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Increasing Patient Throughput in the MGH Cancer
=
Center Infusion Unit
by
Wendi Rieb
S.B., Massachusetts Institute of Technology, 2008
M.Eng., Massachusetts Institute of Technology, 2009
Submitted to the Department of Electrical Engineering and Computer Science and the
Sloan School of Management in partial fulfillment of the requirements for the degrees of
Master of Science in Electrical Engineering and Computer Science
and
Master of Business Administration
in conjunction with the Leaders for Global Operations Program at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
@ Wendi Rieb, MMXV. All rights reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic
copies of this thesis document in whole or in part in any medium now known or hereafter created.
redacted
Author....................Signature
Department of Electrical Engineering and Computer Science and the Sloan School of
Management
May 8, 2015
Certified by.
Signature redacted
Charles Sodini, Thesis Supervisor
LeBel Professor, Departmet of Electrical Engineering and Computer Science
Certified by.
.......
Signature redacted ..........................
Retsef Levi, Thesis Supervisor
J. Spencr Standish Professor, Sloan School of Management
Approved by...........
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/
-Leslie
. ..... ...............
Kolodziejski
Chaiof the Committee on Graduate Students
Department of Electrical Engineering and Computer Science
Approved by.................
L
Signature redacted,Maura Herson
Director, MBA Program, MIT Sloan School of Management
o
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Increasing Patient Throughput in the MGH Cancer Center
Infusion Unit
by
Wendi Rieb
Submitted to the Department of Electrical Engineering and Computer Science and the
Sloan School of Management on May 8, 2015, in partial fulfillment of the requirements for
the degrees of
Master of Science in Electrical Engineering and Computer Science
and
Master of Business Administration
Abstract
This thesis proposes an appointment scheduling algorithm with associated supporting process changes that increases the effective capacity of the Massachusetts General Hospital
Cancer Center Infusion Unit. Currently, chair and bed utilization in the Infusion Unit is
concentrated between 10am-2pm, Monday through Friday, but remains underutilized during
other operating hours. This uneven use of resources has resulted in highly strained staff and
physical resources during rush hour, causing the perception of insufficient capacity. Moreover, when the environment is highly congested, patients experience long wait times and are
more exposed to quality and safety problems. This study will recover unrealized capacity by
smoothing the intra-day utilization of physical resources in the Infusion Unit. The scheduling
algorithm is derived employing a retrospective integer program and validated using prospective simulation modeling. Implementation of these scheduling guidelines demonstrates the
potential to recover 20 chairs, or 33% of capacity, at the average peak of each day, while
smoothing throughput throughout the day. The proposed state can be achieved with minimal adjustments to staffing in the infusion unit and pharmacy, and no adjustment to staffing
in the Oncology Practice. The algorithm also respects the existing primary nursing model,
and treatment specific limitations.
Thesis Supervisor: Charles Sodini
Title: LeBel Professor, Department of Electrical Engineering and Computer Science
Thesis Supervisor: Retsef Levi
Title: J. Spencer Standish Professor, Sloan School of Management
2
Acknowledgments
This thesis would not have been possible without the generous advising and support of many.
Thank you to exceptional academic advisors Professor Retsef Levi of the Sloan School of
Management and Professor Charles Sodini of the Department of Electrical Engineering and
Computer Science; the incredibly enjoyable to work with team from MGH Cancer Center
Mara Bloom, Inga Lennes, M.D., Elizabeth Souza, Erika Rosato, Mimi Bartholomay, Katie
Lafleur, and Michael Duk; the MGH champions of the collaboration with MIT Peter Dunn,
M.D., Bethany Daily, and Cecilia Zenteno. I would especially like to thank Cecilia Zenteno
and Ainara Arcelus for significant contribution to model formulation and creation.
Thank you to my loving family, my husband Karl Rieb, mother Yanling Zhao, and
parents-in-law Charles and Rocio Rieb who give me the my strength and purpose in life.
Finally, I give thanks to the Lord for all his blessings and for guiding me through this
difficult to navigate world.
3
Contents
1
Introduction
1.1
.11
2
3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1
Massachusetts General Hospital . . . . . . . . . . . . . . . . . . . . .
11
1.1.2
MGH Cancer Center . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1.2
Project Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
1.3
Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
17
Literature Review
2.1
Successful Implementation of Resource Management and Scheduling Redesign
17
2.2
Optimization Models and Integer Programming as a Tool . . . . . . . . . . .
18
2.3
Simulation as a Tool
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
Patient Flow in the Cancer Center
3.1
3.2
4
Background
11
23
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.1.1
P ractice . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.1.2
Infusion Unit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3.1.3
Governance of the Practice and Infusion Unit
Cancer Center Structure
. . . . . . . . . . . . .
25
Appointment Types and Patient Flow . . . . . . . . . . . . . . . . . . . . . .
25
3.2.1
Infusion Appointments . . . . . . . . . . . . . . . . . . . . . . . . . .
25
3.2.2
Other Relevant Appointment Types in the Practice . . . . . . . . . .
28
3.2.3
Scheduling Practices . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Current State Analysis
30
4
.....
30
Shadowing and Interviewing . . . . . . . . .
. . . . . . . . . .
30
4.1.2
IT, Databases, and Data Aggregation . . . .
. . . . . . . . . .
32
. . . . . . . . . .
34
.
.
4.1.1
. . . . . . . . . . . . . .
.
Current State Description
4.2.1
Summary of Problems
. . . . . . . . . . . .
. . . . . . . . . .
34
4.2.2
Patient Arrival Scheduling . . . . . . . . . .
. . . . . . . . . .
35
4.2.3
Variation from Scheduled Patient Stay Times
. . . . . . . . . .
37
Solution Approach
. . . . . . . . . . . . . . .
. . . . . . . . . .
46
5.2
Evaluation Method . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . .
47
5.3
Retrospective Optimization Model . . . . . . . . . .
. . . . . . . . . . . . .
47
5.3.1
Integer Program . . . . . . . . . . . . . . . .
. . . . . . . . . . . . .
47
5.3.2
Retrospective Model Results . . . . . . . . .
. . . . . . . . . . . . .
51
Prospective Real-Time Algorithm . . . . . . . . . .
. . . . . . . . . . . . .
57
5.4.1
Scheduling Algorithm Description . . . . . .
.
. . . . . . . . . . . . .
57
5.4.2
Prospective Model Performance Assessment
. . . . . . . . . . . . .
60
5.4.3
Incorporating Patients Choices
. . . . . . .
. . . . . . . . . . . . .
64
Complementary Feasibility Assessment
. . . . . . .
. . . . . . . . . . . . .
68
5.5.1
Primary Nursing Study . . . . . . . . . . . .
. . . . . . . . . . . . .
69
5.5.2
Pharmacy Study
. . . . . . . . . . . . .
72
5.5.3
Nursing Load Study
. . . . . . . . . . . . .
75
.
.
.
.
.
.
.
.
.
. . . . . . . . . . . . . . .
. . . . . . . . . . . . .
.
5.5
.
Objective and Overview
.
46
5.1
5.4
80
6.1
Operational Recommendations . . . . . . . . . . . .
80
6.1.1
Scheduling Recommendations
80
6.1.2
Process Change Recommendations
. . . . .
80
6.1.3
Staffing Recommendations . . . . . . . . . .
81
6.2
Future W ork . . . . . . . . . . . . . . . . . . . . . .
82
6.3
Conclusions
84
.
Recommendations, Future Work, & Conclusions
.
.
.
. . . . . . . .
.
6
. . ...
. . . . . . . . . . . . . . . . . . . . . .
.
5
......................
.
4.2
Data Sources .....
.
4.1
5
A Stay Variation Analysis: Detailed Explanation
86
B Supplemental Current State Plot
91
C Holidays in CY2013
92
D Alternative to Max(Max-Min) Method
93
E Other options to give the patient two scheduling options
95
F Pharmacy Staffing Study - Complete Description
99
6
List of Figures
1-1
Infusion Unit utilization each hour: average
1 standard deviation for 243
days in 2013 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
3-1
Full Patient Flow Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
4-1
Total wait time as a percentage of total infusion time for all infusions in 2012
and 2013..... .. .. ... .. ................ .. . . . . . ...
..
35
4-2
Current state patient/nurse ratio throughout the day . . . . . . . . . . . . .
36
4-3
Boxplot of scheduled durations of all infusions in 2012 and 2013 . . . . . . .
37
4-4
Distribution of infusion appointments and total occupied chair hours in Infusion Unit by appointment hours of scheduled duration . . . . . . . . . . . . .
38
4-5
Current State: Distribution of infusion start times throughout operational hours 38
4-6
Current State: Distribution of PTC Practice appointment start times throughout operational hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-7
39
Proportion of total capacity impacted by stay variation at different hours of
the day . . . . . . . . . . . . . . . . . . . . . .. . ................41
4-8
Proportion of total capacity impacted by stay variation at different hours of
the day......
4-9
..
..
...
.. ............. ... . . . ..... .. . ..
44
Distribution of same-day cancellations throughout the hours of the day
.
45
4-10 Breakdown of add-on treatment types . . . . . . . . . . . . . . . . . . . . . .
45
5-1
Retrospective Model Results: daily utilization
. . . . . . . . . . . . . . . . .
52
5-2
Retrospective Model Results: distribution of daily peak utilization . . . . . .
53
5-3
Retrospective Model Results: Infusion-Only Start Times
54
7
.
.
. . . . . . . . . . .
5-4
Retrospective Model Results: Infusion-Only cumulative start time by appointment duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
5-5
Retrospective Model Results: PTC infusion start times . . . . . . . . . . . .
56
5-6
Retrospective Model Results: PTC cumulative start time by appointment
duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-7
56
Representative Example of Prospective Algorithm Step 3: Max(Max-Min)
Method, with given parameters
. . . . . . . . . . . . . . . . . . . . . . . . .
61
5-8
Prospective Model daily utilization
. . . . . . . . . . . . . . . . . . . . . . .
62
5-9
Prospective Model distribution of daily peak utilization . . . . . . . . . . . .
63
.
66
5-11 Comparison of Daily Peaks for Giving the Patient 1 Option vs. 2 Options . .
67
5-10 Comparison of Utilization for Giving the Patient 1 Option vs. 2 Options
.
5-12 Time difference [hours] between first and second appointment option offered
to patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
. . . . . . . .
70
5-14 Current State: Pharmacy Throughput by Staffing Region . . . . . . . . . . .
73
5-13 Results: Proposed State adherence to Primary Nursing Model
5-15 Proposed state pharmacy load assuming no additional process improvements
or algorithm tweaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
5-16 Pharmacy throughput by staffing region including conservative premix for
8am and 9am appointments
. . . . . . . . . . . . . . . . . . . . . . . . . . .
5-17 Current State: Number of nurses on staff by time of day
5-18 Current State: Patient/Nurse Ratio by time of day
. . . . . . . . . . .
76
. . . . . . . . . . . . . .
77
5-19 Patient/Nurse Ratio proposed state with existing nursing staffing
A-1
75
. . . . . .
79
Histogram of stay variation, differentiating add-ons, cancellations & no-shows,
and operational variation, for 63 days in 2013
. . . . . . . . . . . . . . . . .
87
A-2 Histogram of daily stay variation, overstay, and understay for 63 days in 2013
88
A-3 Proportion of total capacity impacted by stay variation at different hours of
the day. ........
..
............
. .
. ............
.....
90
B-1 Scheduled duration for all infusions in 2012 and 2013 by hour of first appointment segment start time . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
91
D-1
Distribution of daily peaks for Last method, alternative to Max(Max-Min)
method
E-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Giving the patient options: daily utilization assuming patient bias towards
10am-2pm period: distribution of daily peak utilization . . . . . . . . . . . .
E-2
94
97
Giving the patient options assuming patient bias towards 10am-2pm period:
distribution of daily peak utilization.
From left to right: Prospective base
model, Giving the patient one morning option and one afternoon option, Giving the patient two options at least two hours apart, Giving the patient two
options maximizing the time between the options while favoring operations .
F-1
98
Proposed state pharmacy load assuming no additional process improvements
or algorithm tweaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
F-2
Pharmacy throughput proposed state: 8am Cap=35 . . . . . . . . . . . . . .
102
F-3
Pharmacy throughput proposed state: 8am Cap=25 . . . . . . . . . . . . . .
102
F-4
Pharmacy throughput proposed state: 8am Cap=15 . . . . . . . . . . . . . .
103
9
List of Tables
. . . . . . . . . . . . . .
36
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.1
Infusion appointment scheduled duration categories
4.2
Stay Variation Statistics
5.1
Pharmacy Staffing Regions: Current State
A.1
Stay Variation Statistics
C.1
Specific dates in CY2013 excluded from modeling
. . . . . . . . . . . . . . . . . . .
73
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
10
. . . . . . . . . . . . . . .
92
Chapter 1
Introduction
1.1
1.1.1
Background
Massachusetts General Hospital
Massachusetts General Hospital (MGH) is the largest and oldest hospital in New England,
and is consistently ranked as one of the top hospitals in the country. The hospital is an
integrated patient care facility and research powerhouse, with an annual research budget approaching $800 million. Patient volume numbers approximately 48,000 inpatient admissions
and 1.5 million outpatient visits annually, including more than 100,000 emergency room
visits, 42,000 operations, and 3,600 delivered babies [1]. Since 2011, MGH has maintained
a collaboration with MIT Sloan and Leaders for Global Operations [2], resulting in several
successful projects [5][9][17][21][22][18][16]
during this time. In this thesis we describe the
first project that the MGH/MIT Collaboration has with the Cancer Center.
1.1.2
MGH Cancer Center
The MGH Cancer Center is a leading cancer research and care establishment, consistently
ranked among the top 10 Cancer Centers in the United States [15], and regularly cares for
patients from around the globe. Treatment programs are divided into 24 Disease Centers,
and patients receive treatment in one or more Disease Centers depending on the type of
cancer diagnosis. Patient volume has been growing at a rate of 4% annually over the three
11
year period 2011-2014 [6].
The fully integrated Cancer Center is made up of several functional units, including
the Practice, the Infusion Unit, Radiation Oncology, and Surgical Oncology.
The Prac-
tice employs approximately 100 medical oncologists (equivalently referred to as clinicians,
physicians, or oncologists) and 60 medical oncology nurse practitioners (NPs). Physicians
see cancer patients in the Practice, and assign treatment to the other treatment facilities
of the Cancer Center. The Practice also operates a four bed Short Stay Unit, where nonchemotherapy infusions such as hydrations and antibiotics can be administered on short
notice. The Infusion Unit offers infusion treatments including but not limited to chemotherapy, blood transfusions, iron infusions, infused antibiotics, and hydrations.
A selection
of injectable and ingestible treatments in conjunction with chemotherapy are also offered.
Nursing in the clinic follows the Primary Nursing Model, a system whereby a single nurse
is assigned to oversee the full infusion course of treatment of each patient. Schedulers prioritize scheduling the patient to their Primary Nurse whenever possible. The Infusion Unit
contains 60 beds and chairs that are used to deliver infusion treatments. It currently sees approximately 40,000 patient encounters annually, growing at an annual rate of approximately
2.5% [6]. Operational hours are 7:00am to 8:00pm Monday through Fridays, and 8:00am to
5:00pm on Saturdays. Radiation Oncology is the unit patients visit for radiation therapy.
Surgical Oncology is the unit patients visit to receive cancer related surgeries. Radiation
and Surgical Oncology are not affected by this study. This study addresses the problem of
smoothing the intra-day utilization of resources in the Infusion Unit, and its interaction with
the Practice.
1.2
Project Overview
The MGH Cancer Center Infusion Unit currently experiences extremely high volume between
10am and 2pm and is underutilized otherwise (see Figure 1-1). In particular, the average
chair utilization throughout the day (7am-8pm) is 55%, but the midday (11am-2pm) congestion is very severe, and causes the perception of insufficient capacity.
