staffing inconvenience), or to accept access failures and treatment bottlenecks. The man- agement challenge is in designing a schedule that can achieve a balanced workload such as the one in Figure 4.1 (c). Because patient care pathways are complex and

dynamically changing with their disease condition and the amount of information providers have about their disease it is often difficult to predict the effect scheduling various patients. Another complicating factor is that patients follow a stochastic path through a general network of care services. For example, breast cancer patients at the Mayo Clinic as a population require care from over 77 different outpatient services over the course of their treatment.

After developing the general analytical models for controlling patient schedules and smoothing hospital workloads, we demonstrate how this approach can be ap- plied to a critical problem in destination healthcare organizations in general and of particular interest to our partner, the Mayo Clinic: Itinerary Completion. By defini- tion, many patients of destination healthcare organizations come from geographically distant locations. These patients are classified as national or international patients. With these patient types an important access metric is that they complete their treat- ment segment before the weekend. Since most clinical services are not available on the weekend, failure to complete care within the work week forces the patients to pay for hotels and stay over the weekend without any treatment progress, which is emo- tionally challenging for patients and families at a very vulnerable time of their life. Itinerary completion is an important part of patient satisfaction and poor healthcare delivery performance; in fact, some patients decide to return home without complet- ing treatment. The itinerary completion metric was developed to measure the ability of the healthcare provider to complete treatment for national/international patients treatment before the weekend begins.

The core model is divided into two stages as shown in Fig. 4.2. The goal of the workload smoothing stage is to reduce blocking in all of the important services by stabilizing the workload across the week. Because the clinics are staffed at a constant

level over the days of the week, eliminating the workload spike should give patients better access to care in the middle of the week, avoiding delays to getting an appoint- ment and thereby flowing unhindered through their treatment path. The itinerary completion stage establishes the virtual fast-track priority schedule to maximize the probability that national/international patients will complete their treatment within the work week. In Fig. 4.2, for example, the national patients have been mostly moved to the beginning of the week.

Workload Smoothing Stage

Original Smoothed

Itinerary Completion Stage

Ti

m

e

M T W R F M T W R F

Original Optimized

National Patient Slot Local Patient Slot

Day of Wk Day of Wk # Appointments (Workload) 75% Quantile , Optimization No. Appt

Figure 4.2: High level approach to a two stage fast-track model.

We demonstrate the applicability of our patient flow paradigm to the itinerary completion problem by developing schedules that fast-track national/international patients; however, the approach is generalizable to any healthcare organization in which patients with different needs / priority levels arrive according to a controllable patient schedule and flow through a network of care services. This applies not only to destination healthcare organizations, but to all healthcare organizations that manage multiple types of care services.

In Section 4.2, we provide some background on the different approaches to man- aging scheduled arrivals to stabilize flow and workloads, primarily in healthcare sys- tems. In Sec. 4.3 we developed the queueing network model of patient flow through a network of services. Sec. 4.4 builds upon the stochastic models of Sec. 4.3 by de- veloping queueing network blocking models and optimization methods for smoothing

workloads across a network. Sec. 4.5 presents a phase-type modeling approach for capturing itinerary completion of fast-track patients flowing through a congested queueing network with blocking. Sec. 4.6 incorporates the flow models from Sec. 4.3 and 4.4, and the phase-type itinerary completion model from Sec. 4.5 into a second schedule optimization model that fast-tracks priority patients. We demonstrate how the two optimization models can be used to solve the Mayo Clinic itinerary comple- tion problem with a detailed case study in Sec. 4.7. Finally, we draw conclusions and discuss the contribution of this work in Sec. 4.8.

4.2 Patient Flow Management and Optimization in Highly Stochastic