護士排班問題(Nurse Scheduling Problem, NSP)在過去的三十年被大量研究，NSP問題為一個典型的NP-hard問題。班表之優劣是一個會直接影響醫院營運的重要因素，隨著社會的進步與演變，台灣對於勞工的權益越來越重視，因此，在排定班表時更需注意每一位護士的休息時間與權益，才能保障每一位護士之勞工基本權益。與過往研究不同，本研究加入兩種突發情境之模型，在高度約束限制下，解決突發狀況是相當困難的，因此，本研究的問題比傳統的護士排班的問題更加的複雜且艱澀。
以往的手動排班需要耗費大量的時間與人力，許多學者進而透過各式各樣的方法來加快求解此問題，且都有良好的成效，而啟發式演算法與數學規劃法也被大量應用於此問題。其中，數學規劃法在面臨維度過高的NSP問題時，可能導致計算時間過長或無法求得最佳解，而啟發式演算法往往都能在有限的時間內求得近似最佳解的解。常見的啟發式演算法用於求解排班最佳化問題(Rostering Problem)有基因演算法(Genetic Algorithm, GA)、粒子群最佳化演算法(Particle Swarm Optimization, PSO)及模擬退火法(Simulated Annealing, SA)等等，近年來，簡化群體演算法(Simplified Swarm Optimization, SSO)在處理此種離散型的問題都有很亮眼的表現。
在本研究論文中，將採用簡化群體演算法(Simplified Swarm Optimization, SSO)結合遺傳技巧來解決的護士排班問題，並透過與其他著名的啟發式演算法進行比較，來證明SSO在處理離散型且高度約束問題的能力，並調整SSO之原始更新機制，加入遺傳技巧來加強SSO之尋優能力。此外，本研究提出了兩種突發情境，用以測試SSO在遇到突發事件時的解決能力，也能使排班者在發生突發事件時能快速做出決策。

Nurse Scheduling Problem (NSP) has been extensively discussed for the past three decades. The NSP is a typical NP-hard Problem. The quality of the schedule is an important factor that will directly affect the operation of the hospital. With the progress and evolution of the society, Taiwan pays more and more attention to the rights of the workers. Therefore, it is necessary to take care of every nurse when scheduling the class. Rest time and individual rights can protect the basic rights and interests of every nurse.
This study proposed two kinds of sudden incidents. It is quite difficult to solve the sudden incidents under the highly constrained. Therefore, this study is more complicated and difficult than the NSP before.
In the past, manual scheduling required a lot of time and manpower. Many scholars have adopted various methods to solve NSP. Heuristic Algorithms and Mathematical Programming have also been widely applied. Among them, when the mathematical Programming faces the NSP with too high dimension, it may lead to the calculation time being too long or the best solution cannot be obtained, and the Heuristic Algorithm can always find the approximate optimal solution in a limited time.
Common Heuristic Algorithms for solving rostering problem are Genetic Algorithm, Particle Swarm Optimization and Simulated Annealing. Simplified Swarm Optimization (SSO) has a very excellent performance in dealing with such discrete problems in recent years. In this research, the SSO and Genetic Techniques will be used to solve the NSP, and compared with other Heuristic Algorithms to prove the ability of SSO to deal with discrete and highly constrained problems. In addition, this study proposes two types of incidents to test the SSO's ability to resolve sudden incidents.

摘要 1
Abstract 2
目錄 3
表目錄 6
圖目錄 8
第 1 章 、緒論 9
1.1 研究背景 9
1.2 研究動機與目的 11
1.3 研究架構 12
第 2 章 、文獻回顧 14
2.1 排班問題 14
2.2 護士排班問題 15
2.3 啟發式演算法 (Heuristic Algorithm) 17
2.3.1 簡化群體演算法 (Simplified Swarm Optimization, SSO) 18
2.3.2 基因演算法 (Genetic Algorithm, GA) 19
2.3.3 粒子群演算法 (Particle Swarm Optimization, PSO) 19
2.3.4 模擬退火 (Simulated Annealing, SA) 20
2.4 文獻小節 20
第 3 章 、問題描述 21
3.1 問題假設 21
3.2 數學符號 22
3.2.1 索引、集合與參數 22
3.2.2 決策變數 23
3.3 數學模型 24
3.3.1 目標式 24
3.3.2 限制式 24
3.3.3 NSP問題懲罰函數計算之實例 28
第 4 章 、研究方法 29
4.1 編碼 29
4.2 初始解生成方式 30
4.3 簡化粒子群演算法 (Simplified Swarm Optimization) 33
4.3.1 演算法符號 33
4.3.2 演算法步驟與公式 34
4.4 演算法更新機制-遺傳技巧 (Genetic Technique) 38
4.5 突發狀況之模型 41
4.5.1 突發事件一 41
4.5.2 突發事件二 45
第 5 章 、實驗結果與分析 48
5.1 資料集 48
5.2 參數實驗設計 50
5.3 實驗結果 55
5.3.1 其他演算法之測試參數設定 55
5.3.2 小型資料集實驗結果 (MD 1) 56
5.3.3 中型資料集實驗結果 (NICU) 58
5.3.4 大型資料集實驗結果 (GICU) 59
5.3.5 相同運算時間下個演算法之實驗結果 61
5.4 資料實驗結果分析及驗證 62
5.5 實驗結果-突發狀況 64
第 6 章 、結論與未來研究方向 67
6.1 結論 67
6.2 未來研究方向 68
參考文獻 70
附錄 77

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