In addition to
preventing patient volume growth, the non-smooth utilization in Figure 1-1 has several con-
12
Utilization Each Hour
Mean t 1SD Error bars for 243 days in 2013
~70
S40
0 30
60
z 0
Time (hour)
Figure 1-1: Infusion Unit utilization each hour: average + 1 standard deviation for 243 days
in 2013
sequences: (i) long wait times for patients during high utilization hours; (ii) low utilization
of expensive resources during low utilization hours; (iii) higher potential for patient safety
concerns during congested hours.
Several additional challenges make the redesign of patient flow difficult:
1. Multi-resource scheduling. All visits require blood draws prior to treatment. The
results of the blood test confirms whether the patient could have the inftusion treatment
and could also cancel or alter the appointment type. Additionally, 75% of the infusion
visits are coupled with an appointment in the Practice, where the patient is assessed
before receiving chemotherapy. This implies that effective scheduling has to be done
in an integrated way across different resources.
2. Real-time scheduling. The coupled-appointment system requires the Cancer Center
to make scheduling decisions as the appointment needs are revealed. Each patient is
assigned both the dates and the times of her appointments at the same time, without
knowledge of all other appointments that will be scheduled on the same dates as hers.
3. Operational and clinical constraints. Not only does the schedule need to respect
13
the Infusion Unit constraints (e.g., nurse staffing levels), but also the clinic times in
the Oncology Practice, and pharmacy capacity.
4. Patient-centered culture.
Scheduling focus is on an 'optimal' decision for each
patient, which ultimately leads to suboptimal system performance that subsequently
negatively impacts the patient.
5. Schedule variability. The actual length of each patient visit often does not match
the scheduled duration for that appointment.
Sources in variation in the schedule
includes previously unknown treatments that are added to the schedule on the same
day, same-day cancellations due to the patients' clinical conditions (such as the patient
being clinically unsuitable to receive treatment), and the presence of patients that are
part of clinical trials, for which the treatment is highly non-standardized.
Initial analysis identified scheduling practices as one of the primary root-causes of the
uneven use of resources. The current scheduling processes fail to take into account the overall
utilization of the various resources (chairs, nurses, MDs, etc). In addition, there are other
operational and cultural issues that generate unpredictability in the schedule and negatively
impact patient satisfaction, staff morale, and efficient use of resources.
Cancer Center Administration is pressured to find ways to utilize more capacity in the
Infusion Unit.
Patient volume in the Infusion Unit is growing.
Additionally, the Cancer
Center is moving to consolidate its Leukemia and associated Bone Marrow Transplant (BMT)
practices, currently housed in a separate building, into the main Practice and Infusion Unit
facilities. The Cancer Center must explore concepts and strategies from Operations Research
to absorb the growth with the same availability of resources.
To address the issues outlined above, we employed a two-phase optimization approach. In
the first phase, we developed a retrospective integer programming (IP) model that assumed
all appointments on a given day are known in advance. The model respected all the physical, operational and clinical constraints and created an 'ideal' schedule that smoothed the
scheduled utilization. This model provided acumen in the structure of the optimal smooth
schedule.
However, the model did not lend itself directly to devise improved scheduling
14
policies sine in practice, appointments are scheduled gradually over time without he retrospective view. Thus, we leveraged the insights from the retrospective model to design a
practical prospective algorithm that schedules the appointments as they are revealed over
time.
To understand the performance of the prospective algorithm, we tested the perfor-
mance of the algorithm over historical appointment data from 2013, in which the proposed
prospective algorithm was applied to schedule the appointments in each business day assuming all appointments take place on the same day as originally scheduled. The resulting
utilization scenarios (Actual, Retrospective Model, Prospective Algorithm) were compared
by simulating them using the actual appointment durations draw from the patient tracking
system the Cancer Center keeps.
The projected results are impressive. Assuming the current volume stays the same, the
proposed scheduling algorithm will reduce the peak daily utilization from a median of 59
chairs to 39 chairs, a recovery of 33% of capacity.
The standard deviation of the peak
utilization across all studied days decreases from 7.6 chairs to 4.9, demonstrating decreased
schedule variation across different operating days. The 97.5th percentile of the peak daily
utilization is reduced from 69 chairs to 49 chairs, a similar recovery of 33% of capacity. The
benefits of smoother utilization are twofold:
1. Capacity Recovery. Existing but unrealized capacity can be recovered and utilized.
This will provide available capacity to meet future growth in demand, and enable
initiatives in the Cancer Center, such as the transition of the Leukemia and associated
BMT infusion programs into the Infusion Unit, without the capital intensive need to
build new facilities. Additionally, reduction of peak load can lead to reduced staffing
levels and thus additional cost reduction.
2. More Predictable Operations. Smoother utilization relieves the staff from the midday strain, making the workload per staff member more manageable. More predictable
operations also reduces patient wait times, improving the patient visit experience.
3. Staffing Impact.
Reduction of the peak load of each day potentially enables the
reduction of infusion nursing staffing.
Nurses are currently staffed to accommodate
the peak patient load of each day, so if the peak is lower, fewer nurses should be
15
needed throughout the day. The potential to consolidate the Practice and the Infusion
Unit scheduling teams into one unified team may also reduce redundant headcount.
Additionally, several studies were conducted to look at the impact of the new patient
load on nursing and pharmacy staffing requirements. This study analytically demonstrates
that the improved state can be achieved with relatively minimal changes to staffing shifts
and no additional headcount in the Infusion Unit and Pharmacy.
Process changes that
incorporate treatment premixing are proposed for the pharmacy in order to maintain the
current headcount. The study assumes no adjustment to staffing in the Oncology Practice.
The Cancer Center Administration, recognizing the importance and potential impact of such
changes in its daily operations, is currently pursuing implementation of proposed scheduling
guidelines by contracting with an IT consulting company to build a custom IT scheduling
tool. The custom IT is currently under development and expected to come online within
months of the publication of this thesis.
1.3
Thesis Organization
This thesis is organized as follows.
Chapter 2 provides a review of prior work. Chapter
3 moves onto a description of the patient flow in the Cancer Center. The current state is
described in Chapter 4. Establishment of patient flow and current state informs necessary
variables and constraints to be built into the optimization model. Chapter 5 includes all
methods and results of both the optimization and simulation models, along with a description
of the scheduling guidelines central to the problem solution. Chapters 6 proposes concrete
operational recommendations rising from this study, and summarizes the impact of the work.
16
Chapter 2
Literature Review
The problems of congestion and need for improved resource utilization has been explored in
other cancer treatment facilities. Scheduling redesign has been identified in several works
as an important process improvement tool. Optimization and simulation modeling have
also been used widely to identify and measure the potential impact of scheduling and other
process changes.
The following overviews prior works addressing problems related to this
study.
2.1
Successful Implementation of Resource Management and Scheduling Redesign
Resource utilization and scheduling improvement studies have been explored to address similar congestion and uneven workload problems in other cancer care facilities. We present
several related works that have seen successful implementation, demonstrating the effectiveness of improved scheduling practices and appointment management systems in improving
operations in cancer infusion treatment facilities.
Chabot et al.
[7] identified the problem of inefficient use of nursing time in the Infu-
sion Center of the Tower Hematology Oncology Medical Group in Los, Angeles, CA. Their
solution was to schedule patients based on a classification system. In the implementation
of the solution, treatments were classified based on the number of premedications, type of
17
drug or infusion and administration details, special observations related to administration,
and acuity. Nurses were assigned loads that were balanced and spread out according to the
classification system. Double bookings were eliminated and nurses were given lunch periods.
Three years after implementation, results are very positive. The same size staff has been
able to treat 10% more patients, and surveys have shown improvement in nurse and patient
satisfaction in the Infusion Center. This relates to our study as we also consider double and
triple bookings a barrier to an efficient schedule. While we do not balance nursing workload as a part of this study, we consider overall utilization which directly impacts nursing
workload.
Gruber et al. [13] tackled the problem of improving efficiency and customer satisfaction,
and decreasing costs in the Chemotherapy and Infusion Center (CIC) of the Roswell Park
Cancer Institute in Buffalo, NY. Department administrators pursued changes by describing a
'Perfect Day' for patients and staff, leading to elimination of the 10 hour nurse shift, changing
staff start times, cross-training RNs to administer chemotherapy and infusion treatments,
establishing scheduling procedures, altering hospital aide assignments to include non-nurse
tasks, planning work zones and patient care assignments, revising the patient appointment
schedule, and working with physicians to change prescribing practices. Implementation of the
changes has led to an increase in the number of treatments starting on time from 11% to 94%,
and an increase in patient volume of over 20% was enabled without additional resources. This
relates to our study as it presents another example of successful implementation of scheduling
heuristics that resulted in increased patient throughput without additional resources.
2.2
Optimization Models and Integer Programming as
a Tool
We have also identified several recent studies that use optimization programs to solve resource
utilization problems in healthcare settings. An optimization program consists of a set of
decision variables for an objective function subject to a set of constraints. A particular type
of optimization program is the integer program (IP). In an IP, some or all of the decision
18
variables are restricted to be integers, and in special cases are restricted to be binary (0 or
1). Integer programming has been employed on several instances to describe optimal states
of cancer treatment facilities.
Turkcan et al. [24] tackled the problem of reducing treatment delays in chemotherapy
administration facilities. Integer programming assigns patients to appointment times and
nurses optimizing to minimize treatment delays due to insufficient resources.
Treatment
delay in the proposed state compared to current practice reduced on average from 4 days to
3.1 days. The standard deviation of delay also decreased from 7.7 days to 4.1 days, demonstrating the capability of Operations Research methods to reduce patient visit variation. At
the time of publication, this study outlined several additional analyses that must conducted
before implementation could be considered.
This relates to our study in that it demon-
strates the value of an IP in identifying ideal appointment times to reduce patient delay, an
important goal of our study.
Chen et al. [8] consider the interesting problem of optimizing scheduling while taking
into account same day call-in patients.
They model the problem as a stochastic integer
program and take into account random and heterogeneous service times, no-show rates, ancillary physician tasks and appointment delay costs. Their optimization program yielded the
optimal sequence of patients, and resulted in the Routine-Block policy whereby all routinely
booked patients are seek in one block, perhaps preceded by same-day patients. Their study
also found that the optimal sequence was largely independent of parameters such as service
time variability, patient waiting costs, and overtime surcharges. This is relevant to our study
as the MGH Infusion Unit also must see same-day add-on patients in addition to regularly
booked patients.
Condotta et al.
[10], in conjunction with the UK National Chemotherapy Advisory
Group and Department of Health, considered the problem of optimally scheduling patients
that have multiple appointments that must be booked in a specified multi-day pattern.
Integer programming is employed to first fix the appointment date for all patients, and then
create the intra-day schedule. The objective in this study is to minimize patient wait times
and the peak nurse workload.
In the solution, patients are scheduled based on how the
requirements of their treatment matches a template schedule, with the running schedule
19
further improved through rescheduling.
The optimization demonstrated the potential to
reduce patient waiting days from an average of 14 days down to as low as 4.7 days, and the
potential to treat an additional 89 patients monthly in addition to the 476 current patient
average. This study is relevant to ours in that our study also considers appointments that
are scheduled in a specific pattern. Our study uses integer programming as a tool to guide
the creation of a scheduling algorithm.
Conforti et al.
[11 approached the problem of increasing the throughput in a cancer
radiotherapy clinic. The study uses integer programming to schedule oncology patients for
radiotherapy treatments. The objective is to maximize the number of scheduled patients in
each day while taking into account patient priority, the number of treatment sessions of each
patient, the number of weeks a patient must be treated, and treatment specific limitations
such as the need to carry out particular treatments in consecutive days. The optimized
schedule potentially reduces wait times and shortens wait lists for radiotherapy treatment,
although has not been implemented in a real clinical setting at the time of publication.
This study relates to ours by demonstrating another application of integer programming in
identifying optimal scheduling patterns.
2.3
Simulation as a Tool
Our study will simulate scheduling using different scheduling guidelines to iteratively arrive
at a prospective scheduling algorithm. Simulation generates a virtual environment mimicking
real clinical settings. Several recent studies demonstrate simulation as a useful tool to quickly
explore potential outcomes of imposing different process changes.
In his masters thesis, Frank van Rest [25] explored the problem of booking chemotherapy
in a way that would match capacity to demand in the BC Cancer Agency of Vancouver,
Canada.
The study considers the options of either adding minimal capacity, or employ-
ing a tolerance whereby patients are booked within a certain number of days to the target
appointment date, in order to minimize slack capacity and the need to postpone appointments. Using simulation as the primary tool, the most promising results were obtained by
not increasing capacity and asserting a tolerance of one day, meaning patients are booked
20
to the least busy day within one day of the target appointment date. In this scenario, slack
capacity was reduced by 42%, and the need to postpone appointments due to insufficient
capacity was reduced by 76% from the baseline. This study is relevant to ours as it showed
how scenarios can be easily tested through simulation to achieve target results.
The Vancouver Centre (VC) of the British Columbia Cancer Agency (BCCA) used simulation as an important tool to demonstrate the simultaneous impact of operations, scheduling, and resource allocation on patient wait time, clinic overtime, and resource utilization.
That study demonstrated the potential to achieve a reduction of up to 70% in patient wait
times and 25% in physical space requirements, while maintaining throughput. Maintaining
throughput is achieved by not altering historic patient volume when inputting data for simulation. This way of defining maintained throughput will be applicable for this thesis as well.
The BCCA conducted its project in the Ambulatory Care Unit (ACU) to address the issue
of resources shortages during peak hours of the day, a problem similar to the one described
in Section 1.2. During those hours, the ACU experienced shortages of physician office space,
clerical support, and examination rooms. Results of simulation identified, amongst other
things, the need for improved patient scheduling in order to achieve desired outcomes. The
ACU study relies on simulation to suggest, amongst other non-scheduling recommendations,
an increase in booked time for patient appointments by 30% and the accommodation of same
day add-ons at the end of the each day. At the time of publication, the ACU study was still
being evaluated for implementation by senior management. [20]
Santibiinez et al [12], together with Gocgun and Puterman [19] conducted a 17-month
study at the BCCA to tackle excessive wait listing, late appointment notifications, pharmacy
congestion, and unbalanced workload between nurses. The authors employ both optimization and simulation modeling to tackle both, inter and intra-day chemotherapy scheduling.
The study is broken down, respectively.
In the first part, randomly arriving patients are
assigned to future appointment dates within clinically established windows of time. In the
second part, patients assigned to particular dates are then assigned specific appointment
times. A computer-based scheduling tool was built, which simultaneously determines appointment times, balances workload and complexity across and within nursing shifts, levels
pharmacy workload throughout the day, and accommodates patient time requirements and
21
preferences. Scheduling redesign reduced by 57% the median percentage of appointments
exceeding appointment notification lead time target one week. Additionally, median waitlist
size decreased by 83%. Implementation of scheduling process redesign has proven successful,
as demonstrated by aforementioned metrics along with increased patient satisfaction and
reduced staff stress levels shown through survey results. This study shows the direct benefit
of simulation for scheduling redesign and in testing proposed scheduling processes.
Finally, Liang et al. (14] show with discrete event simulation that delays due to inefficient
care delivery can be eliminated with improved scheduling practices and better planning and
coordination. A mathematical programming model is developed to generate, given a fixed
number of appointments to be booked, appointment distribution guidelines that aim to
balance the visit schedule in both the practice and the infusion unit. The authors evaluate the
effectiveness of their scheduling strategy by running a system wide simulation that emulates
the patient flow of the Lahey Hospital and Medical Center Department of Hematology and
Oncology. Performance is assessed by measuring patient waiting times, total time in system,
the total clinic working hours, and chair utilization. This is very similar to the process to
be used in our study, where first we will use optimization programming to gain insights into
scheduling, then use simulation to test possible scheduling processes in order to generate a
final proposed set of scheduling rules.
