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# 中 華 大 學

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## 中 華 大 學 碩 士 論 文

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### ABSTRACT

In the current study, there are many people committed to researching ways to come up with the best roster when scheduling working hours. No one noticed that no matter how perfect a roster appeared, there would always be someone that had different opinions.

It often results in complaints from those who have different point of views. Sometimes nurses would have something that comes up at the last minute so they would have to switch shifts with other nurses. Therefore, the purpose of this research is to come up with a program to help nurses quickly search out ways to switch shifts with other nurses.

Presently, there has yet been seen a published study concerning the changing of shifts. The changing of shifts between nurses still requires direct contact and co-ordination between people. So this paper is dedicated to finding out a way for those who want to change shifts on a certain date to pull up the schedules of those who have shifts on the same date and convert the information into graphics. The graphics then uses backtracking to find all the loops in the different shifts and filters out the shifts that can be changed.

Keywords: shift, backtracking, graphics, loop.

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### 目 錄

1-1護理人員換班問題概述...1

1-2護理人員換班問題之目的與架構...4

2-1基因演算法………...5

2-2禁忌搜尋法………...6

2-3變動鄰域搜尋法………...7

2-4整數規劃法……….………..7

2-5爬山法………..………...8

3-1回溯法的原理. ………..………..10

3-2回溯法的應用...11

4-1圖形演算法基本概念 ...16

4-2護理人員換班表之圖形轉換 ...19

4-3迴圈的意義 ...22

4-4找尋換班的圖形中所有迴圈的方法 ...23

5-1程式執行過程...25

5-2程式執行的結果...27

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### 1-1 護理人員換班問題概述

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(一) level 1 護理人員是屬於最基層的護士。

(二) level 2 護理人員是具有重症病人整體性的護理能力。

(三) level 3 護理人員是為培養副護理長所設立的層級，訓練重點是認識護理人 員法規，認識每位護理人員的專業能力。

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### 2-1 基因演算法

「基因演算法」一名詞，首度用在1967年Holland的學生，Bagley發表的畢業 論文中，1975年Holland正式發表[15]。

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### 2-4 整數規劃法

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[27]，將護理人員輪並採用「排休」與「派班」二階段限制規劃模式依序求解。

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### 3-2 回溯法的應用

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step 1. 將第一個皇后放入第 0 列的第 0 格(如圖 3-3 的 a 圖)，在陣列的第 0 格填上 0。

step 2. 將第二個皇后放入第 1 列的第 0 格，發現與第一個皇后在同一行，

step 3. 將第三個皇后放入第 2 列的第 0 格，發現第 2 列第 0~3 格通通不能 放(如圖 3-3 的 c 圖)。

step 4. 退回第 1 列，將第 2 個皇后從第 2 格移到第 3 格，跟第一個皇后互 不衝突，在陣列的第 1 格填上 3。

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step 5. 將第 3 個皇后放入第 2 列的第 0 格，發現第 2 列第 0 格不能放，放 入第 1 格後跟前面兩個皇后互不衝突(如圖 3-3 的 d 圖)，並在陣列的第 2 格填上 1。

step 6. 將第四個皇后放入第 3 列，發現第 3 列第 0~3 格通通不能放(如圖 3-3 的 e 圖)。

step 7. 退回第 2 列，第三個皇后放入第 2 格和第 3 格會跟第 2 個皇后互相 衝突，所以再退回第 1 列。第二個皇后已經是最後一格，所以退回第 0 列。

step 8. 將第一個皇后放入第 0 列的第 1 格(如圖 3-3 的 f 圖)，在陣列的第 0 格填上 1。

step 9. 將第二個皇后放入第 1 列的第 0~2 格，發現與第一個皇后會互相衝 突。放入第 3 格後與第一個皇后不會互相衝突(如圖 3-3 的 g 圖)，在陣 列的第 1 格填上 3。

step 10. 將第三個皇后放入第 2 列的第 0 格與第一個和第二個皇后不會互相 衝突，在陣列的第 2 格填上 0。

step 11. 將第四個皇后放入第 3 列的第 0 格與第三個皇后互相衝突，第 1 格 與第一個和第二個皇后互相衝突，第 2 格與前三個皇后都不會互相衝突 (如圖 3-3 的 h 圖)，在陣列的第 3 格填上 2。

step 12. 找到第一組正確解，陣列表示為(1,3,0,2)。

step 13. 以此類推，可以找到第二組正確解為(2,0,3,1)。

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int Place(k,i) {

for(j = 0; j <= k-1; j++)

if(x[j] == i || Abs(x[j]-i) == Abs(j-k)) return(0);

return (0);

}

int NQueens(k,n) {

for( i = 1; i <= n-1; i++) {

if( Place(k,i) {

x[k] = i;

if( k = n-1) write(x[i : n]);

else NQueens(k + 1,n);

