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  • Dynamic Optimization Addressing Chemotherapy Outpatient Scheduling

    by

    Shoshana Hahn-Goldberg

    A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

    Mechanical and Industrial Engineering University of Toronto

    Copyright by Shoshana Hahn-Goldberg 2014

  • ii

    Dynamic Template Scheduling Addressing Chemotherapy

    Outpatient Scheduling

    Shoshana Hahn-Goldberg

    Doctor of Philosophy

    Mechanical and Industrial Engineering

    University of Toronto

    2014

    Abstract

    Chemotherapy outpatient scheduling is a complex problem containing uncertainty. Chemotherapy centres

    are facing increasing demands and they need to increase their efficiency. However, there are very few

    studies looking at using optimization methods on the chemotherapy scheduling problem.

    In this dissertation, the chemotherapy outpatient scheduling problem is defined within the scheduling

    literature. Next, we propose a methodology for choosing what information to include from the problem

    domain when creating a mathematical model of a real world problem. Several constraint programming

    models, representing different problem definitions of the deterministic chemotherapy scheduling problem,

    are created and evaluated for their solvability and the quality of their solutions. The chosen optimization

    model was tested within a dynamic framework in order to accommodate the dynamism and uncertainty

    inherent in chemotherapy outpatient scheduling. Termed dynamic template scheduling, this novel

    algorithm uses the chemotherapy centres past records and the chosen model to create a template of open

    slots. As requests for appointments arrive, we use the template to schedule them. When a request arrives

    that does not fit the template, we update the template. To accommodate last minute additions and

    cancellations to the schedule, we test a shifting algorithm that moves patient start times within a

    predefined time limit.

    We demonstrate that chemotherapy centres can use records of past appointments to inform future

    schedules and that integrating optimization methods into the scheduling procedures can improve

  • iii

    efficiency and increase throughput. This research makes a contribution to scheduling research by

    developing a novel technique that combines proactive and reactive scheduling to address dynamic

    problems with real-time uncertainty. This research also makes a contribution to health care scheduling

    applications by solving a case of chemotherapy outpatient scheduling, a practically important problem

    that has had very little treatment in the literature.

  • iv

    Acknowledgments

    Mitacs and Bykart software for funding support.

    Professors Michael Carter and Chris Beck for their valuable supervision.

    Professor Daniel Frances and Dr. Maureen Trudeau for their support and feedback throughout.

    Philomena Sousa, Kathy Beattie, and Thane Fitzgerald for their advice and information.

    Professors Dionne Aleman and Elizabeth Jewkes for taking the time to act as appraisers.

    Wen-Yang Ku for his help with the MIP modeling.

    The Centre for Innovation in Complex Care for allowing me to work and do this at the same

    time.

    My family for an incredible amount of help and support.

    Moishie Goldberg for support and a large amount of assistance with the programming involved

    in this work.

  • v

    Table of Contents

    Contents

    Acknowledgments .......................................................................................................................... iv

    Table of Contents ............................................................................................................................ v

    List of Tables ................................................................................................................................. ix

    List of Figures ................................................................................................................................ xi

    List of Algorithms ......................................................................................................................... xii

    List of Appendices ....................................................................................................................... xiii

    Chapter 1 ......................................................................................................................................... 1

    Introduction ................................................................................................................................ 1

    1.1 Background ......................................................................................................................... 1

    1.2 Objectives ........................................................................................................................... 3

    1.3 Plan of Dissertation ............................................................................................................. 3

    1.4 Summary of Contributions .................................................................................................. 5

    Chapter 2 ......................................................................................................................................... 7

    Literature Review ....................................................................................................................... 7

    2.1 Classic Deterministic Scheduling Models .......................................................................... 7

    2.1.1 Deterministic Flow Shop Problems ........................................................................ 8

    2.1.2 Deterministic Resource Constrained Project Scheduling Problems ..................... 10

    2.2 Constraint Programming ................................................................................................... 12

    2.2.1 Search .................................................................................................................... 13

    2.2.2 Propagation ........................................................................................................... 13

    2.2.3 Global Constraints ................................................................................................ 13

    2.2.4 Constraint-Based Scheduling ................................................................................ 14

  • vi

    2.3 Scheduling With Uncertainty ............................................................................................ 14

    2.4 Scheduling Applications in Health Care ........................................................................... 17

    2.4.1 Radiation Therapy ................................................................................................. 18

    2.4.2 Operating Room Scheduling ................................................................................. 20

    2.4.3 Outpatient Appointment Scheduling ..................................................................... 22

    2.5 Chemotherapy Research ................................................................................................... 24

    2.6 Methodologies for Modeling Real World Problems ......................................................... 25

    2.7 Summary ........................................................................................................................... 27

    Chapter 3 ....................................................................................................................................... 29

    Chemotherapy Outpatient Scheduling Application ................................................................. 29

    3.1 The Chemotherapy Treatment Process ............................................................................. 29

    3.2 Problem Data .................................................................................................................... 31

    Chapter 4 ....................................................................................................................................... 34

    Developing and Choosing an Optimization Model .................................................................. 34

    4.1 Method of Evaluating Problem Definitions ...................................................................... 35

    4.2 Base Model Formulation ................................................................................................... 37

    4.3 Modifications and Corresponding Problem Definitions ................................................... 41

    4.4 MIP Model ........................................................................................................................ 42

    4.5 Simulation Model .............................................................................................................. 44

    4.6 Model Validation .............................................................................................................. 45

    4.7 Experimental Design ......................................................................................................... 45

    4.8 Experimental Results and Discussion ............................................................................... 47

    4.8.1 Solvability and Quality Experiments .................................................................... 47

    4.8.2 Comparison with MIP .................................