22
Chapter 3
Patient Flow in the Cancer Center
3.1
Cancer Center Structure
The Cancer Center is a fully integrated cancer treatment establishment, offering patients a
full recovery solution from treatment clinics, such as the Infusion Unit, Radiation Oncology,
and Surgical Oncology, to supportive clinics, such as Pallative Care, Psychiatric Oncology,
Oncology Chaplaincy, and the Images Boutique, which features wigs, relaxation tapes, and
cosmetic services [3].
On a given day, a patient may have appointments in any number
of these clinics, making scheduling a challenging and requiring the collaboration between
several different care facilities.
This study is specifically focused on patient flow throughout the Infusion Unit, including
its immediate inputs and outputs, such as the Practice. Operations of other Cancer Center
facilities will remain unaffected by the recommendations of this study.
3.1.1
Practice
Patients see their medical oncologist in the Practice.
This is where patients are initially
diagnosed, scan results are reviewed, and treatments are assigned, referring the patient to
other facilities of the Cancer Center. Like other clinicians in Academic Medical Centers, the
Cancer Center physicians divide their time between clinic sessions, research, teaching, and
other administrative duties. As a result, clinicians are available to see patients only during
23
specific fixed four-hour blocks that are scheduled throughout the week. Appointments to see
existing patients are scheduled for 20 minutes. New patients in the Practice are assigned
longer appointments, during block periods of time known as New Patient Multiclinic (NPM).
NPM hours differ for each Disease Center. Clinicians taking new patients exclusively see
new patients during NPM, further reducing the possible times during the week when they
are available to see existing patients that go through chemotherapy.
The Practice also operates the Short Stay Unit. Short Stay is a four bed facility located
within the Practce that is able to administer non-chemotherapy infusions such as hydrations,
antibiotics, and symptom treatments such as anti-nausea medications. The unit is staffed
from 9am-5pm.
At 5pm, patients still being treated in Short Stay are relocated into the
Infusion Unit, which is open until 8pm.
Short Stay takes very few appointments, and is
primarily used for same-day treatment needs.
3.1.2
Infusion Unit
Patients receive chemotherapy and other infusion treatments in the Infusion Unit. Chemotherapy may be administered as an infusion, an injectible, or as an ingestible.
Other non-
chemotherapy infusion treatments administered in the Infusion Unit are treatments necessary to support chemotherapy and chemotherapy symptom management. These include iron
transfusions, blood transfusions, hydrations, antibiotics, and anti-nausea treatments. Infusions and associated care are provided by the self-contained Infusion Unit staff of nurses and
nursing assistants.
Patient care in the Infusion Unit follows the Primary Nursing model. In this care model,
each patient is assigned a Primary and an Associate Nurse. Schedulers prioritize booking
patients with their Primary Nurse. Should the Primary Nurse be unable to care for the
patient during their visit, scheduling and triage then prioritize assigning that patient to
their Associate Nurse. The goal of the Primary Nursing Model is for one nurse to be fully
familiar with the treatment progress and specific needs of each patient, in order to deliver
higher quality, more personalized care. Nurse availability is affected by a number of factors,
including assigned shift times, vacation days, emergency leaves of absences, and last minute
unavailability due to high nurse load.
24
3.1.3
Governance of the Practice and Infusion Unit
The Practice is managed by Cancer Center Administration, which reports up one of the
physician management structures to Senior Vice President Ann Prestipino. Cancer Center
Administration manages in entirety the operations of the Practice and all physicians in the
facility.
Additionally, Cancer Center Administration oversees the collaboration across all
Cancer Center treatment facilities. The Infusion Unit is managed by Patient Care Services.
Patient Care Services is the official name of the Department of Nursing of Massachusetts
General Hospital, managing over 4000 nurses across the hospital. The nursing arm of the
hospital is separate in management structure from all physician management structures, and
reports to Senior Vice President Jeanette Ives Erickson. All SVPs of MGH report directly
to the President of the General Hospital and MGH Corporation. The separate management
hierarchies of the Practice and Infusion Unit complicates decision making and requires the
alignment and balance of different organizational, operational, and clinical perspectives. It
also contributes to somewhat siloed operations and duplicate of functions such as scheduling
teams.
3.2
Appointment Types and Patient Flow
The full patient flow diagram of patients moving through the Practice, Infusion Unit, and
Radiation Oncology is shown in Figure 3-1. While the overall flow is quite complex, this
study addresses only those that lead to the Infusion Unit.
3.2.1
Infusion Appointments
There are two appointment paths to infusion: (i) Patient to Chemotherapy (PTC); and (ii)
Infusion-Only. For PTC appointments, patients first see their oncologist in the Practice prior
to arrival in the Infusion Unit. For Infusion-Only appointments, patients arrive directly to
the Infusion Unit for infusion treatment. PTC appointments are scheduled for three segments
per visit:
1. Blood draw in the Practice
25
vita is
.
...
.
cho ck im
.......
.......
M9
Mood Draw
171i
Ch C*
In
Figure 3-1: Full Patient Flow Diagram
2. Medical oncology visit in the Practice to review check in with physician, and review
scans and blood work
3. Infusion in the Infusion Unit
Infusion-Only patients are scheduled for two segments per visit:
1. Blood draw in the Infusion Unit
2. Infusion in the Infusion Unit once blood work is reviewed by Infusion Nursing
All segments must be scheduled 1-2 hours apart from any other segment. This constraint
balances the need to leave enough time to process blood results and not prolonging patient
wait time beyond what is necessary.
Upon arrival in the Infusion Unit, either from the Practice or directly, patients are greeted
at the Front Desk for check-in. Front Desk staff mark the patient as arrived in the patient
tracking software application. This places the patient on a queue to be assigned an infusion
bed or chair by staff at the Central Pod. The patient waits in the waiting room until they are
called by nursing assistants. When both chair and the designated nurse are ready, a nursing
assistant calls that patient and takes vitals in a dedicated vitals space. The patient is then
26
taken to either to blood draw or their assigned bed or chair, depending on the appointment
type of the patient.
Blood draws scheduled in the Infusion Unit are completed in the Triage room, which
has two chairs separate from the 60 infusion chairs. Results are processed in the centralized
phlebotomy lab one floor away from the Infusion Unit, and reviewed by infusion nursing or
medical oncology. Successful review of blood work confirms chemotherapy can be administered and enables nursing to initiate the order to mix the treatment. For stable patients
with a history of successful blood work, nurses have the discretion of ordering pharmacy
mixing ahead of blood draw results. Unsuccessful blood work results can be overridden by
the patient's oncologist, or chemotherapy will be postponed until a later date, when the
patient condition improves. Between blood draw and infusion start, the patient returns to
the waiting room.
Once blood work is verified and pharmacy mixing is complete, the nursing assistant
escorts the patient to their assigned bed or chair. The assigned nurse for the visit meets the
patient at the chair to perform the seating process, including verifying the patient's charts,
hanging the infusion treatments, and initiating the infusion. The nurse will also converse
with the patient about social updates, and evaluate the patient's condition based on their
knowledge of that patient's charts and history. A second nurse always verifies the patient's
demographic information and the infusion treatment mix before infusion is initiated.
Once infusion has begun, the nurse leaves to attend to other patients, returning in regular
intervals to check up on the patient. Nursing assistants bring the patient magazines, pillows,
and other items to aid in comfort during the infusion. Hospital volunteers circle around the
beds and chairs passing out lunch, drinks, ice cream, and other snacks.
The patient has
an emergency call button that notifies the Central Pod to page the nurse should immediate
attention be needed.
Immediate attention is needed for a variety of potential complications, such as the infusion
needle losing the artery, or averse allergic reactions to the treatment. In the scenario when
a complication becomes too advanced for infusion nursing to treat, the patient is admitted
into the MGH inpatient facilities for advanced care. Should a patient require admission to
inpatient care, he or she must occupy an Infusion Unit chair until a bed becomes available
27
in the inpatient care facility, which is generally not until late afternoon hours.
Upon completion of the infusion, the assigned nurse removes the infusion needle from the
patient, verbally and visually confirms the patient is well, then allows the patient to find
their way out of the Infusion Unit.
3.2.2
Other Relevant Appointment Types in the Practice
While there are over 100 types of appointments in the Practice, most fall into one of three
categories: PTC, Follow-ups (FOL), and New Patients (NEW). PTC, as described above, are
appointments in the Practice for patients that are receiving chemotherapy on the same day.
FOL appointments are scheduled for patients that are in remission from cancer. Patients
in remission have regular (once, twice, or three times a year) follow-up visits with their
provider to detect cancer recurrence.
These appointments are relevant because they are
scheduled during the same blocks of provider availability as PTC appointments. Each FOL
appointment is scheduled at the conclusion of the previous one, and as such are scheduled 1,
1/2, or 1/3 years in advance, in contrast to PTC appointments which are scheduled at most
6 weeks in advance. This means FOL appointments generally receive first pick priority for
spots in each provider's schedule. FOL appointments also outnumber PTC appointments
3.3 to 1. NEW appointments are appointments scheduled for new patients that are seeking
diagnosis or are newly diagnosed with cancer.
NEW appointments are scheduled during
dedicated New Patient Multiclinic (NPM) hours. Since NPM hours are reserved specifically
for NEW appointments, PTC appointments cannot be scheduled during these times.
3.2.3
Scheduling Practices
The Practice and Infusion Unit operate separate, in-house scheduling teams. When a physician orders chemotherapy or other chemotherapy-related infusion for a patient, that patient
sits down face-to-face with a scheduler in Practice Scheduling. As a result, Practice schedulers are likely to form a relationship with patients they are scheduling. The Practice scheduler checks the order sheet for the target date of chemotherapy start, and asks the patient
for their preferences on time of day. The Practice scheduler then calls Infusion Scheduling.
28
Over the phone and looking at two separate scheduling software applications, the Practice
scheduler and Infusion scheduler schedule the patient for their blood draw, infusion, and in
the event the visit type is PTC, their Practice appointment as well.
Add-ons in the Infusion Unit are not scheduled through the regular scheduling process.
These are appointments where physicians determine same-day that a patient needs treatment
in the Infusion Unit. Patients arrive in the Practice for a non-chemotherapy visit, and can
be sent as a same-day add-on to the Infusion Unit to receive treatments such as hydrations
and other symptom treatment infusions. In these scenarios, the physician calls the Triage
desk of the Infusion Unit and arranges for the arrival of the patient same-day. Triage nursing
assigns the patient to a chair and a nurse, prioritizing the patient's Primary or Associate
nurse if available.
A common practice in scheduling is double and triple booking. This is where two or
three patients are booked to a single provider or infusion nurse in the same time slot. This
practice exists because there are no constraints in the scheduling software being used to
prevent this, so schedulers are able to schedule a patient to their provider during their
preferred appointment time, regardless if the provider is already seeing another patient in
that time. Double and triple booking results in long delays on the appointment date as the
provider or nurse must see two or three times the number of patients assigned to one period
of time. Any delays generated in the Practice ripple down to infusion appointments, making
the infusion schedule more unpredictable.
29
Chapter 4
Current State Analysis
This chapter describes the symptoms surrounding the uneven utilization shown in Figure
1-1, and then identifies policies and processes in and around the Infusion Unit that have
resulted in the uneven utilization. First we describe the methods and data sources used in
the current state analysis, then presents the results of the analysis.
4.1
Data Sources
4.1.1
Shadowing and Interviewing
Shadowing and interviewing key stakeholders revealed important insights into the operations,
patient flow, and cultural underpinnings of the Cancer Center.
Key stakeholders shadowed include:
o Practice oncologists of several Disease Centers
o Practice nurses of several Disease Centers
o Infusion nurses of several Disease Centers
o Infusion Central Pod Control desk where patient room assignment are made and patient tracking information is entered
30
"
Infusion triage nurses Nurses who receive same day add-on requests, manage nursing schedules, make last minute patient nursing reassignments, and manage nursing
operations
" Pharmacy
" Phlebotomy lab
" Practice scheduling
* Infusion scheduling.
Key stakeholders interviewed include:
* Executive Director of the Cancer Center
" Operations Manager of the Cancer Center
" Operations Manager of the Practice
" Operations Manager of Infusion
* Director of Clinical Services: director of nursing in the Practice
" Infusion Nursing Director
" Infusion head of nursing
" Physician Administrator in the Practice
In addition to information presented in Chapter 3, other key cultural and political takeaways from this phase are summarized below:
" All stakeholders see quality of patient care as their primary motivator to drive change
in the Infusion Unit.
* All stakeholders agree that smoothing the daily utilization curve of the Infusion Unit
is central to the solution to observed problems.
31
"
The separate management structure of the Practice and the Infusion Unit significantly
complicates any process to drive change.
" All stakeholders agree that scheduling processes can be improved, but question the
longevity of implemented improvements. The congestion problem has been tackled in
several occasions in the past without permanent results. Past initiatives include mandating all Infusion-Only appointments arrive at 7am, increasing the presence of nurse
practitioners in the Infusion Unit to facilitate patient condition sign offs and pharmacy
orders, and encouraging patients to do blood draw in advance of the appointment at
Cancer Center satellite locations. A central problem that reoccurs is the bending of
scheduling processes to the preferences of patients. It has become standard to allow patients to choose their appointment times, and stakeholders see this as a major cultural
barrier to change.
" Very limited (if any) number of data-driven approaches have been used in the past to
address utilization problems observed in the Infusion Unit. Stakeholders are eager for
data to validate stated observations about the operations of the Infusion Unit.
* The Pharmacy has over the years adopted many best practices of operations management, and overall functions very efficiently. Capacity problems in the pharmacy are
generated by the non-uniform inflow of patients, not vice versa.
4.1.2
IT, Databases, and Data Aggregation
To establish the current state analytically, information for approximately 75,000 patient
visits across calendar years 2012 (CY2012) and 2013 (CY013) was aggregated and analyzed.
The Cancer Center manages several databases of patient and provider information that can
be used for analysis and modeling input. Each patient has a unique patient Medical Record
Number (MRN) that can be used to cross reference patient visits across data sources. A
recent hospital wide initiative is moving scheduling IT systems to a single integrated service
called EPIC. Rollout of EPIC in the Cancer Center commenced in August of 2014, and as
such several of the systems described below are not used moving forward. Regardless, these
32
systems have been used in this study to extract historical patient visit information, which
are consistent regardless of the IT system used to store the data. A summary of IT systems
and data sources are below:
" Spectrasoft. Spectrasoft is the scheduling software used by the Infusion Unit. This
system is used to schedule patients to appointment times and nurses. Changes to each
appointment (such as treatment changes, time changes, and cancellations) are also
completed in Spectrasoft. Each time a change is made, the system notes the time and
date of the change, but does not preserve information about the appointment prior to
the change. The system also tracks essential demographic and treatment information
about each patient.
" IDX. IDX is the scheduling software used by the Practice. This software is used to
schedule all patient visits in the Practice. IDX also tracks changes to appointments,
and essential patient demographic and treatment information.
" Billing. The Billing database stores the treatments and services billed for each patient
visit.
" Patient Tracking. Patient Tracking is used by the Infusion Unit to track the location
of a patient after arrival.
The patient is tracked in a number of locations: waiting
room, triage room, or infusion chair or bed (including the exact chair or bed number).
Patient Tracking time stamps arrival and departure from each location. It is important
to note that Patient Tracking is a manually entered tracking tool. This means that
human error is a significant source of data inaccuracies.
For example, sometimes a
patient completes infusion and leaves the Infusion Unit, but the Central Pod is not
notified and does not mark the patient departed in Patient Tracking at the moment
the patient leaves the facility.
