Resource allocation and Risk Analysis of Dialysis Centres

158 Pages·2015·1.09 MB·English

by  Mahsa Shateri

Resource allocation and Risk Analysis of Dialysis Centres
by
Mahsa Shateri
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
(cid:13)c Copyright 2015 by Mahsa Shateri
Abstract
Resource allocation and Risk Analysis of Dialysis Centres
Mahsa Shateri
Doctor of Philosophy
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
2015
The number of hemodialysis patients is growing every year. The majority of these pa-
tients visit centres at least three times a week for their treatment. Two types of nurses
perform general dialysis procedures on the patients. These are registered nurses (RNs)
and registered practical nurses (RPNs). Hemodialysis patients may experience compli-
cations during their treatment. When complications occur, patients need the assistance
of RNs. The time RNs spend with patients increases the duration of their treatment.
It is essential for all centres to hire enough nurses to maintain the quality of service for
the growing number of patients while minimizing nursing cost. However, facilities have
different nurse-to-patient ratio because they are unique in terms of the combination of
patients and the workload policies regulating their nurses. Moreover, since there are no
generally accepted guidelines, the staffing decisions at each centre are highly subjective.
As a result, it is very difficult for the decision makers to create consistent guidelines to
determine the number of nurses required in each centre.
In this research, we assume that the centre has a given list of specific patients, each of
which is defined by patient type. Two approaches are used to help dialysis units schedule
their patients and minimize nursing cost while having enough nurses to maintain quality
of service. In the first approach, an MIP model and a heuristic algorithm are developed
separately to minimize the number of nurses (RPNs or RNs) to set up, monitor, and
disconnect patients from dialysis machines. The methods find the start time of the
dialysis session for each patient. An M/M/s queuing equation is then used to find the
number of RNs needed to attend to any potential complications of scheduled patients.
ii
In the second approach, the methodologies are merged into a non-linear model to find
patient schedules that minimize the number of RNs and RPNs. Tabu Search is used to
solve the non-linear model. Further, the models and results presented in this study can
be treated as benchmarks for decision makers to find the approximate number of nurses
needed for each unit as well as a forecasting tool to estimate the average number of nurses
needed for any patient size population based on their historical data.
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Dedication
This thesis is dedicated to all end stage renal disease patients in the world with the hope
that this study helps dialysis units to provide you with better quality service and open
doors to many improvements in related healthcare applications.
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Acknowledgements
I am most grateful to my wonderful supervisor, Professor Michael W. Carter, for his
continuous support throughout this thesis. Thank you for giving me the opportunity
to work on such an exceptional topic and for your generosity in sharing your knowledge
and experience. Your encouragements helped me to vastly improve my knowledge of
this research. I learned to connect healthcare strategies, policy and decision making,
forecasting, and optimization applications in developing such realistic benchmark tool. I
am very honored for pursuing this stage of my studies under your supervision.
This research was not possible without the support of the Ontario Renal Network
team. In particular, I am very grateful to Mr. Graham Woodward, Ms. Janet Graham,
and Sarah Bastedo for introducing me to this topic. Regardless of their busy schedules,
they always found time to help me with challenges of this study and to verify my findings.
I would like to thank the clinical director of the nephrology program of the Ottawa
Region, Ms. Connie Twolan, and the clinical director of the nephrology program of the
Waterloo Wellington region, Mr. Peter Varga, for their valuable input in this thesis.
Iamverythankfultomycommitteemembers, ProfessorDanielFrancesandProfessor
Roy H. Kwon, for their advice throughout the course of the research. In addition, I
would like to thank my internal examiner, Professor Timothy C. Y. Chan for his valuable
comments on my thesis. Moreover, I would like to thank my external examiner, Professor
Amy Cohn for taking the time and providing me with her detailed comments on this
research.
I could never thank my caring parents, Mr. Mohammad Shateri and Ms. Parvin
Borzo, and adorable brother, Mr. Hamed Shateri, enough for all their unconditional
love, sacrifices, and support through my life. It is for them that I find myself stronger,
more independent, and determine to reach my goals.
Most importantly, I would like to thank my amazing husband, Dr. Pezhman Hassan-
pour, for his love, encouragements, and support throughout the last decade of my life. I
feel very lucky to have you in my life and cannot imagine my life without you. Last but
not least, I would like to thank my two precious babies, Rayka Hassanpour and Karina
Hassanpour, for filling my life with meaning, joy, and happiness.
