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研究生： 王媛瑩
Wang, Yuan-Ying
論文名稱： 超額預約解決病患不準時與未出現之預約排程問題
Appointment Scheduling with Overbooking Considering Patient Unpunctuality and No-Shows
指導教授： 陳建良
Chen, Jian-Liang
口試委員: 陳子立
Chen, Tzu-Li
張秉宸
Chang, Ping-Chen
學位類別： 碩士
Master
系所名稱： 工學院 - 工業工程與工程管理學系
Department of Industrial Engineering and Engineering Management
論文出版年： 2024
畢業學年度： 112
語文別： 英文
論文頁數： 76
中文關鍵詞： 預約排程 、遲到 、未出現 、超額預約 、近似動態規劃
外文關鍵詞： Appointment Scheduling, Unpunctuality, No-Show, Overbooking, Approximate Dynamic Programming
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    • 病患遲到和未出現是不可避免的情況，明顯干擾了醫療機構的運作。預約過程中的不確定性不僅增加了病患的等待時間，還降低了資源利用率，如設備和人力資源。許多先前的研究假設若病患會出現，則會準時抵達，然而，對於大多數醫療系統來說，病患的遲到情況會發生，因此應該在預約排程中加以考慮。透過超額預訂，醫療系統可以減少病患遲到和未出現所帶來的負面影響。
    本研究將病人遲到和未出現的行為納入考慮，建立了醫療系統中多服務者的預約排程隨機優化問題。我們提出馬可夫決策過程（Markov Decision Process, MDP）來優化排程決策，以決定每個時段的預約病患人數。目標是最大化系統每天獲得的總利潤。鑑於狀態空間的龐大規模，提出了基於模擬的近似動態規劃（Approximate Dynamic Programming, ADP）來解決排程問題。此演算法結合決策後狀態變量以及聚合技術，顯著地減少計算時間並獲得了近乎最優的解決方案。
    為了評估所提出演算法的性能和有效性，我們將其應用於三個場景。結果顯示在大多數情況下，ADP 算法能夠提供接近最優的解決方案，同時顯著減少計算時間。最後，在管理層面，透過敏感性分析，本研究為醫療系統的預約排程提供相關建議。

    Patient unpunctuality and no-shows are inevitable, significantly disrupting healthcare operations. The uncertainties in the appointment process not only increase patients waiting time but also lower resource utilization, such as equipment and human resources. Many previous studies assumed patients were punctual if they showed up. However, for most healthcare systems, patients sometimes arrive later than the appointment time, which should be considered in the appointment scheduling. With overbooking, the healthcare system can mitigate the negative impact of patient unpunctuality and no-shows.
    This study formulates the stochastic optimization problem for appointment scheduling in a multiple-server healthcare system, incorporating patient behavior such as unpunctuality and no-shows. A Markov Decision Process (MDP) is proposed to optimize scheduling decisions that determine appointment patient numbers in each slot. The objective is to maximize the total profit the system receives each day. Given the large state space, a simulation-based Approximate Dynamic Programming (ADP) is proposed to solve the scheduling problem. Combining the techniques of post-decision state variables and aggregation, the algorithm significantly reduces the computation time and obtains near-optimal solutions.
    To evaluate the performance and effectiveness of the proposed ADP algorithm, it is applied to three scenarios. The resulting scheduling outcomes demonstrate that in most cases, the ADP algorithm delivers near-optimal solutions while significantly reducing computation time. Finally, for the managerial aspects, sensitivity analyses are conducted to offer practical guidance for optimizing patient scheduling processes in healthcare system.

    摘要 Abstract 致謝 Contents List of Tables List of Figures Chapter 1 Introduction ............... 1 1.1 Background and Motivation ............... 1 1.2 Research Objective ............... 5 1.3 Organization of Thesis ............... 5 Chapter 2 Literature Review ............... 6 2.1 Uncertainties in Healthcare System ............... 6 2.2 Overbooking ............... 7 2.3 Dynamic Appointment Scheduling ............... 8 Chapter 3 Problem Definition ............... 15 3.1 Problem Description ............... 15 3.2 Notation and System Description ............... 15 3.3 Assumptions ............... 17 3.4 Markov Decision Process ............... 18 3.4.1 Decision Epochs ............... 18 3.4.2 State Space ............... 18 3.4.3 Action ............... 21 3.4.4 Transition Probabilities ............... 21 3.4.5 Rewards ............... 23 3.4.6 Optimality Equations ............... 23 Chapter 4 Methodology ............... 25 4.1 Backward Induction ............... 25 4.2 Approximate Dynamic Programming ............... 26 4.2.1 Simulation-Based Algorithm ............... 26 4.2.2 Post-Decision State Variable ............... 27 4.2.3 Monte Carlo Simulation ............... 28 4.2.4 Aggregation Techniques ............... 29 4.2.5 Smoothing Strategies ............... 31 4.2.6 ADP Algorithm ............... 32 Chapter 5 Experiment Results ............... 35 5.1 Experiment Setup ............... 35 5.2 Algorithm Tuning ............... 36 5.2.1 Design of Experiments ............... 36 5.2.2 Analysis Results ............... 37 5.3 Optimality Comparison ............... 44 5.4 Benchmark Policies Comparison ............... 46 5.5 Managerial Aspects ............... 52 5.5.1 Overbooking with Show-Up Rate ............... 52 5.5.2 Scheduling Details Analysis ............... 55 5.5.3 Impact of System’s Capacity ............... 56 5.5.4 Impact of Unpunctuality Allowance ............... 58 5.5.5 Impact of Financial Factors ............... 60 Chapter 6 Conclusion ............... 63 Reference ............... 66 Appendix ............... 69 Appendix A Tukey Pairwise Comparison Results ............... 69 A1. Small Case ............... 69 A2. Medium Case ............... 71 A3. Large Case ............... 73 Appendix B Scheduling Results Comparison ............... 75 B1. Small Case ............... 75 B2. Medium Case ............... 76

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