" Add-ons. The add-ons database is a manually kept database of add-ons and conversions. This database exists as large, physical binders kept by Triage Nursing. Each day,
Triage Nursing hand-writes a page of add-on and conversion information and adds the
page to a binder. In addition to inherent human error, not all add-ons and conversions
33
are reported to Triage Nursing. As such, this data source is considered a reference, not
a reliable source. Add-ons were identified for input into the model and other data analysis by selecting for arrived patient visits that were not previously scheduled, identified
by looking at the latest appointment change date stored in Spectrasoft.
9 Provider Schedules. Provider working schedules are manually collected by the practice administrators and show physician clinic hours available for chemotherapy patient
visits as of June 2014. This data source spans all physicians who see chemotherapy
patients across all Disease Centers.
4.2
Current State Description
4.2.1
Summary of Problems
The uneven utilization of bed and chairs in the Infusion Unit, and resulting congestion during
peak hours, has the following daily symptoms:
1. Prolonged patient wait times. Patient wait times as a percentage of their total
appointment cycle time is shown in Figure 4-1. The median wait time as a percentage
of cycle time increases each hour in the morning, peaking at noon during the peak of
congestion before decreasing again. From 10am-2pm, the 75th percentile of patients
are waiting for 20% of their appointment duration.
2. Overloaded nurse workload. Nurse workload is measured by the patient/nurse ratio
metric. In the Infusion Unit, nurse workload should not exceed 2:1 at any time. Figure
4-2 shows the patient/nurse ratio in the Infusion Unit throughout the day. Before 10am
and after 5pm each day, on average nurses are highly underutilized, demonstrating
a waste of expensive nursing resources.
From 11am to 3pm, in the mean plus one
standard deviation case across all days analyzed, the patient/nurse ratio exceeds the
safe guideline of 2. This creates the potential for nurse overload and patient safety
concerns.
Shortages of nursing resources during these hours also contributes to long
waiting times for patients waiting to be seated by their assigned nurse.
34
3. Inability to accept add-on patients. Add-on patients are individually accepted
into the Infusion Unit when the patient's physician phones in the request to Infusion
Triage Nursing. During peak hours, the congestion at times is so high that Triage
Nursing rejects additional add-on patients.
This is an important problem as some
add-ons need rather urgent treatment. While this phenomenon is not reflected in data,
both triage nursing and physicians in the Practice state that this is a regular occurrence
in the Infusion Unit that can occur several times weekly.
Total Wait Time/Total Cycle Time
,100
80
60
N40
20
0
7
8
9
10 11 12 13 14 15 16 17
Appointment Start Time
Figure 4-1:. Total wait time as a percentage of total infusion time for all infusions in 2012
and 2013
The nonuniform utilization is the result of current scheduling practices and high variation
of actual patient stay from scheduled stay, which will be explored in the following sections.
4.2.2
Patient Arrival Scheduling
A central cause of the nonuniform utilization of resources in the Infusion Unit is non-smooth
scheduled patient arrivals. The scheduled arrival of patients in the Infusion Unit actually
approximately mimics the observed utilization behavior.
Scheduled duration of infusions vary depending on the treatment, ranging from 30 mintime
utes to over seven hours, in half-hour increments. The Cancer Center buckets length of
of an infusion in order to simplify how they consider appointments of different lengths. The
buckets are defined as follows:
35
Current State: Patient/Nurse Ratio
Average
Ave+1SD
++
2.5
2.0
....
S1.5
0.0
r-
oc0
C)
00ci ~
p~~,
0
Time
Figure 4-2: Current state patient/nurse ratio throughout the day
Table 4.1: Infusion appointment scheduled duration categories
Category
Scheduled duration
Brief
Short
Medium
1 hour or less
(1, 3] hours
(3, 5] hours
Long
(5,7] hours
Extended
over 7 hours
For all appointments in 2012 and 2013, Figure 4-3 shows the boxplots of scheduled
durations. On average across all appointments, patient visits are scheduled for 2.1 hours.
Approximately 75% of all appointments are scheduled for 0.5 to 3 hours. We can next break
down the appointments to see the composition of appointments by scheduled duration. This
composition is shown in Figure 4-4. Figure 4-4 also shows the composition of total time,
across the aggregate number of hours all 60 beds and chairs were occupied in the Infusion
Unit, allocated for each different appointment duration. While brief and short appointments
make up 75% of all appointments, they account for approximately 50% of all occupied chair
hours. These plots also show that the composition of appointments by scheduled duration
tends to remain steady year over year.
It is important to study appointment information across the different hours of the day to
36
Scheduled Durations
of All Infusions
6
5
4
0
Year
Mean
N
CY2012
2.14
39,529
CY2013
2.13
37,156
Figure 4-3: Boxplot of scheduled durations of all infusions in 2012 and 2013
identify causes of congestion at certain hours of the day. Figure 4-5 shows which half hour
of the day both PTC and Infusion-Only patients are scheduled to arrive for treatment. The
current schedule is heavily biased towards the beginning of the day. Approximately 80% of
all PTC appointments are scheduled to begin before 1pm, which is only 6 hours into the
13 hour operational day (46% of the day). Similarly, approximately 80% of Infusion-Only
appointments are scheduled before 2:30pm, 58% into the day. Figure 4-6 shows the Practice
appointment start times for PTC appointments. Practice PTC start times are also heavily
biased towards the first half of the day, with 80% of the daily volume of PTC appointments
starting before noon. The start of PTC Practice appointments directly affects the start
times of PTC infusion appointments, as the blue curve of Figure 4-5 approximately lags the
blue curve of Figure 4-6 by one hour.
4.2.3
Variation from Scheduled Patient Stay Times
In addition to non-smooth scheduled arrival of patients, actual duration of patient stay can
also vary greatly from scheduled duration.
This stay variation contributes to operational
unpredictability and delays. We first quantify the impact of stay variation on the schedule
in the Infusion Unit, then look at sources of variation.
Patient stay deviation from expected (scheduled) duration is identified as any difference
37
Distribution of Infusion Appointments Distribution of Total Chair Hours by
Hours of Scheduled Duration
by Hours of Scheduled Duration
40,000
90,000
35,000
30,000
80,000
m12
N1
.9
-
70,000
MES11
-
60,000
050000
25000
2
20,000 +--
06
to*40000
.5
6 30,000
u4
-
- - -
15,000
E10,000
.7
.3
20,000
5,000
10,000
2012
0
2013
2
2012
Year
Mar
2012
2.4h
N
39,529
m 0.5
2013
2013
2.13,h
37,156
Figure 4-4: Distribution of infusion appointments and total occupied chair hours in Infusion
Unit by appointment hours of scheduled duration
Infusion Appointment Start Times FY14QI
100%
1 ,000
.
E
CL
8su0
10Mwft
a0
0% U
600
60%
2
400
40%
U-
200
20%
oi,
%
0
7 8
9 10 1112 13 14 15161718 19
0
Hour of Day
%
MInf Only
=PTCT
-PTCT Cumu lative % -nf Only Cumulative
Figure 4-5: Current State: Distribution of infusion start times throughout operational hours
38
Practice PTC Visits by Time of Day
100%
1,200
0
01,000
80%
E
5
800
0
600
60%
oU.
40%
I
400
i
200
h~i-z
20%
E
U
no/.
n
MVisits
-Cumulative
freq. (%)
Figure 4-6: Current State: Distribution of PTC Practice appointment start times throughout
operational hours
between the appointment's scheduled duration and the actual time patients occupy a bed or
chair during their treatment. Three concepts have been defined to conduct this analysis:
" Stay variation is defined as the difference between actual appointment duration and
scheduled duration.
" Overstay is any stay variation that is positive - that is, the actual appointment duration was longer than the scheduled duration.
" Understay is any stay variation that is negative - that is, the actual appointment
duration was shorter than the scheduled duration.
In order to quantify stay variation, we study three months (Oct - Dec 2013) of appointment data. An important distinction between overstay and understay is that overstay must
be accommodated, whereas understay cannot necessarily be recovered.
Overstay usually
represents a patient, who has arrived and must receive treatment. Understay represents last
minute unexpected resource availability, which may or may not be reallocated.
39
Thus the
net stay variation represents the minimum number of unscheduled chair hours that must
be accommodated in the Infusion Unit, assuming that all understay is perfectly reallocated
to be used by overstay.
Overstay represents the maximum number of unscheduled chair
hours that must be accommodated, assuming no understay can be repurposed to be used for
overstay. (Complete details and results of the analysis method are given in Appendix A.)
Figure 4-7 shows the average overstay and the net stay variation (overstay - understay)
by time of day, as a percentage of the available capacity (60 chairs). The results are staggering. On average, each day the Infusion Unit sees a total of 97 hours (12% capacity) of
overstay (std. dev. 17.5 hours). When understay is taken into account, the Infusion Unit
accommodates, on average, a total net stay variation of an additional 65 hours (std. dev.
20 hours). We observe that the overstay begins to increase sharply at 10am, remains high
to absorb the consequences of the congestion, and tapers off again at the end of the day
when far fewer patients are arriving. While the overstay is canceled out by the understay
throughout the morning (on average), at noon it quickly surpasses any freed up capacity,
and overtakes the afternoon by using up to 27% of the capacity.
There are many reasons patients stay longer or shorter than the scheduled duration of the
appointment. We highlight several main sources of variability in the Infusion Unit's patient
flow:
1. Operational variation. This consists of any unplanned change to the length of the
infusion visit due to disruptions in the regular operations.
Examples include delays
due to a nurse being busy, pharmacy backlog in mixing treatments, delay in blood
draw processing, a patient reacting to treatment, changes in a patient's regimen after
the pre-treatment clinical evaluation, and unexpected hospitalizations that require patients to wait in the Infusion Unit until a bed becomes available in the inpatient units.
We note that the operational variation could increase or decrease the appointment's
duration significantly, sometimes by several hours. Figure 4-8 shows how much of all
observed stay variation can be attributed to cancellations and no-shows, add-ons, and
operational variation.
Statistics for Figure 4-8 are given in Table 4.2. Operational
variation accounts for the vast majority of stay variation. There are sources of operational variation we expect will decrease naturally with more uniform utilization. These
40
% of Total Chair Capacity Utilized by
Overstay &Stay Variance
-Stay Variance/Capacity
-Overstay/Capacity
30%
25%
20%
t
15%
U
10%
+0
5%
0%
-5%
. .C. .0 <. 0.< .. a.
to
a
Qr4
N
r
N
m
(0t
a
00
Time (hour)
Figure 4-7: Proportion of total capacity impacted by stay variation at different hours of the
day
41
include delays due to nurse being busy and pharmacy backlog in mixing treatments.
Some sources can in part be preventable. Blood draw can be performed in many cases
up to 36 hours in advance, so implementing a system where patients draw blood the
day before their infusion appointment can eliminate blood draw delays for that patient.
Many other sources are due to clinical situations as they evolve and cannot be predicted for or prevented. These include patient reactions to treatment, changes to the
patient's regimen, and unexpected hospitalizations.
Excess capacity should be kept
available in the schedule to absorb unavoidable and unpreventable sources of patient
stay variation.
2. Cancellations and No-Shows. the former are appointments that could be canceled
either by the patient's initiative or by the provider's recommendation after assessing
the patient before receiving treatment. No-shows correspond to patients that did not
arrive to a previously booked appointment.
Both represent same day freeing up of
capacity that may or may not be reallocated for other patients.
Cancellations and
no-shows as a proportion of all stay variation is shown in Figure 4-8, with statistics
given in Table 4.2. The distribution of cancellations throughout the day is shown in
Figure 4-9.
More cancellations occur during the more congested hours of the day,
contributing to greater schedule uncertainty at that time. Same day cancellations can
often not be avoided as they generally occur as a result of clinical issues discovered
same day. No-show rates can possibly be reduced with a more active appointment
reminder system.
3. Same-day add-ons.
These are previously unscheduled patients who need to be
treated on that same day, usually following recommendation of the patient's oncologist in the Practice.
The Infusion Unit accommodates them subject to chair and
bed availability. Add-ons as a proportion of all stay variation is shown in Figure 4-8,
with statistics given in Table 4.2.
The breakdown of add-on appointment types is
shown in Figure 4-10. Of all add-ons, 27.7% are hydrations. The number of add-on
hydrations can likely be reduced through initiatives that more actively promote patient self-hydration at home between visits to the Cancer Center. Such initiatives have
42
great potential to reduce the number of add-ons, making Infusion Unit operations more
predictable.
4. Extended Stays.
Some patients are assigned by their physician to receive treat-
ment(s) in addition to the ones already scheduled for them, after they arrive for their
appointment. This usually happens after evaluation by the physician during a PTC
visit. Extended stays can increase the time the patient occupies a chair greatly beyond
their scheduled appointment duration.
43
Histogram: Stay Variation
* Addons
* Cancellations & No Shows
* Operational Variation
25005 2000
C
1 L500
1000
E
-
500
00
v-4 r m ,t In
%.
Stay Variation (Minutes)
Figure 4-8: Proportion of total capacity impacted by stay variation at different hours of the
day
Table 4.2: Stay Variation Statistics
Source of Variation
Mean [minutes]
Standard Deviation [minutes]
Stay Variation
Operational Variation
Add-ons
Cancellations and No-Shows
8.1
26.6
144.2
-162.7
111.7
80.2
107.9
-102.1
44
Distribution of PTC visits where
infusion was canceled same-day
=% -Overall
10.0%
--
-
-
1.
%
14.6%-
- --
- -
5 8.6%
8.0%
%
....
5
-
6.0%
--
-
-18.0% 16.0% 14.0% ~1.41.%
12.0% ~10.5%
.
4.0%
2.0%
0.0%
0.0%
7
8
9
10
11 12 13
Time of Day
14 15
16 17
Figure 4-9: Distribution of same-day cancellations throughout the hours of the day
ADDON TREATMENT TYPES
N Hydration
mOther treatments
U Blood transfusion
Figure 4-10: Breakdown of add-on treatment types
45
Chapter 5
Solution Approach
5.1
Objective and Overview
The goal of the project is to design scheduling rules and guidelines to smooth the chair
utilization in the Infusion Unit throughout the day. Specifically, we aim to minimize peak
utilization on a daily basis by scheduling patient appointment times accordingly. Note that
the project does not aim to change the decisions about the date of the appointment. The
development of the scheduling rules were done in three phases:
(i) using a retrospective
integer programming model, we generated unrealistic but ideally optimized daily schedules
in order to gain insights into how scheduling should have been executed; (ii) using the insights from (i), we developed a realistic real-time prospective algorithm; (iii) the prospective
algorithm was tested and evaluated based on simulation using actual appointment data from
CY2013. The simulation results are conservative in that it maintains all original patient stay
durations, including delays that could be eliminated as a result of a smoother utilization.
Parallel to the development of scheduling rules, we conducted complementary analysis to
asses feasibility of implementing the proposed prospective algorithm, and identify additional
process changes that should be implemented to ensure smooth transition to the new scheduling process. These additional studies looked at the effects of new scheduling processes on
nursing and pharmacy workload.
In the subsequent discussion, we refer to two states that describe the progression of the
solution:
46
1. Optimal state. This is the state of the Infusion Unit as identified by the optimization
model.
2. Proposed state. This is the state of the Infusion Unit that can be achieved according
to simulation by following a set of scheduling guidelines.
5.2
Evaluation Method
To assess the smoothness of the daily chair utilization in the Infusion Unit, we analyze the
distribution of the peak daily utilization Pd across all calendar days studied in 2013. Peak
daily utilization is the highest instantaneous occupation of chairs during one operational
day. We measure the success of this study by how much the distribution of peaks under the
proposed scheduling algorithm is reduced compared with the current state.
Both the Retrospective Model and Prospective Real-Time Algorithm will generate schedules for each day for all booked appointments. Prior to calculation of peaks, same-day addons for each day are inserted into the schedule at the time of their original arrival in the
Infusion Unit. This allows the plotting of utilization and calculation of daily peaks to reflect
that same day add-ons are not booked in advance, but must be accommodated upon arrival.