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Contents
1 Introduction 1
1.1 Introduction to Dialysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Contribution and Structure of this Thesis . . . . . . . . . . . . . . . . . . 6
2 Literature Review 8
3 Definitions of Parameters 14
3.1 Data Gathering Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Revising the Duration of Treatment for Each Patient Type . . . . . . . . 15
3.2.1 Example: calculation of the duration of treatment . . . . . . . . . 18
4 Optimal Schedules for General Procedures of Dialysis 27
4.1 Mixed Integer Programming Model Development . . . . . . . . . . . . . 28
4.2 Patient Schedule - Mixed Integer Programming Model . . . . . . . . . . . 28
4.2.1 Strategies to Reduce the Computation Time of the MIP Model . . 32
4.3 Extension to MIP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.1 Example 1 - Very Stable Patients . . . . . . . . . . . . . . . . . . 33
4.4.2 Example 2 - Patients with Mixture of Different Types . . . . . . . 39
4.5 Minimizing Number of Nurses Based on Shifts . . . . . . . . . . . . . . . 46
5 Practical Schedules for Patients 50
5.1 Patient Schedule - Heuristic Algorithm . . . . . . . . . . . . . . . . . . . 50
5.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.1 Example 1 - Very Stable Patients . . . . . . . . . . . . . . . . . . 53
5.2.2 Example 2 - Patients with Mixture of Different Types . . . . . . . 58
5.2.3 Mathematical Model and Heuristic Algorithm - Results Comparison 62
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6 Effect of Complications on Each Patient Type 64
6.1 Calculation of the Number of RNs for Complications . . . . . . . . . . . 64
6.2 Calculation for the Required Number of RNs . . . . . . . . . . . . . . . . 66
6.2.1 Example - Patients with Mixture of Different Types . . . . . . . . 67
7 Non-linear Approach for Scheduling Patients 70
7.1 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.2 Tabu Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.3 Example - Patients with Mixture of Different Types . . . . . . . . . . . . 76
7.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8 Additional Applications of Developed Models 79
8.1 Forecasting the Average Number of Nurses and Patient-to-Nurse Ratio
Based on the Number of Patients . . . . . . . . . . . . . . . . . . . . . . 79
8.2 Additional Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.2.1 Effect of Transferring Very Stable Patients to Self-Care Units or
Home Dialysis on Nurse Staffing Cost . . . . . . . . . . . . . . . . 85
8.2.2 Effect of Having More Patients Transfer from Catheter into Fistula
Vascular Access on Nurse staffing cost . . . . . . . . . . . . . . . 85
8.2.3 Effect of Separating Patients with Different Accesses on Nurse
Staffing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8.2.4 Effect of Change in Policies Related to Risk on Nurse Staffing Cost 88
9 Conclusions and Future Work 90
9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
9.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
A Probability of Complications for Every Patient Type 92
B Scenarios 2 and 3 - Estimation of Number of Nurses 98
C Scenarios 4 to 6 - Estimation of Number of Nurses 108
D Scenarios 7 and 8 - Estimation of Number of Nurses 122
E Questionnaire 133
Bibliography 137
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List of Tables
1.1 Characteristics of Vascular Accesses . . . . . . . . . . . . . . . . . . . . . 4
3.1 Frequency of Each Complication Happening for Every Patient Type Dur-
ing Each Hour of Treatment . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Frequency of Each Complication Happening for Every Patient Type Dur-
ing Each Hour of Treatment . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Probability of Patients Experiencing Complication During a Time Interval
in Each Hour of Treatment for Every Patient Type . . . . . . . . . . . . 23
3.3 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Average Service Times Required for an RN to Assist Each Patient Type
for Every Complication in Minutes . . . . . . . . . . . . . . . . . . . . . 25
3.5 Probability of Each Patient Type Experiences Complications for Every
Hour of Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6 Average Number of Times Each Patient Type Experiences Complications
for Every Hour of Treatment . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.7 Weighted Average Service Times in Minutes for Each Patient Type for
Every Hour of Treatment and Total Extra Required Time in Minutes for
Treatment Due to Complications . . . . . . . . . . . . . . . . . . . . . . 26
4.1 Duration of Before- and Post-Dialysis, and Regular Check-up for Each
Patient in Minutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Maximum Number of Required Nurse at Anytime During a Day and
Patient-to-Nurse Ratio for Each Scenario . . . . . . . . . . . . . . . . . . 34
4.3 Number of Time Intervals versus Number of Nurses . . . . . . . . . . . . 35
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4.4 MIP-SampleScheduleforaScenariowithThirtyVeryStablePatientsand
the Times Each Patient Uses a Nursing Assistance For General Procedures
of Dialysis. The Columns Represent the Time Intervals . . . . . . . . . . 35
4.4 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.5 MIP - Number of Times Nurses Needed for Every Ten Minutes Time In-
terval for the Sample Schedule with Thirty Very Stable Patients. The
Columns Represent the Time Intervals. . . . . . . . . . . . . . . . . . . . 39
4.6 Duration of Before and Post-Dialysis, Extra Time for Treatment of Com-
plications, and Regular Check-up for Each Patient in Minutes . . . . . . 40
4.7 Maximum Number of Required Nurse at Anytime During a Day and
Patient-to-Nurse Ratio for Each Scenario . . . . . . . . . . . . . . . . . . 41
4.8 Number of Time Intervals versus Number of Nurses . . . . . . . . . . . . 41
4.9 MIP - Sample Schedule for a Scenario with Thirty Patients and the Times
EachPatientNeedsNursingAssistanceForGeneralProceduresofDialysis.