} } }

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1. 每位護理人員的編號。

2. 護理人員當天的排班別。

3. 可以換班的排班別。

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### 4-4 找尋換班的圖形中經過某節點所有迴圈的方法

int place(int k, int i) //k 為目前迴圈長度 {

if (k 大於使用者設定的長度) return(0);

if (k 為 0 時 i 不是起點) return(0);

if (k 為 0 時 i 是起點) return(1);

if (邊 k-1 到 k 時) return(0);

for (j=1; j<k; j++) if (x[j]==i) return(0);

return(1);

}

{

for (i=0; i<n; i++) {

if (判斷式 Place 回傳 true) {

if (形成迴圈) {

if (每個班 level 3 有人上班) {

} } }

else (find_cycle(k+1));

} }

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### 參考文獻

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[2] C. Valouxis and E. Housos, “Hybrid Optimization Techniques for The Workshift and Rest Assignment of Nursing Personnel”, Artificial Intelligence in Medicine, Vol. 20 (2000) pp. 155-175.

[3] U. Aickelin and K. Dowsland, “Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem”, Journal of Scheduling 3 (3) (2000) pp. 139–153.

[4] 郭金青，《整數目標規劃應用於護士排班之個案研究》，國立中正大學企業管 理研究所碩士論文，兩階段限制規劃模式求解護理人員輪值問題，民國85 年。

[5] 郭娓吟，《整數目標規劃應用於護理人力-以中部某醫院附設護理之家為例》， 中國醫藥學院醫務管理研究所碩士論文，民國91年。

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[8] H. E. Miller, P. William and J. R. Gustave, “Nurse Scheduling Using Mathematical Programming,”Operations Research 24 (5) (1976) pp. 857-870.

[9] H. Millar and M. Kiragu, “Cyclic and Non-Cyclic Scheduling of 12h Shift Nurses by Network Programming,” European Journal of Operational Research 104 (1998) pp. 582-592.

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1139–1146.

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“Metaheuristics for Handling Time Interval Coverage Constraints in Nurse Scheduling”, Applied Artificial Intelligence 20 (3) (2006) pp.743-766.

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1139–1146.

[15] J.H. Holland, “Adaptation in natural and artificial systems”. Ann Arbor, MI:

University of Michigan Press, (1975).

[16] F. Glover, “Tabu Search: A Tutorial”, Interfaces, Vol. 20 (1990) pp. 74-94.

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[18] E.K. Burke, P. Cowling, P. De Causmaecker and G. Vanden Berghe, “A Memetic Approach to the Nurse Rostering Problem”, Applied Intelligence 15 (3) (2001) pp. 199–214.

[19] U. Aickelin and J. Li, “The application of Bayesian optimization and classifier systems in nurse scheduling”, in: Proceedings of the 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII) Springer Lecture Notes in Computer Science 3242 Springer, Birmingham, UK (2004) pp. 581–590.

[20] K.A. Dowsland, “Nurse Scheduling with Tabu Search and Strategic Oscillation”, European Journal of Operational Research 106 (2) (1998) pp. 393–407.

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de Sousa (Eds.), Metaheuristics: Computer Decision-Making, Kluwer, 2004, pp.

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[23] P. Hansen and N. Mladenovic’, “An introduction to variable neighborhood search”, in: S. Voss et al. (Eds.), Meta-heuristics: Advances and trends in local searchs paradigms for optimization, Kluwer Academic Publishers (1999) pp.

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[25] N. Mladenovic’ and P. Hansen, “Variable neighborhood search", Computers and Operations Research 24 (11) (1997) pp. 1097–1100.

[26] 李俊德，《兩階段限制規劃模式求解護理人員輪值問題》，國立交通大學運輸 科技與管理學系所碩士論文，民國 96 年。

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[27] 韓復華、李俊德，〈兩階段限制規劃模式求解護理人員輪值問題〉，《管理與 系統》，第 14 卷，第 1 期，民國 96 年。

[28] U. Aickelin and J. Li, “A Bayesian optimization algorithm for the nurse scheduling problem”, in: Proceedings of 2003 Congress on Evolutionary Computation (CEC2003), IEEE Press, Canberra, Australia (2003) pp.

2149–2156.

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[31] B. Cheang, H. Li and A. Lim, “Nurse Rostering Problems – a Bibliographic Survey”, European Journal of Operational Research 151 (2003) pp. 447-460.

[32] C. Valouxis and E. Housos, “Hybrid Optimization Techniques for The Workshift and Rest Assignment of Nursing Personnel,” Artificial Intelligence in Medicine, Vol. 20 (2000) pp. 155-175.

[33] 林純玉，《護理人員排班程式設計與實作》，中華大學生物資訊學系碩士班碩 士論文，民國 98 年。

[34] 黃翔瑞，《改良爬山演算法於護理排班程式設計》，中華大學生物資訊學系 碩士論文，民國 100 年。

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