5.3
Retrospective Optimization Model
The Retrospective Model is an integer program (IP). The model ran on each day separately,
assuming that all appointments scheduled on each day must still be scheduled on that same
day. The objective function of the integer program solves for the patient arrival schedule
that results in the minimum peak Pd utilization each day.
5.3.1
Integer Program
We now describe the IP. First, we define some notation:
9 P : set of appointments on the day we are interested in.
47
* T : set of appointment possible start times. The set T is obtained by discretizing the
operating hours into 30-minute intervals from 8am to 6pm. To accommodate infusion
nursing stated constraints, no infusion will begin past 6pm, however started infusions
may continue until the end of operational hours.
T := {8, 8.5, ... , 18}
o Hit : set of times [t - durationi,t], representing all appointment start times that will
cause patient i to occupy a chair at time t.
o PTC: subset of P representing all PTC appointments
o RST
restricted-schedule treatments are a set of appointments identified by infusion
nursing that would introduce greater risk if moved to the tails of the day
* D : set of oncologists
* DrTIMES : oncologist availability by oncologist
The decision variables will determine the optimal Infusion and Practice start times, for each
patient. Decision variables are defined as follows:
* For all patient i E P, with a scheduled treatment duration durations, we define xit to
be 1 if patient i is starting treatment at hour t
C T of that day; it is 0 otherwise.
* Additionally, for all PTC patients, let yi, be 1 if patient i E PTC
; P is scheduled
to see the provider at time s, with s restricted to the schedule of the corresponding
provider, and 0 otherwise.
We now describe the objective function and constraints. The optimization problem is defined
below, followed by descriptions of the objective function and each constraint:
48
min
S.t.,
Ut
(5.1)
z
xih <
z
Vt e T
(5.2)
iEP hElht
z < 60
(5.3)
ViCEP
xis =
(5.4)
tET
Sxit(t + durationm) <
Vi E P
19.5
(5.5)
teT
E
yi, ;> xit
Vi E PTC,t E T
(5.6)
sEDrTIMES:t-2<s<t-1&doctorsched[dri ,s]>0
yis < I
Vd E D, s E DrTIMES
(5.7)
yis = 1
Vi E PTC
(5.8)
Vi E RST
(5.9)
iEP:dr[i]=d
sEDrTIMES
E yi, < 16
tET
rxt > 9
Vi c RST
(5.10)
tcT
E {0, 1}
Vi, t
(5.11)
yis C {0, 1}
Vi,s
(5.12)
xit
The objective function and constraints are described below:
(5.1) Objective function: To minimize the maximum utilization (peak) of the day
(5.2) ut is defined as the utilization of the Infusion Unit at time t. This adds the number
of people starting treatments at time h < t to the number of people with treatment durations
that continue past t.
(5.3) Capacity. Chair capacity is 60, thus no more than 60 chairs may be occupied at
any time.
(5.4) Demand. Demand must be met. Here this means each patient i that is scheduled
for infusion that day must be scheduled for one and only one starting time xit.
49
(5.5) End of day. No treatment durations may extend past 7:30pm. The clinic closes
doors at 8:00pm.
Scheduled durations may not extend past 7:30pm such that 30 minute
grace period is given to treatments that extend past scheduled time.
(5.6) Providers' Practice Schedule. For this study we will assume no change to provider
schedules. This constraint comes from Cancer Center Administration policies. A PTC patient i must see the provider between 1 to 2 hours before the appointment time in the Infusion
Unit. The patient's provider d is dri and the provider's schedule is given by doctorsched, indexed by doctor d and times t. A provider dri holds clinic at time i if doctorsched[dri,t]
doctorsched[dri,t]
=
=
1;
0 otherwise.
(5.7) Provider Capacity. A provider can only be scheduled to see one patient during each
appointment time slot. This is a departure from existing practice, and has been identified
as an important constraint to minimize variability and delays during each day. Elimination
of double and triple booking still yielded a feasible schedule for all days tested, however non
infusion linked appointments may need to be pushed to the beginning and ends of providers'
schedules.
(5.8) Practice Appointment. Each PTC patient must be scheduled for one and only one
appointment with their provider.
(5.9) Restricted-schedule treatment end of day. All appointments whose appointment
types are identified by RST must start before 4pm.
(5.10) Restricted-schedule treatment start of day. All appointments whose appointment
types are identified by RST must start before after 9am.
The Retrospective Model takes as input information about booked patient visits from
243 operating weekdays in calendar year 2013. Appointments falling on days that have been
identified as outliers have been removed from the data set. Outlier days include Saturdays
when operational hours are abridged, and holidays as listed in Appendix C.
We used CPLEX 11.2.1 and AMPL on a PC with 2.83GHz and 3 GB of RAM to run the
Retrospective Model. For each day, the integer program solved for between 2,000 and 2,500
constraints, and between 3,500 and 4,000 binary decision variables. The optimality gap for
solutions each day is between 2% and 5%. The average time to solve the integer program
50
for a single day is 0.50 seconds (122 seconds for 243 days).
5.3.2
Retrospective Model Results
Figures 5-1 and 5-2 describe the optimized state of the Infusion Unit over CY2013. The
distribution of the peak in the optimal state is significantly improved compared to the distribution of the peak in the current state. The utilization plot of Figure 5-1 shows the mean
utilization per time of day across CY2013 as a solid line, with one standard deviation error
bars. Figure 5-1 shows that with optimized patient arrival times into the Infusion Unit, the
average peak daily utilization can be greatly reduced. Additionally, periods of high underutilization in the current state demonstrate increased utilization, resulting in a smoother
utilization curve. This behavior is described numerically in Figure 5-2, which is generated
by calculating the peak utilization of each of the 243 days, Pd, and analyzing the distribution
of the 243 resulting data points. This figure shows that the current state average daily peak
can be reduced by 21 chairs, or 35% of total capacity, at the median. This represents a 36%
peak reduction.
Further, the current state maximum peak daily utilization
Pd,ma
across
2013 is also reduced by 21 chairs, and the coefficient of variation across days reduces from
13.3 to 11.9. The results also demonstrate a marked reduction in variation across different
days of operation.
In order to identify scheduling trends that result in the optimal state, results are bucketed
and analyzed along three dimensions: (i) Infusion-Only vs. PTC; (ii) appointment start time;
and (iii) appointment start time by duration. Analyzing these results shows that InfusionOnly appointments and PTC appointments are scheduled very differently by the optimized
retrospective model. We now discuss scheduling insights separately for Infusion-Only and
PTC appointments.
51
-Retrospective
-Original
70
60
.50
u40
0
30
20 20
0
000
r4
I
Wr4
N
W4
(0
r-4
mr UN
r 4V
w
r4
r
Wy4
W4
00
M'
V4
Time (half hour)
Figure 5-1: Retrospective Model Results: daily utilization
52
0
N
Ariina
0w
etrospect
70-
70
65-
65
10
60
_60
5-5-
55
.2
z
30
0
ZU
Z
a.m
Count
10%maximum
Count
10.0
fl
maximum
0quartile
50%median
Womaximum
median
50%
maximum
02
59
71
5quartile
miium
Mean
Std Dew
CV
50
546
569
mium
2
Mean
td Dev,
CV
572
7.62
133
41
38
50
35
2
3787
4.540
11.9
Figure 5-2: Retrospective Model Results: distribution of daily peak utilization
53
Infusion-Only Start Times.
100%
90%
--
80%
-
-2 6 0%
---------- ---- --70%
Original
.
-
- - -
00%
20%
cL 50%
--
-
-
--
-
-
... ....
- -
- -
-
- -
- - --
- -
- - - - - -
-
100%
-
U Optimized
-
- -
90%
-
80%
.
--- ..%
4...
0%
...
.....
U
C
LL.Il
20%
10%
0%
20%
10%
-.. -
-..
.-.8
9
10
11
12
13
14
15
16
17
0%
18
Start Time (hour)
Figure 5-3: Retrospective Model Results: Infusion-Only Start Times
Infusion-Only
We analyze the Retrospective Model solution and see several insights regarding Infusion-Only
appointments. Figure 5-3 shows the current state and optimal state number of Infusion-Only
appointments that start at each time of the day. Figure 5-4 shows the cumulative amount
of Infusion-Only appointments that have started throughout the day, where appointments
are bucketed by their scheduled duration.
The following insights can be inferred from analyzing Figures 5-3 and 5-4:
9 In the Retrospective solution, nearly all (86%) Infusion-Only appointments for all
days analyzed in CY2013 are scheduled to start at 8:00am, regardless of duration.
The intuition is that PTC appointments cannot begin at 8am because the patient is
required to see the physician first. Physician schedules begin as early as 8am, so the
first PTC appointments that can arrive in infusion are one hour after that, or 9am. As
such, scheduling early Infusion-Only appointments fills the capacity from 8am-9am to
reduce underutilization in that period. Infusion-Only appointments not scheduled to
54
Optimized Infusion Only Start Times by Duration
00%
a0%
-brie
60%
F
-shor
med ium
E 40%
20%
-exte nded
0%
7
8
9
10
11
12 13 14 15
Start Time (Half Hour)
16
17
18
Figure 5-4: Retrospective Model Results: Infusion-Only cumulative start time by appointment duration
start at 8:00am fall into two categories:
- The appointment type is in RST and must begin between 9am-4pm.
- The specific day has an abnormally high number of Infusion-Only appointments,
such that if all Infusion-Only appointments were to start at 8am, the daily peak
would increase.
After a certain number of Infusion Appointments have been
scheduled at 8am, the rest are scheduled later in the day.
* The maximum number of Infusion-Only appointments beginning at 8am across CY2013
is 35.
PTC
We now discuss insights from Retrospective results regarding PTC appointments. Figure
5-5 shows the current state and optimal state number of PTC appointments that start at
each time of day. Figure 5-6 shows the cumulative amount of PTC appointments that have
started throughout the day, where appointments are bucketed by their scheduled duration.
The following can be inferred from analyzing Figures 5-5 and 5-6:
* Except for a larger volume at 9:00am, start times are relatively evenly distributed across
all possible start times throughout the day. This is a departure from the Current State,
55
PTC Infusion Start Times
16%
-
14%
--
100%
-
Original U Optimized---
-
-
80%
12%.-.-.-.-.-
70%
.3: 10%
-
F-
8%
0
6%
--
-
--
60%
U
50%
.2
40%
U
30%
4%20
20%
2%
10%
0
-.-.-.-.
-...
-....
-...
-..-...
16
15
14
13
12
Start Time (hour)
%
0%
9
8
10
11
17
18
Figure 5-5: Retrospective Model Results: PTC infusion start times
Optimized PTCT Start Times by Duration
.
...
-
1J
.......
2i(U
-
.... -brief
............
....
.....
..........
...
............
..........
...................
....... ..........
40%
.
-5
60%
-
0
.
......... ............ ......... ...... ............................
80%
-short
-medium
-long
20%
-extended
0%
7
8
9
10
11 12 13 14 15
Start Time (half hour)
16
17
18
duraFigure 5-6: Retrospective Model Results: PTC cumulative start time by appointment
tion
56
where the majority of PTC appointments begin in the morning, and minimal begin
after 4:00pm.
9 PTC appointments are typically scheduled, such that they end as close as possible to
the end of of operating hours in the Infusion Unit. Figure 5-6 shows that all appointments regardless of duration surge to fully scheduled at the latest hour the appointment
can be scheduled, such that the appointment ends before closing time. This is done
because the end of the day 6pm-8pm is a period when no appointments are scheduled
to begin. As such existing appointments must extend into that period to reduce underutilization. In effect, PTC appointments are scheduled uniformly throughout the
day in such a way to fill in periods of underutilization.
5.4
Prospective Real-Time Algorithm
The Prospective Model schedules patients in real-time one by one, based only on what is
known about appointments already scheduled up to that point. The scheduling algorithm
has been refined until a final set of proposed guidelines are arrived at iteratively, which
surprisingly results in a utilization curve that closely mimics the utilization curve of the
optimized state. We will first describe how the proposed algorithm arrives at a single appointment time for each patient. Then we explain how the algorithm is further developed
to incorporate patient desires by giving them two scheduling options to choose from.
All constraints set forth in Section 5.3.1 are implemented in the Prospective Model as
they were described in the Retrospective Model. In this way, the Prospective Model mimics
the environment of the Retrospective Model exactly except for the scheduling algorithm
imposed on each appointment. Any variation of utilization results between the Prospective
and Retrospective Model can then be directly attributed to the scheduling algorithm, rather
than to modeling methods.
5.4.1
Scheduling Algorithm Description
The proposed scheduling algorithm treats Infusion-Only and PTC appointments differently.
57
Infusion-Only Appointments
Results of the Retrospective Model show that Infusion-Only appointments were scheduled as
early as possible, depending on whether it was RST, and that the number of appointments
scheduled at 8am never exceeds 35 across 2013. The scheduling guidelines for Infusion-Only
appointments are as follows:
1. If the appointment type is not identified as a restricted-schedule treatment, schedule
the appointment at 8am
2. If the appointment type is identified as restricted-schedule treatment, schedule the
appointment at 9am.
3. If at 8am, 35 appointments are already scheduled, schedule the appointment according
to the Max(Max-Min) method described below.
58
PTC Appointments
Based on the fact that the optimal PTC infusion starting times in the Retrospective Model
results showed an almost perfectly even distribution throughout the day, we designed scheduling rules that are agnostic and, at the same time, assign start times to each incoming appointment in a way that preserves the smoothness of the utilization as much as possible. In
essence, the algorithm does the following:
1. Find all feasible appointment slots that minimally affect the peak
2. Within this set, find the slots with the lowest minimum utilization in the time period
affected by selecting that slot
In detail, when a patient needs to schedule an appointment, the following algorithm is
executed using information provided about the patient and appointment to be scheduled:
1. [Step 1] Determine feasible appointment times in the Practice given provider's availability, PracticeTimes.
2. [Step 2] Determine feasible appointment start times in the Infusion Unit based on
PracticeTimes, Infusion Unit constraints and whether appointment is a restrictedschedule treatment, InfusionTimes.
3. [Step 3] Among options that minimize the peak, determine optimal appointment
time(s), OptimalTimes, that fall into the interval with the lowest minimum.
This
process is referred to as the Max(Max-Min) method, with an illustrative example
presented in Figure 5-7:
(a) [Step 3.a] For each start time S E InfusionTimes, calculate what would be the
new utilization levels
U(s)d,t
and new p(s)d should the appointment be scheduled
at time s
(b) [Step 3.b] Update InfusionTimes +- {s* E InfusionTimess* = argmin{p(s)d}}.
Update Pd +- p(s*)d.
59
(c) [Step 3.c] For each start time s E InfusionTimes, compute u,(s) = min{u(s)d,tt
=
s, ... , s + duration}, the minimum utilization within that appointment's duration
given start time s.
(d) [Step 3.d] For each start time s E InfusionTimes, compute gap(s) = pd -u.(s),
the difference between the day's peak utilization and the minimum utilization
associated with start time s.
(e) [Step 3.e] Compute OptimalTimes <- {s** E InfusionTimess** = argmax{gap(s)}},
the set of starting times that maximize the gap computed in Step 3.c.
4. [Step 4] Select randomly from OptimalTimes as the start time of the appointment.
5. [Step 5] Update the patient's provider availability and the current utilization table to
include the corresponding new appointments.
5.4.2
Prospective Model Performance Assessment
The proposed real-time algorithm is highly promising. Figures 5-8 and 5-9 show the results
of the base Prospective Model, comparing the results to those of the Retrospective Model
and Current State. Despite the loss of information between the optimization and simulation
models, the utilization curve generated by following the prospective scheduling algorithm
closely mimics that produced by integer programming (Figure 5-8). During a large portion
of the day, the two utilization curves approximately overlap - the average difference from
9am-lpm of the mean utilization between the results of the Retrospective and Prospective
models is only 0.4 chairs. At no instant during the day do the two mean utilization curves
differ by more than 4 chairs.