The Columns Represent the Time Intervals . . . . . . . . . . . . . . . . . 42
4.9 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.9 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.9 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.9 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.10 MIP - Numberof Times NursesNeeded for Every Ten MinutesTime Inter-
val for the Sample Schedule with Thirty Patients. The Columns Represent
the Time Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.1 Heuristic Algorithm - Sample Schedule for Scenario with Thirty Very Sta-
ble Patients and the Times Each Patient Needs a Nurse For General Pro-
cedures of Dialysis. The Columns Represent the Time in Minutes . . . . 53
5.1 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.1 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.1 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2 HeuristicAlgorithm-NumbertimesNursesNeededforEveryTenMinutes
Time Interval for the Sample Schedule with Thirty Very Stable Patients.
The Columns Represent the Time Interval. . . . . . . . . . . . . . . . . . 57
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5.3 Heuristic Algorithm - Sample Schedule for Scenario with Thirty Patients
and the Times Each Patient Needs a Nurse For General Procedures of
Dialysis. The Columns Represent the Time in Minutes . . . . . . . . . . 58
5.3 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.3 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.3 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Heuristic Algorithm - Number of times Nurses Needed for Every Ten Min-
utes Time Interval for the Sample Schedule with Thirty Patients. The
Columns Represent the Time Interval . . . . . . . . . . . . . . . . . . . . 62
5.5 Results Comparison of the MIP Model and the Heuristic Algorithm . . . 63
6.1 Number of Time Intervals versus Number of RNs . . . . . . . . . . . . . 68
6.2 Maximum Number of Required Nurse at Anytime During a Day and
Patient-to-Nurse Ratio for Each Scenario . . . . . . . . . . . . . . . . . . 68
6.3 Total Number of RNs Based on MIP Model and Heuristic Algorithm . . 69
7.1 Results comparison of Linear Model and Non-Linear Model Based on the
MIP Model as Initial Value . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.2 Results comparison of Linear Model and the Non-Linear Model Based on
Heuristic Algorithm as Initial Value . . . . . . . . . . . . . . . . . . . . . 78
7.3 ResultsComparisonfortheAverageNurse-to-PatientRatioforNon-Linear
Models Based on the MIP Model and Heuristic Algorithm as Initial Values 78
7.4 Maximum Percentage Allowed to Increase the Rates of Complications . . 78
8.1 Total and Average Number of Required RNs and RPNs for Mixed Com-
bination of Patients with 98 Percent Coverage within a Minute Time . . 80
8.2 Forecast Values for the Maximum Number of Total Nurse, Patient-To-
Nurse Ratio, and Average Number of Required RNs and RPNs for Differ-
ent Number of Patients Based on Equations in Figures 8.1 and 8.2 . . . . 82
8.3 Maximum and Average Number of Required Nurse and Nursing Staff Uti-
lization Rates for Patients with Catheter Access Having 90 Percent Cov-
erage within a Minute Time . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.4 Maximum and Average Number of Required Nurse and Nursing Staff Uti-
lizationRatesforPatientswithFistulaAccessHaving90PercentCoverage
within a Minute Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
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