Optimization of Surgery Scheduling in Multiple Operating Rooms with Post Anesthesia Care Unit

170 Pages·2017·3.93 MB·English

Lehigh University
Lehigh Preserve
Theses and Dissertations
2017
Optimization of Surgery Scheduling in Multiple
Operating Rooms with Post Anesthesia Care Unit
Capacity Constraints
Miao Bai
Lehigh University
Follow this and additional works at:http://preserve.lehigh.edu/etd
Part of theIndustrial Engineering Commons, and theSystems Engineering Commons
Recommended Citation
Bai, Miao, "Optimization of Surgery Scheduling in Multiple Operating Rooms with Post Anesthesia Care Unit Capacity Constraints"
(2017).Theses and Dissertations. 2502.
http://preserve.lehigh.edu/etd/2502
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Optimization of Surgery Scheduling in Multiple Operating
Rooms with Post Anesthesia Care Unit Capacity Constraints
by
Miao Bai
Presented to the Graduate and Research Committee
of Lehigh University
in Candidacy for the Degree of
Doctor of Philosophy
in
Industrial and Systems Engineering
Lehigh University
May, 2017
(cid:13)c Copyright by Miao Bai 2017
All Rights Reserved
ii
Approved and recommended for acceptance as a dissertation in partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
Date
Dissertation Co-advisor
Dissertation Co-advisor
Accepted Date
Committee Members:
Professor Gregory L. Tonkay, Committee Chair
Professor Robert H. Storer
Professor Frank E. Curtis
Dr. Camilo Mancilla
iii
Acknowledgments
Iwouldliketoexpressmydeepestappreciationtomyadvisors, ProfessorStorerandProfes-
sor Tonkay. Professor Storer has been a mentor and a friend. Professor Tonkay has set me
an example in great teaching. Their guidance has made my six years at Lehigh a rewarding
and interesting life experience.
I would like to thank Dr. Theman for his great help. He has opened the door to medical
practice for me. His insights and experience make this dissertation much more valuable.
I would also like to thank my dissertation committee members, Professor Curtis and Dr.
Mancilla for their support and feedback.
I would like to thank my girlfriend Xin Dai for her endless support. She has accompanied
me through ups and downs. Her encouragement has kept me confident in myself. Without
her, this dissertation would not have been possible.
iv
Contents
Acknowledgments iv
List of Tables x
List of Figures xi
Abstract 1
1 Introduction 3
2 Literature Review 7
2.1 Surgery Scheduling with Given Sequences in ORs . . . . . . . . . . . . . . . 7
2.1.1 PACU not Considered . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 PACU Considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Surgery Sequencing and Scheduling . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 PACU not Considered . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 PACU Considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Reactive Surgery Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Proactive-Reactive Surgery Scheduling . . . . . . . . . . . . . . . . . . . . . 13
3 Surgery Scheduling in multiple ORs with PACU capacity constraints 15
3.1 Problem Statement and Model Development . . . . . . . . . . . . . . . . . . 15
3.1.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
v
3.1.2 Continuous-time Model . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 SAA-Gradient Descent Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Sample Average Approximation . . . . . . . . . . . . . . . . . . . . . 30
3.2.2 SAA-Gradient Descent Algorithm with Random Restarts (SAA-GDR) 32
3.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.1 SAA-GDR Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Comparisons with Other Algorithms . . . . . . . . . . . . . . . . . . 38
3.3.3 Impact of PACU Constraints . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Surgery Sequencing and Scheduling in multiple ORs with PACU capacity
constraints 44
4.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Two-Stage Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.1 Surrogate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.2 Lagrangian Relaxation of SURSAA . . . . . . . . . . . . . . . . . . . 51
4.2.3 Subgradient Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.4 Scheduled Start Times . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 Setup of the Experiments . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Correlation Study of Original and Surrogate Objectives . . . . . . . 58
4.3.3 Number of Scenarios and Iterations. . . . . . . . . . . . . . . . . . . 59
4.3.4 Comparison with Benchmark Solution Strategies . . . . . . . . . . . 61
4.3.5 Comparison with Hybrid Methods . . . . . . . . . . . . . . . . . . . 64
4.3.6 Impact of PACU constraints . . . . . . . . . . . . . . . . . . . . . . 65
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5 Proactive-Reactive Surgery Scheduling under Disruptions and the “To-
follow” Policy 69
vi
5.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.1 Proactive Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.2 Patient Punctuality, Preoperative Activities and Surgery Cancellations 71
5.1.3 Surgery, Recovery in the PACU and OR blocking . . . . . . . . . . . 72
5.1.4 Surgical Emergencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.1.5 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.1.6 Reactive Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 Discrete Event Dynamic System and Perturbation Analysis . . . . . . . . . 78
5.2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.2 Sample Penalty Evaluation and the Objective Function . . . . . . . 81
5.2.3 Proactive and Reactive Optimization Models . . . . . . . . . . . . . 82
5.2.4 Differentiability of the Sample Penalty Function . . . . . . . . . . . 83
5.2.5 Perturbation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Sample Gradient Descent Algorithm . . . . . . . . . . . . . . . . . . . . . . 88
5.3.1 Sample Average Approximation . . . . . . . . . . . . . . . . . . . . . 88
5.3.2 Sample-gradient Descent with Random Restarts . . . . . . . . . . . 89
5.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.4.1 Selection of Weights in the Objective and Generation of Test Problems 91
5.4.2 Convergence Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4.3 Proactive and Reactive Scheduling . . . . . . . . . . . . . . . . . . . 93
5.4.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.4.5 Impact on PACU utilization . . . . . . . . . . . . . . . . . . . . . . . 96
5.4.6 Insights on “To-follow”, Requested Patient Arrival and Rescheduling 98
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6 Conclusions and Future Research 101
Bibliography 104
vii
A Appendices for Chapter §3 115
A.1 Discrete Event Dynamic System . . . . . . . . . . . . . . . . . . . . . . . . 115
A.2 Nondifferentiability and Discontinuity in the Sample Cost Function . . . . . 119
A.3 Consistency of the SAA estimators . . . . . . . . . . . . . . . . . . . . . . . 120
A.4 Lower and Upper Bounds Derivation in §3.3.1 . . . . . . . . . . . . . . . . . 122
A.5 Setup of the Experiments in §3.3.1 and 3.3.2. . . . . . . . . . . . . . . . . . 123
A.6 Convergence Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
A.7 Comparison of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
A.8 Time-indexed SAA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.9 NOPACU Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
B Appendices for Chapter §4 133
B.1 Comparison with Benchmark Methods in Test Problems . . . . . . . . . . . 133
B.2 Setup of Random Test Problem . . . . . . . . . . . . . . . . . . . . . . . . . 134
B.3 Time-indexed Mixed Integer Model . . . . . . . . . . . . . . . . . . . . . . . 134
B.3.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
B.3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
C Appendices for Chapter §5 142
C.1 Cancellations and Add-ons . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
C.2 Development of the DEDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
C.2.1 Notation in the DEDS . . . . . . . . . . . . . . . . . . . . . . . . . . 142
C.2.2 State Update in the DEDS . . . . . . . . . . . . . . . . . . . . . . . 144
C.3 Feasible Region Ψ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
C.4 Proof of Differentiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
C.5 Consistency of Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
C.6 Projection Algorithm Φ(ψ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
C.7 Weight Selection in the Objective Function . . . . . . . . . . . . . . . . . . 154
C.8 Lower and Upper Bound Estimations in Convergence Test . . . . . . . . . . 156
viii
Biography 158
ix