Figure 5-9 shows that the median peak across 2013 in the proposed state is 39 chairs. This
is only 1 chair more than the median peak in the optimal state, and an improvement of 20
chairs, or 33% of capacity, over the current state. The same improvement is observed for the
maximum peak across 2013. The maximum peak utilization generated by the Prospective
Model across 243 days of 2013 is 52 chairs. That number is safely below capacity, only 2
60
Goal: To sdiedule PTC appointment with given parameters:
15-5 16116-51 i71 17.5 i18 18.s5 19 .5
IF,115
18I1 .-5 19113.5 1101 1.0-S I 111151121 12-51 131 13.5 114
3
121 2 121 2 131
U
13
3 141
5 1
4
5
4
3
3 1212
2 2
1
1
infusiomTimes = 11.5,14.5, 17-5, 18}
Appointment duratiaow 15 hours
Step3.a
S =11.5
t
U(11.5
181 8-S5191:9-.51101 I-10. ILLS.1121121131 13.S1141 14-S 151 :15-S51161 16-5 JI71 17.5113118-519 191 .-51
1 1
4413 1312212212
2 21221313 13 1 45 61I
p(115), =6
s =145
151 5.16j 16.5 17j 17.5j1818-S19j 195
t a 8.51919.5110110-511 11 l.51112.5 131 13.5 141 14.51S
2121111
14 122121
14
S
555S41
u(14-5)t21 2223313314
p (145)o = 5
1
s =17.5
1I181515195
Il &S 18591:9.5110110.51I111-1I12112-51131135114114-5IS Ih 15.I6116.5117S
212213
121
a(17-.
1313
13
14
55 51IS14 14131
3
1221213
3
211
I
p (17-5), = 5
_____
s =18
t181
U(11
P
1
&51919511011051 Ill11.5112112.51131135114114-SI1151 15.5IJ11665117117-51 I18.5I9nI.I
132121
5 141 4 131 3 121 2 121 2
5
3 131 3 141 5
2212231
(1d)= 5
Step 3.b
Infusion7iwes = 1145, 17.5, 181
PIg=5
Step 3.c
14.5, u.(14.5) = 4
s =175, u.(17-5)= 2
s = 8, u.(18)= 2
s
=
Step 3d
s = 14.5, gap 114.5):= 5 - 4 = 1
3
s =17.5, gap (17S)= 5 - 2=
s =18, gap (18)= 5 - 2= 3
Step 3.e
OptknMlTumes
= {17-5,
18}
Figure 5-7: Representative Example of Prospective Algorithm Step 3:
Method, with given parameters
61
Max(Max-Min)
-Retrospective
-Original
-Prospective
70
60
0 50
0.
-c 20
10
0
i
-I
i4 M- -IMq- q4e--I
i 4N
Time (half hour)
Figure 5-8: Prospective Model daily utilization
chairs more than the optimal state, and 19 chairs (32% of capacity) improvement over the
current state.
The bottom of Figure 5-9 shows the mean, standard deviation, and coefficient of variation
of the daily peaks for the current state, Retrospective Model, and Prospective Model. The
coefficient of variation in the daily peaks for the current state is 13.3, whereas that for the
proposed state is 12.4. The proposed algorithm reduces the variation in the daily peak,
suggesting that following the algorithm will generate more predictable utilization of chairs
from day to day.
62
ACi
75-
76
70-
Ses
70-
6560-
6D-
55-
55
4so
50
50u
5D-
40
40i
40
35- 'b
35
-
~552
_Retrospec
-
-
SOrigkwa
isv-----
35
30
301
0
0 10 20 30 40
Count
maxiftwm
quartite
median
quartie
Mnimum
10 2D 30 40
0
50
-Count
71
69
62
59
53
40
28
7U2
7 .62
33
Aiwd
xmum
quartile
median
quartile
minimum
5D
46
41
38
35
30
27
3737
4.540
119
10 20 30 40 50
Count
maiUnum
quartile
median
quartile
mfiwnum
52
49
42
39
36
28
25
393
4M8
12A
Figure 5-9: Prospective Model distribution of daily peak utilization
63
The model is built in R and run on a 1.8GHz PC with 4GB RAM. The runtime 243 days
is 227 seconds, averaging 0.93 seconds runtime for each day. The Prospective Model must
be run, for each appointment at booking. Using an average 135 booked appointments per
day, this equates to 0.007 seconds model runtime for each booking.
5.4.3
Incorporating Patients Choices
We now describe how the algorithm is amended to give each patient two scheduling options.
Stakeholders supporting giving the patient more than one option believe it will smooth the
cultural transition for patients and schedulers during implementation. Some patients are
very ill or very elderly and thus have strong preferences for appointment time of day. Other
patients are generally accustomed to receiving a choice during scheduling, and resist being
given only one option.
To arrive at the two options to present to the patient, the algorithm sequentially traverses
through a series of buckets of increasingly less constrained set of possible appointment times.
The traversal terminates at the first bucket that contains at least two options. All buckets
still satisfy hard constraints set forth by the Retrospective Model. The hierarchical series of
buckets are in the following order:
1. Appointments that fully satisfy Max(Max-Min)
2. Appointments that satisfy either Max(Max-Min) or NextMax(Max-Min), where NextMax(MaxMin) is the calculation of Max(Max-Min) should Max(Max-Min) be removed from the
list
3. Any appointment that does not increase the existing peak of the day Pd
4. Any appointment in InfusionTimes
Upon termination of bucket traversal, the patient is presented with the earliest and latest
options from that bucket as their two options to select from.
For example, if OptimalTimes is the list of appointment options, {14, 14.5, 15}, the
patient would be offered 2pm and 3pm as options. If however OptimalTimes is the list
64
{ 14}, the algorithm would then also consider appointment times that satisfy NextMax(MaxMin). If the new list is {10, 10.5, 11, 14}, the patient would be offered 10am and 2pm as
options.
Biased patient selection
To simulate patient selection between the two options, we make the assumption that the
current state of high utilization during the hours of 10am-2pm reflects patient preference
to book appointments in this period. The simulation attempts to capture this preference
behavior using the following patient selection modeling:
1. If the patient is given two options in the period 10am-2pm, the patient selects randomly
between the two options.
2. If the patient is given one option in the period 10am-2pm, and one option outside this
period, the patient selects the option within the 10am-2pm period with probability p.
In order to demonstrate the worst case scenario, results will be shown for p = 1.
3. If the patient is given two options outside the 10am-2pm period, the patient selects
randomly between the two options.
Results
Figure 5-10 compares the utilization in scenario where the patient is given one scheduling
choice with the scenario where the patient is given two choices.
Giving the patient two
choices, to a small extent, diminishes the smoothness of the utilization curve, with greater
non-uniformity observed from 12pm to 3pm. The intuition is that more patients are choosing
the 10am-2pm period of time, so the number of patients begins to build around 10am,
affecting the time delayed period of 12pm to 3pm.
Overall the utilization curve giving
the patient two choices is still very smooth compared to the current state.
Figure 5-11
compares the daily peaks that would result from giving the patient only 1 option, or giving
the patient two options. There is a clear operational tradeoff for giving the patient a second
choice, assuming the patient is biased towards the currently congested period. The median
65
-Giving Patient I Option -Giving Patient 2 Options
60
50
'r. 40
030
10
0
00
M~
0
t-I
rq
r4
N
V4
ME
u-4
IV
%_4
W
in
V-I 4
r%
u-I
a%
00
u-I r4
0
Time (half hour)
Figure 5-10: Comparison of Utilization for Giving the Patient 1 Option vs. 2 Options
peak across 243 days increases from 39 to 41, and the max peak increases from 52 to 57.
The coefficient of variation across days increases from 12.4 to 13.9, representing increased
variation and thus less predictable day to day schedule.
However, the tradeoff in peak
utilization can be justified by a smoother transition to the new scheduling process and
respect for patients who need choice due to age or clinical need.
66
GMng Patient I Choice GI ving Patient 2 choices
li
70-
70-
65-
65
60-
60
50-
50
45-
45
40-
40
35-
35
30
30
25~
0 10 20 30 40 50
Count
25
-
z.
55~
55-
b
0 10 20 30 40 50
Count
52
10%maximum
49
42
39
57
54
quartie
median
36
auartide
45
41
38
28
26
412
5.77
139
28
25
393
428
12A
minimum
Figure 5-11: Comparison of Daily Peaks for Giving the Patient 1 Option vs. 2 Options
67
Figure 5-12 shows how many hours between the two appointment options were given for
all appointments.
The options given to patients for the most part do present the patient
with the perception of choice. In 60% of cases, the patient was given two options at least two
hours apart. In 19% of cases patients are given options only 30 minutes apart. In these cases
imposed to
the perception of choice is not strong, however limits on patient choice must be
maintain the operational advantage of the proposed algorithm.
0
to
Figure 5-12: Time difference [hours] between first and second appointment option offered
patients
Two other methods to give the patient 2 choices were also tested as a part of this study.
They are less promising, and available in Appendix E.
5.5
Complementary Feasibility Assessment
affect
The implementation of the scheduling algorithm changes the patient load, which will
and
the workload of staff throughout the day. It is important to ensure the staffing of nurses
staffing
pharmacists can handle the new pattern of patient arrivals. Otherwise shortage of
In order
will cause delays, reversing the positive outcomes of the scheduling process changes.
hurdles
to present a complete solution that actively considers and resolves these possible
to implementation, additional analyses must be conducted to verify that the scheduling
with
algorithm can be implemented by current staffing patterns, or can be accommodated
minor changes. The following studies were conducted to enable implementation:
* Primary Nursing Study: Verifies the new scheduling algorithm respects the Primary
68
Nursing Model currently used in the Infusion Unit
" Pharmacy Study: Analyzes the effect of the new scheduling algorithm on pharmacy load, and suggests process improvements in the pharmacy that will accommodate
changes in load
" Nursing Load Study: Considers current nursing staffing in the Infusion Unit and
any necessary changes
This chapter will describe how each study was conducted, and the results and conclusions
derived from each study.
5.5.1
Primary Nursing Study
Methodology
As described in Chapter 4, the Primary Nursing Model is considered a crucial aspect of
patient care in the Infusion Unit that cannot be compromised.
Analysis is conducted to
confirm that the scheduling algorithm proposed by this thesis does not negatively impact
the Primary Nursing Model. Negative impact here is defined as resulting in fewer patient
visits assigned to the patient's primary nurse compared to the current state. The Primary
Nursing Study cross references the new schedule of patients produced by the Prospective
Model with databases of patient Primary and Associate Nurse assignments and nursing shift
assignments to determine how many patient visits can be assigned to the patient's Primary
or Associate Nurse.
Additional data sets were required to complete this study:
* Patient Primary Nurse Assignment: Acquired from patient records held by MGH
" Patient Associate Nurse Assignment: Derived from patient scheduling records,
where the nurse that the patient saw next most often after the Primary Nurse was
defined as the Associate Nurse for that patient
" Infusion Unit nursing shift schedules: Acquired from Infusion Unit triage nursing
69
Prospective Model
Original
Figure 5-13: Results: Proposed State adherence to Primary Nursing Model
The left diagram of Figure 5-13 shows the distribution of patients who see their Primary
and Associate nurses in the current state during calendar year 2013. In the current state,
taking into account all last minute patient nurse reassignments, 69% of patient visits were
assigned to the Primary Nurse. Another 19% were assigned to the Associate Nurse. In 12%
of all patient visits, both the Primary and Assoicate nurse were not present or otherwise
unavailable to take care of the patient during that visit.
Using the output of the Prospective Model, for each patient appointment, the study does
the following:
1. Look up patient's Primary Nurse
2. Look up the Primary Nurse's availability schedule for the appointment date and time
3. If the Primary Nurse is available (working and does not have another patient scheduled
at that time), assign the Primary Nurse to be the nurse for the appointment
4. If the Primary Nurse is unavailable:
(a) Look up patient's Associate Nurse
(b) Look up the Associate Nurse's availability schedule for the appointment date and
time
70
(c) If the Associate Nurse is available (working and does not have another patient
scheduled at that time), assign the Associate Nurse to be the nurse for the appointment
(d) If the Associate Nurse is unavailable, assign a randomly selected nurse from the
same Disease Center to the appointment
This method cannot account for any last minute nursing assignment changes.
For ex-
ample, should a nurse take a last minute leave of absence, that nurse's patients for the day
would be reassigned to other nurses on staff for the day. Results should be considered the
best case scenario based on nursing staffing.
Results
Figure 5-13 compares adherence to the Primary Nursing Model in the current state and proposed state. The study confirms that the proposed scheduling algorithm does not negatively
impact Primary Nursing. In the proposed state, 84% of patient visits can be assigned to the
Primary Nurse, whereas in the current state 69% of appointments did so. Additionally, only
2% of appointments in the proposed state could not see either a Primary or Associate nurse,
compared to 12% in the current state.
The reason for the projected improved adherence to the Primary Nursing Model could be
explained as follows. Nurses, with few exceptions, work 10 or 12 hour shifts. In the current
state, each nurse is staffed all day, while seeing most of their patients from 10am-2pm.
During this 4 hour period, the Infusion Unit experiences nursing constraints due to high
utilization. As a result, patients may be reassigned to other nurses in the event that their
Primary Nurse is occupied. In the proposed state, patient arrivals are spread more evenly
across operational hours.
This disperses the arrival of a nurse's patients throughout the
day, resulting in fewer reassignments. Nursing schedules did not turn out to be a significant
constraint in the proposed state because nurses that are scheduled to work each day are also
scheduled to work nearly all hours in that day.
The Primary Nursing Study concludes that adherence to the Primary Nursing Model is
not expected to be a barrier to implementation of the proposed scheduling algorithm.
71
5.5.2
Pharmacy Study
Pharmacy Work Flow
The Infusion Unit has a dedicated, co-located pharmacy that mixes infusion treatments inhouse. The pharmacy operates 7am-8:30pm on weekdays to accommodate all operational
hours of the Infusion Unit. Infusion Unit nursing gives the signal to mix a treatment to the
pharmacy once the patient has arrived in the waiting room and orders are received from
the patient's oncologist.
The pharmacy operates as an assembly line with four stations:
Processing, Quality Assurance, Mixing, and Checkout. Registered pharmacists (RPh) staff
Processing, Quality Assurance and Checkout, and technicians staff Mixing. All pharmacists
are cross trained to be flexible to move to any of the RPh-staffed stations at any time.
Currently the pharmacy is staffed to accommodate the period of high patient arrivals
from 10am-2pm. This means the number of pharmacists working is highest in the middle
of the day. With the new patient arrival patterns of the proposed algorithm, the time the
highest number of infusions begin is 8am, when currently the pharmacy is minimally staffed.
This study will consider what process changes can enable the pharmacy to accommodate
the shift in patient load without the need for additional headcount.
Methodology
Pharmacy staffing level is measured by how many RPh are on staff at any time. Technicians
are staffed according to how many RPh are on duty. The pharmacy staffs according to seven
different staffing regions. Each staffing region is a unique combination of time of day and
number of RPh on staff. The current state staffing regions are structured as shown in Table
5.1.
To minimize impact on the pharmacy, we assumed that the shift hours stay as in the
current state. Staffing regions defined in Table 5.1 will be preserved, and this study only
considers how the number of RPhs needs to be shifted within these regions. This study finds
pharmacy process changes that would allow the throughput per region across all regions in
the proposed state not to exceed that of current state when fully staffed.
Pharmacy throughput is defined on an hourly basis. Hourly throughput is defined as the
72
Table 5.1: Pharmacy Staffing Regions: Current State
Staffing Region
Region
Region
Region
Region
Region
Region
Region
1
2
3
4
5
6
7
Time Period
Current state number of RPh on staff
7:00am-8:00am
8:00am-9:00am
9:00am-12:00pm
12:00pm-3:30pm
3:30pm-4:30pm
4:30pm-5:30pm
5:30pm-8:30pm
3
8
11
12
8
4
1
Current State: Pharmacy Throughput by Staffing Region
to
0
2a
.
........
Regioni
Region2
Region3
Region4
Region5
Region6
Region7
Pharmacy Staffing Region
Figure 5-14: Current State: Pharmacy Throughput by Staffing Region
number of treatments mixed during a period of one hour. Specifically we measure how many
treatments are checked out from the pharmacy each hour. The throughput per staffing period
is defined as the hourly throughput that represents the highest throughput hour during that
staffing region. Figure 5-14 shows the current state maximum hourly throughput per staffing
region. When the pharmacy is fully staffed (Region 4), the pharmacy's throughput capacity
is on average 17 treatments per hour. At maximum, the pharmacy is capable of an output
of 27 treatments per hour, fully staffed. This number serves as the capacity of the pharmacy
with no additional headcount.
The goal of the Pharmacy Study is to find process changes that will enable all staffing
73
Prospective Model Proposed State:
Pharmacy Throughput by Staffing Region
ko
... . . .
II
Region1
.
.
0
-s
Region2
Regon3
Region4
Regaon5
Regton6
Region7
Pharmacy Staffing Region
Figure 5-15: Proposed state pharmacy load assuming no additional process improvements
or algorithm tweaks
regions in the proposed state not to exceed that of Region 4 of the current state. When that
is true, we can conclude that the new pharmacy load can be accommodated in the pharmacy
with only staffing shift adjustments and no additional headcount.
Results
Figure 5-15 shows the proposed state pharmacy throughput by staffing region. This figure
shows that the proposed state cannot be sustained in the pharmacy without additional
headcount. The throughput required of Region 1 exceeds 17 in the median and exceeds 27
in the maximum. Throughput required of Region 2 also exceeds 27 in the maximum.
The Pharmacy Manager provided a conservative list of treatments that can be mixed 24
hours in advance. This list includes treatments that are considered low risk and low cost
to premix. We propose that the day before during periods of low demand, the pharmacy
premix this conservative list of treatments according to scheduled treatments beginning at
8am and 9am each day.
Pharmacy load decreases dramatically after 5:30pm, but is still
staffed until 8pm. The period 5:30pm-8pm is a time of spare pharmacy capacity that can
be used to premix for the next day.
74
Prospective Model Proposed State:
Max Daily Pharmacy Throughput by Staffing Region
Conservative Premix
0.
0~
Regioni
Region2
Regon3
Region4
Region5
RegionS
Regionl
Premix
Figure 5-16: Pharmacy throughput by staffing region including conservative premix for 8am
and 9am appointments
Figures 5-16 show the pharmacy throughput by staffing region incorporating conservative premix of 8am and 9am appointments. The maximum throughput in the pharmacy
throughout all days and all staffing regions remains below 27, and the median remains well
below 17. Implementing premix will allow the pharmacy to accommodate the new patient
load without additional headcount.
Several other options for the pharmacy were also explored as a part of this study, and
results of those options are shown in Appendix F.
5.5.3
Nursing Load Study
Methodology
The Nursing Load Study seeks to identify potential need for infusion nursing staffing changes
in the Infusion Unit. The Finance Department of Patient Care Services budgets nursing
staffing assuming patient/nurse ratio of 2:1. This ratio is set in order to maintain patient
safety and prevent nurse overwork.
Patient/nurse ratio higher than 2:1 is considered un-
desirable but is accepted occasionally in the current state. The Infusion Unit is flexible to
adjust nursing shifts, however is averse to adding additional staff. The Nursing Load Study
seeks to confirm that no additional nursing headcount must be added, and to consider any
potential need to adjust nursing shifts for a few nurses.
Nursing shifts are scheduled for 10 or 12 hours. Over 30 nurses are scheduled during fully
75
Infusion Unit Nursing Staffing: Current State
-Average
--.Max --
Min
35
4)
4.20
150
0
q - r4J evl qr uLn
r-
t,-.
co 4m 0
0
oo
0
Time
Figure 5-17: Current State: Number of nurses on staff by time of day
staffed periods of each day to care for patients in 60 chairs. Due to last minute vacations,
nurses
family emergencies, injuries, and other leaves of absences, on average the number of
working during fully staffed hours is 28 nurses. Figure 5-17 shows the average, minimum,
and maximum number of nurses working throughout the day across the one months analysis
period of September 22, 2014 to October 17, 2014.
=
The Nursing Load Study determines patient/nurse ratio according to: Patient/Nurse
5-17.
Ut/Nt. Nt is the number of nurses on staff at time t in the current state (Figure
Ut is the utilization at time t (Figure 1-1), equivalent to the number of patients receiving
treatment at each time of day. The current state mean and mean plus one standard deviation
deviation
patient/nurse ratio is computed as shown in Figure 5-18. The mean plus 1 standard
ratio exceeds 2:1 for four hours of the day, 11am-3pm. For all other times of the day, expensive
nurse resources are underutilized.
by
The Nursing Load Study computes the patient/nurse ratio for the proposed state
proposed state
replacing ut of the current state with ut of the proposed state to compute the
patient/nurse ratio.
76
Current State: Patient/Nurse Ratio
Average
.....
Ave+1SD
2.5
0
2.0
cr1.5
1.0
Time
Figure 5-18: Current State: Patient/Nurse Ratio by time of day
77
Results
The results of the Nursing Load Study are shown in Figure 5-19. The study conclusively
determines no additional nursing headcount must be added in order to implement the proposed scheduling algorithm. For all hours of the day, at average utilization, the ratio remains
below 2:1. For most operating hours 7:00am-6:30pm, average patient/nurse ratio approaches
half the target ratio, suggesting the potential to reduce nursing staffing during that period.
The mean plus 1 standard deviation patient/nurse ratio also remains below 2 for all but one
hour 6:30-7:30pm. In order to fully respect the target ratio, and because there is projected
excess of nursing resources from 7:00am-6:30pm, the Infusion Unit should consider changing
the nursing shift of one or two nurses to cover the end of the day 6:30pm-8:00pm.
The
Patient Care Services Finance Department has stated that the shifting of nursing schedules will not be a problem, and will be completed in phases as the proposed algorithm gets
rolled out. Finance Department representatives also agree no additional nursing headcount
needs to be added to the staff before implementation of the scheduling algorithm. As such,
the Nursing Load Study concludes that nursing staffing considerations are not a barrier to
implementation of the proposed algorithm.
78
Patient/Nurse Ratio
Patient: Average, Average+1SD utilization from Prospective Model
Nurse: Average current nurse staffing
-Average
--
Ave+1SD
3.0
0
m2.5
v 2.0
1.5
1.0
0.5
0.0
r, o
q
i
r4
rI
rr
to
ri
ro
ri
p
Time
Figure 5-19: Patient/Nurse Ratio proposed state with existing nursing staffing
79
Chapter 6
&
Recommendations, Future Work,
Conclusions
6.1
6.1.1
Operational Recommendations
Scheduling Recommendations
Based on the positive results of modeling the proposed state, and the demonstrated potential
to recover 33% of capacity at the median peak of the day, the study recommends implementing the proposed scheduling algorithm that gives the patient two scheduling choices.
Specifically, the study recommends scheduling Infusion-Only appointments at the beginning
of the day (as described by Section 5.4.1, and PTC appointments according to the Max(MaxMin) method (Section 5.4.1). The number of patients beginning infusion at 8am should be
set to 35 patients. During implementation, Cancer Center management should evaluate the
load the 35 patient cap imposes on the various resources in the Infusion Unit to determine
whether a different cap should be considered.
6.1.2
Process Change Recommendations
The algorithm should be built into new, custom scheduling IT. There are many benefits.
First, it makes the transition smoother for schedulers, as they would not need to learn the
algorithm themselves, but simply click buttons in a similar process as they do now. Second,
80
it allows the schedulers to tell patients that the IT does not allow them to book appointments
outside of options provided. This provides schedulers a way out when patients object that
they used to be able to pick any appointment time they choose. Third, it would reduce the
number of ways schedulers and physicians can work around or ignore the algorithm in favor
of patient preferences.
Scheduling between the Practice and Infusion Unit should be centralized.
Recall that
in the current state, schedulers sitting in both the Practice and Infusion Unit schedule the
same appointment.
This has political difficulties as both the Practice and Infusion Unit
consider in-house scheduling to be a source of power over patient flow. However, there are
no operational justifications for why the existing scheduling structure should be maintained,
other than inertia.
The pharmacy should implement the process of premixing the conservative list of treatments provided by the Pharmacy Manager. Premixing has been implemented in the past
during a pharmacy shutdown period, so the various parties responsible for and affected by
premixing have successfully completed the transition before. The premix load of on average
12 treatments should be processed from 5:30pm-8pm. No new pharmacy orders are regularly
expected to arrive during this time because all patients have already been scheduled to arrive. The Pharmacy Manager has stated she expects the premix load to be easily completed
in that length of time.
6.1.3
Staffing Recommendations
There is no projected need for additional headcount in order to implement the proposed
scheduling algorithm. Minimal staffing adjustments are recommended:
" Practice: No change is recommended in the Practice, as the study took Practice
schedules as given. There is potential to study and recommend an optimized physician
schedule that would further improve the utilization of the Infusion Unit, but that is
outside the scope of this work.
" Infusion Nursing: The schedules of one or two nurses should be adjusted to be the
later shift ending at 8pm. Triage nursing states that there are many nurses willing to
81
make that adjustment as those times work better in their lives. The Finance Department also plans to monitor staffing as the changes are rolled out to observe times of
day when staff reduction might be possible.
" Infusion Support Staff: The expected increase in patient load during morning hours
might require the addition of one more staff member to the Front Desk and one more
to the Central Pod at 7am. The Infusion Unit Operations Manager plans to shift
resources from later in the day to early in the day, as the demand on the Front Desk
and Central Pod diminish at the end of the day once all patients are checked in and
assigned a chair. Support staff management also state their entire staff is cross trained
and able to switch between roles as needed.
" Pharmacy: With the new proposed process changes in the pharmacy, pharmacy will
need one additional pharmacist to begin at 7am. Pharmacy management states there
are many existing pharmacists that would prefer the earlier shift and does not see
a problem making this adjustment. Pharmacy will adjust staffing iteratively as the
process changes are rolled out.
" Scheduling Team: The now separate Practice and Infusion Unit scheduling teams
should be unified into a single scheduling team.
This has the potential to reduce
redundant headcount on the scheduling team.
6.2
Future Work
During the course of this study, we identified several areas of the MGH Cancer Center that
could benefit from further analysis and process improvements:
9 Stay Variation Study Extension The Stay Variation study quantified the high
impact of unscheduled chair utilization in the Infusion Unit on daily operation. Patient
stays are highly variable depending on the illness level of the patient, reactions they may
have to treatments, and operations limitations of the Cancer Center such as pharmacy
or phlebotomy lab delays, or staff and physical resource limitation. In addition to stay
82
variation of arrived scheduled patients, there are other unexpected events during the
day such as add-ons, conversions, cancellations, and no-shows that create unforeseen
variation. The stay variation analysis can be extended to identify sources of variation,
quantify their real effect on the operations of the infusion unit, and bucket sources of
variation into categories of predictable, preventable, and uncontrollable.
The study
extension can then suggest methods to predict for predictable sources of variation,
mitigate preventable stay variation, and plan for excess capacity in the schedule for
uncontrollable sources of variation.
" Pharmacy Premix Study Optimization modeling may be able to direct pharmacy
premixing in a more systematic process. There may be an optimal set of treatments
to premix that depends on patient type, treatment type, illness acuity, and pharmacy
capacity.
" Pharmacy Ready Study While the pharmacy filling operations run very smoothly,
there is often highly variable delay from when treatments are discharged to when the
nurse has them in possession. This depends on the delivery method of the treatment
to the nurse and nursing availability. There is potential for improvement.
" Scheduling Unification Many process changes would need to be put in place should
scheduling in the Practice and Infusion Unit be centralized.
" Scheduling of Same Day Add-ons Analysis can be performed on how to accommodate same day add-ons. In this study, they are asserted in the schedule as they arrive.
However, the schedule can try to anticipate the rate and arrival times of add-ons based
on past add-ons data. The schedule can try to reserve capacity for add-ons, or identify
if add-ons should be accommodated during specific times of the day.
" Patient Seating and Discharge There are often unnecessary delays in seating a
patient to begin infusion or disconnecting and discharging patients at the completion
of treatment. Process improvements may address this issue.
" Practice and Infusion Unit Communication We were approached many times to
help resolve the issue of being able to reach people in either the Practice or Infusion Unit
83
from the other facility to submit orders, sign off on patient abnormalities, and general
consultation. There may be process improvements that can address this concern.
* Practice Scheduling Study In the current state, follow-up (FOL) appointments,
which are likely more flexible as they are very infrequent (see Chapter 3), are scheduled
earlier than PTC appointments and thus have priority pick of prime appointment times.
There is potential for Practice schedule redesign such that FOL and PTC appointments
are scheduled in such a way to minimize impact on the Infusion Unit.
* Remote Blood Draw Study The MGH Cancer Center has facilities at MGH North
in Danvers, MA, and MGH West in Waltham, MA. Operations can be greatly simplified
in the Infusion Unit if the Cancer Center can systematically and analytically find ways
for patients to have their blood drawn at these satellite facilities a day in advance of
their treatments.
6.3
Conclusions
This thesis proposes a novel, high impact patient scheduling algorithm for the Massachusetts
General Hospital Cancer Center Infusion Unit that has demonstrated the potential to recover
33% of physical capacity on the peak utilization of each day. Rigorous analysis and modeling
of both the current state and the proposed state support the immediate implementation of
the proposed algorithm.
Cancer Center management is actively pursuing implementation and is eager to see the
algorithm function within months. The proposed state described by the Prospective Model
can be achieved with minimal adjustments to staffing in the infusion unit and pharmacy,
and no adjustment to staffing in the Practice. The algorithm also respects existing primary
nursing model, and treatment specific limitations.
Recovered capacity can be utilized to
absorb growth that will lead to higher revenues, relieve existing resource shortages at peak,
and to enable the Cancer Center to consolidate infusion operations currently housed in other
facilities into the Infusion Unit to generate more operational efficiency. If the entirety of the
potential 33% physical capacity recovery could be used to administer additional treatments,
84
the Infusion Unit could see annual increase in patient volume of approximately 10,000 patient
visits. Immense positive revenue impact aside, 10,000 additional chemotherapy treatments
could be administered with existing facilities to sick cancer patients, a human impact that
is unquantifiable.
85
Appendix A
Stay Variation Analysis: Detailed
Explanation
Details of the Stay Variation analysis are presented in this Appendix.
First, we aggregate all stay variation for all appointments across this period. The resulting
distribution of stay variation minutes is shown in Figure A-1, with the descriptive statistics
given in Table A.1.
Across all appointments in this time period, average stay variation is
an overstay of 8.1 minutes, with high standard deviation of 111.7 minutes.
Looking only
at operational variation without the effects of add-ons, cancellations, and no-shows, the
stay variation is still positive. Each standard, previously scheduled appointment on average
exceeds scheduled duration by approximately 25 minutes (standard deviation 80.2 minutes).
Table A.1: Stay Variation Statistics
Source of Variation
Mean [minutes]
Standard Deviation [minutes]
Stay Variation
8.1
111.7
Operational Variation
26.6
80.2
Add-ons
144.2
107.9
Cancellations and No-Shows
-162.7
-102.1
Next, it is informative to understand how stay variation affects each day of operation
as a net of all overstay and understay. The distribution from Figure A-1 is aggregated for
each day separately to derive the per day stay variation. The histogram and corresponding
86
Histogram: Stay Variation
* Addons
" Cancellations & No Shows
-
25004-0
4,
-
* Operational Variation
2000
1500
.
0
4,
z
0
000
000000
00
0000
00000O
00
O
w
Stay Variation (Minutes)
Figure A-1: Histogram of stay variation, differentiating add-ons, cancellations & no-shows,
and operational variation, for 63 days in 2013
87
Daily Stay Variation, Overstay, and Understay Statistics [Hours/Day]
Understay
Overstay
Stay Variation
140
140
140
120
120
120
100
100
40-
40-
40-
D
0
20
-20
20.6
5 10 15
Number of Days
0
10
quartile
minimUAM
Number of Days
M323
_____-60
maximurn
14"2
quartile
median
quartile
144.
106.6
96.
878
1297
quartile
median
0 5 10152025
15
Number of Days
__
maximum
5
74A
65A
512
2618
179
649
minimum
205
31.6
61.6
9612
97D
175
181
maximum
-13.5
quartile
median
quartile
-132
-25.7
-32b
-372
-52.9
minimum
~
-9.
-32.1
83
-263
Figure A-2: Histogram of daily stay variation, overstay, and understay for 63 days in 2013
statistics of per day stay variation in hours is shown in Figure A-2. Each day, the Infusion
Unit accommodates on average total net stay variation of 65 hours, with a standard deviation
of 20.5 hours, across all appointments that day. In other words, on average 65 chair hours of
utilization is dedicated to unscheduled and unplanned use each day, assuming overstay and
understay can cancel each other out directly.
An important distinction between overstay and understay is that overstay must be accommodated, whereas understay cannot necessarily be recovered. Overstay usually represents
a patient who has arrived and must receive treatment.
Understay represents last minute
unexpected resource availability, which may or may not be reallocated. Thus the net stay
variation represents the minimum number of unscheduled chair hours that must be accom-
88
modated in the Infusion Unit, assuming that all understay is perfectly reallocated to be used
by overstay. Overstay represents the maximum number of unscheduled chair hours that must
be accommodated, assuming no understay can be repurposed to be used for overstay.
Thus, it is important to quantify overstay separately. Overstay is aggregated for each
day, and the statistics are also shown in Figure A-2. The results are staggering. On average,
each day the Infusion Unit sees 97 hours of overstay, with a standard deviation of 17.5 hours.
In other words, in the worst case, on average up to 97 chair hours of utilization per day is
dedicated to unscheduled use.
To complete the picture of unscheduled chair utilization, stay variation and overstay are
analyzed for the exact period of the day they affect. This is necessary to determine whether
stay variation affects low utilization periods of the day when they can likely be accommodated, or high utilization periods of the day when they would exacerbate the congestion
already observed during those times. We look at when stay variation and overstay are occurring according to time stamped patient tracking data. We consider the time the patient
is scheduled to occupy a chair to be the time the patient arrives in a chair plus the number
of hours they are scheduled for treatment. Any time the patient does or does not spend in
that chair beyond those hours are considered hours of the day attributed to stay variation.
We count the total number of chairs attributed to stay variation and overstay each half
hour and normalize to the capacity, that is, the total number of chairs available during the
period. This provides the proportion of capacity that is used to accommodate unscheduled
treatment time for each hour.
Results of this analysis are shown in Figure A-3. Since overstay represents the worst case
unscheduled time that must be accommodated and stay variation represents the best case
unscheduled time that must be accommodated, the space between the two curves of Figure
A-3 represents all possible actual variation accommodated by the Infusion Unit. It is fair to
say that the variation seen by the Infusion Unit increases when the Infusion Unit begins to
become congested (Figure 1-1), remains high to absorb the consequences of the congestion,
and tapers off again at the end of the day when far fewer patients are arriving. Reducing the
congestion during periods of high utilization should also reduce variation in the schedule, as
lower and more uniform use of resources should reduce delays and wait times. Controlling
89
% of Total Chair Capacity Utilized by
Overstay & Stay Variance
-Overstay/Capacity
-Stay
Variance/Capacity
30%
25%
20%
15%
u
U
10%
5%
0%
-5% 0%)
Time (hour)
Figure A-3: Proportion of total capacity impacted by stay variation at different hours of the
day
patient inflow through systematic scheduling should both smooth the intra-day utilization
and reduce variation in the schedule.
90
Appendix B
Supplemental Current State Plot
Infusion Visit Duration by
Scheduled Infusion Start Time
1600
1400
1200
1000
c 800
600
--
400 -200
-
r'j
to
N-
Do
N-4
00
Mn
0
r-I
-
-
-
-
-
-
MN
C4,
e
qc
r4
T-
-1
Hour of Day (Number of Appointments)
Figure B-1: Scheduled duration for all infusions in 2012 and 2013 by hour of first appointment
segment start time
91
Appendix C
Holidays in CY2013
Table C.1: Specific dates in CY2013 excluded from modeling
Reason
Date
i
1/1/2013
1/21/2013
2/14/2013
2/18/2013
4/15/2013
4/16/2013
5/27/2013
7/3/2013
7/4/2013
9/2/2013
10/14/2013
10/31/2913
11/11/2013
11/27/2013
11/28/2013
12/24/2013
12/25/2013
12/31/2013
New Years Day
Martin Luther King Jr. Day
Valentine's Day
President's Day
Patriot's Day & day of Boston Marathon Bombing
Day after Patriot's Day
Memorial Day
Day before Independence Day
Independence Day
Labor Day
Columbus Day
Halloween
Veteran's Day
Thanksgiving
Day after Thanksgiving
Christmas Eve
Christmas
New Year's Eve
92
Appendix D
Alternative to Max(Max-Min)
Method
Several methods to compute OptimalTimes in Step 3 of the prospective algorithm were
evaluated.
Results for the most promising alternative to the Max(Max-Min) method are
presented in this appendix.
This method selects the latest appointment start time in
InfusionTimes. The 'Last' method demonstrates a significant improvement over the current state, however is not the final recommendation because results are not as promising as
the Max(Max-Min) method.
93
ASJOrkna_
75
Prospective(Las)
75
70
0maimu
65
'ja 65
60 --
_
60
55
55
45
4.5...
40q-
-3
4al
35
35--
304
30
median
4
59mdin
0 10 26 30 40 50
0 10 2D 30 40
Count
Count
maximum
71
maximum
73
59
median
quafile
43
40
minimum
23
Old!69
hmedian
:% quartile
59
5
53
40
GDf
minimum
(W1
28
Ni Summary Statiseis
Smmary Statistks
57.2
7.62
13.3
43.9
7.19
16.3
aie
Std N
tew
Figure D-1:
TSN31
Distribution of daily peaks for Last method, alternative to Max(Max-Min)
method
94
Appendix E
Other options to give the patient two
scheduling options
This study explored three ways to give the patient two options to choose from during scheduling. The most successful was presented in Chapter 5. The other two, which do not match
the chair capacity and are likely to cause serious delays, are presented below. Results of all
three methods are compared below as well.
Giving the patient 1 AM and one PM option
The first expansion gives the patient one appointment option in the morning and one in the
afternoon. Morning and afternoon are defined in order to allocate approximately the same
number of time slots in the morning and afternoon:
" Morning: 8:00am-12:30pm
" Afternoon: 1:00pm-6:00pm
To determine the two choices to offer the patient, the list of possible infusions InfusionTimes
is filtered into two different, mutually exclusive and exhaustive lists, morning and afternoon. The morning and afternoon lists are separately passed to the Max(Max-Min) method.
OptimalTimes is calculated separately for the morning and afternoon, and the resulting
lists are OptimalTimesAM and OptimalTimespM. One option to present to the patient
95
is selected randomly from OptimalTimesAM, and one option is selected randomly from
OptimalTimespM.
Giving the patient 2 options at least 2 hours apart
The second expansion gives the patient two choices that are at a minimum 2 hours apart.
The working group speculates that giving the patient two choices at least two hours apart
is sufficient to give the patient the perception of choice.
The first option presented to
the patient is selected from OptimalTimes, per the original Max(Max-Min) method. The
algorithm then subsets InfusionTimes to select for elements e where the difference between
that element and the first option is greater than or equal to 2 hours:
Ie - Option1 ;> 2. The
second option is selected randomly from that subset.
Results of giving patients options
Giving the patient options requires a tradeoff in operational efficiency. The utilization curves
and distribution of daily peaks for the base model and three expansions offering the patient
options are shown in Figures E-1 and E-2. These show results assuming that the patient
is biased towards choosing options in the period 10am-2pm, as described in Section 5.4.1.
Figure E-1 demonstrates that there is indeed a tradeoff between operational considerations
and patient preference. All utilization curves for the Prospective Model expanded to give
the patient options shows a less smooth curve, with a higher maximum point and a clear bias
in utilization towards the middle of the day. To examine this more analytically, we turn to
Figure E-2. Figure E-2 shows that the maximum peak across all days exceeds the capacity
of 60 chairs for both the method that gives the patient one option in the morning and one
in the afternoon, and the method that gives patients two options at least two hours apart.
Should the Infusion Unit choose to implement either of these two methods, there would be
patients who cannot receive their infusion treatments on the desired date, and must move to
a day with more available space in the schedule. Utilization approaching capacity of 60 will
also lead to longer wait times in the waiting room, per queuing theory. The time difference
maximizing method is a good compromise between patient preference and operations. In
this method, the median daily peak across all days increases by 2 from 39 to 41 compared
96
-AMPMBiased
-Prospective
-2HRBiased
-
60-
-
-MaxTimeDiffBiased
50-
40
130
0
a~o
CO
O
q-4
e-I
e-4
N
y
(V
-4 y
*|
q-4
-4
Uti
y
D
w-t
f%
-4
e-
m
vM4 N
Time (half hour)
towards
Figure E-1: Giving the patient options: daily utilization assuming patient bias
l0am-2pm period: distribution of daily peak utilization
to the base model. The maximum daily peak across all days increases by 5 from 52 to
57 compared to the base model. This tradeoff accommodates patient preference and will
facilitate transitioning to this new scheduling process, so the time difference maximizing
expansion will be used moving forward.
97
V
H-isdSamieifBae
spectiftAP-isda
70
70
70
65
65
65
65-
60
60
60
60
55
55
55
55
50
5D
50
50
45
45
45
40
40
40-
40
35
35
35
35
3D
30
30
30
25
-- r-r-0 10 20 30 40 50
25-
-
Count
25 -T-T
0 20
r
0 10 20 30 40 50
mamm
62
quartie
42
quatile
58.
51
medilan
39
quartile
36
28
median
Quartile
minimum
25
393
4B58
12A
minimum
n--r--
40
-
60
counit
COLnt
52
49
rm imumn
45
-
maimumn
25
T
T-r
0 10 20 30 40 50
Count
69
"Umrn
median
ile
47
42
32.
minamum
21
54
49
quartile
45
45
33.1
quartile
M
28
28
minimum
482
7.24
463
655
14.1
57
54
61
quawtile
-
S
70-
142
26
41.2
5.77
13.9
Figure E-2: Giving the patient options assuming patient bias towards 10am-2pm period:
distribution of daily peak utilization. From left to right: Prospective base model, Giving
the patient one morning option and one afternoon option, Giving the patient two options
at least two hours apart, Giving the patient two options maximizing the time between the
options while favoring operations
98
Appendix F
Pharmacy Staffing Study
-
Complete
Description
There are three process improvement or scheduling algorithm tweak options we explored in
order to reach the desired conclusion:
1. 8am Cap In order to reduce the number of treatments that must be mixed before
8am when the influx of Infusion-Only appointments will occur, the maximum number
of appointments scheduled at 8am can be adjusted. In the model described in Section 5.4.1, the 8am cap is set at 35 appointments, which is the maximum number of
appointments that occurred at 8am per the results of the Retrospective Model. This
study will consider the effect on pharmacy load of lowering that cap to 25 and 15
appointments.
2. Premixing Premixing is the practice of mixing treatments early during times when
there is spare mixing capacity, in order to lighten the load during busier times. This
study will consider whether premixing should be considered as a process improvement
in the proposed state, in order to lighten the load during any staffing region that
exceeds the current state Region 4 limits. The downside of premixing is that should
the patient not arrive, or arrive with unexpected vitals changes or blood work results,
the premixed treatment may need to be disposed of, generating waste.
Premixing
has been demonstrated to work operationally in the pharmacy in the past during a
99
pharmacy renovation period. The practice was then abandoned after the renovation
period in order to eliminate waste due to premixing.
3. Premixing Mix Premixing can only be performed for a small subset of treatments.
For example, some treatments are volatile and must be administered within a short
number of hours after mixing. These treatments would not be feasible to premix and
hold in stock until the patient arrives much later. Among treatments that are feasible
for premix, the treatment mix that is selected for premix is subjective. For this study,
the pharmacy has provided two sets of premix treatment mix:
" Conservative premix: A conservative mix of treatments that only selects for feasible premix treatments that have very low chance of waste, as identified by the
Pharmacy Manager
" All premix: A list of all treatments considered feasible for premix, as identified
by the Pharmacy Manager
First we must establish what the load on the pharmacy is expected to be in the proposed
state, without considering tweaking the 8am cap or premixing. Figure F-1 shows the proposed state pharmacy throughput by staffing region. Clearly this figure demonstrates the
proposed state cannot be accommodated in the pharmacy without additional headcount.
The throughput required of Region 1 exceeds 17 in the median and exceeds 27 in the maximum. Throughput required of Region 2 also exceeds 27 in the maximum.
Results shown in Figure F-1 suggest that premixing for Region 1 and Region 2, and
altering the 8am cap should be considered. Figures F-2, F-3, and F-4 show the results of
adjusting the 8am cap, premixing, and adjusting the premix mix in various combinations.
The desired conclusion of this study is achieved by the conservative premix with 8am cap
of 35, shown in Figure F-2. This is a desirable outcome. Not adjusting the 8am appointment cap means close adherence to the proposed scheduling algorithm. Reduction of the
8am cap would require a tradeoff in daily utilization peak reduction, which is undesirable.
Additionally, the conservative premix can be chosen over premixing all possible treatments.
Premixing only the conservative premix mix will minimize waste generated by the process
change, and facilitate implementation of the process change in the pharmacy. Based on these
100
Prospective Model Proposed State:
Pharmacy Throughput by Staffing Region
-C
C-A
-
C)
C.
0
C)
.
-
In
0
-
0
....
......
RegionI
Region2
Region3
Region4
Region5
Region6
Region7
Pharmacy Staffing Region
Figure F-1: Proposed state pharmacy load assuming no additional process improvements or
algorithm tweaks
results, this study recommends implementing a conservative premix of Region 1 and Region
2 treatments, and allowing the 8am appointment cap to remain at 35.
101
Prospective Model Proposed State: 8am Cap = 35
Max Daily Pharmacy Throughput by Staffing Region
Conservative Premix
0
4-j
00
All Premix
0
Q
Regwln
Regqw2
Regwo3
Region5
Reion4
Reg"on
Reg"n
Prmn-x
Figure F-2: Pharmacy throughput proposed state: 8am Cap=35
Prospective Model Proposed State: Sam Cap = 25
Max Daily Pharmacy Throughput by Staffing Region
Conservative Premix
0
0
0
0.
-
All Premix
-4
----
Regioni
0+
00
Region2
Regio3
Region4
RegionS
Region6
Regionl
Premix
Figure F-3: Pharmacy throughput proposed state: 8am Cap=25
102
Prospective Model Proposed State: Sam Cap = 15
Max Daily Pharmacy Throughput by Staffing Region
Conservative Premix
Al Premix
0
Regionl
Region
Region3
Region4
Regonr5
Region
Reglon7
Ptrvmix
Figure F-4: Pharmacy throughput proposed state: 8am Cap=15
103
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