小結 - 計算結果與分析討論 - I-Shou University Institutional Repository:Item 987654321/18558

第四章計算結果與分析討論

第四節小結

透過Lingo 程式軟體得到結果，分別計算型一問題、型二問題及效率型問題之效率，

測試四組題目共 81 個題目，其中型二問題及效率型問題與啟發式求解之效率無差別，

均為最佳效率，而型一問題之效率也是最佳解效率。

求解可能性，分別求解型一問題、型二問題及效率型問題，給定週期時間、工作站數，

將得到結果利用效率之公式，求解其效率。

本研究之研究結果分為以下幾點:

1. 彙整雙邊生產線平衡問題之型一問題、型二問題及效率型問題之數學模式，並將模式重新整理後，增加其求解功能。

2. 利用測試題目進行求解型一問題及型二問題。並得到型一及型二問題之最佳解。

3. 利用數學模式，給定週期可允許週期時間之下，工作站從 m=1,2,…,mmax，求解效率型問題，得到其最小工作站數及最佳解之效率值，來提供未來相關研究之參考依據。

第二節未來研究與建議

本研究主要利用數學規劃模式求解雙邊生產線平衡問題之型一、型二問題及效率型問題，透過Lingo 來求解數學模式，將得到結果透過效率之公式，得到其效率。

由於針對大型任務求解時，較為緩慢才可以得到其結果，所以在未來有進行相關研究之人員，可以透過數學規劃模式結合啟發式演算法，來進行求解，以提高電腦求解之效率。

本研究針對未來建議有兩項:

1. 可與啟發式演算法做結合，提高電腦求解效率，來解決大型任務問題。

2. 探討雙邊生產線平衡問題之同步任務問題，並求解其效率。

參考文獻中文部分:

吳爾飛、金燁、汪崢(2005)，雙邊裝配線第二類型平衡問題研究，計算機及成製造系統，

11(11)，pp.1604-1608。

李雅婷(2010)，E 型簡單生產線平衡問題模式與求解方法之研究，義守大學工業工程與管理學系研究所碩士論文。

林金雄、盧仁傑、姚威宏(2000)編譯，製造程序規劃(初版)，新北市新莊區:全威圖書。

查艦、徐學軍、余建軍、宋莉波(2010)，利用 Petri 網求解 U 型裝配線平衡問題，工業工程，13(2)，pp.110-115。

柴康偉、張蓓蒂、蔡爭岳(2003)，生產線最佳化配置之研究－以個案公司為例，遠東學報，20(3)，pp.443-450。

葉丁鴻和顏伯蒼(2012)，利用數學規劃模式找出在有雙邊同時作業任務時的雙邊生產線平衡問題最佳解，創新研發學刊，8(2)，pp.110-120。

鄭巧仙、李明、李元香、唐秋華(2014)，求解雙邊裝配線平衡問題的改進蟻群算法，電子學報，42(5)，pp.841-845。

藍俊雄、陳輝恭、李舒怡(2010)，有限空間下之自動化雙邊生產線平衡，資訊、科技與社會學報，17，pp.1-11。

英文部分:

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Gökçen, H. & Agpak, K. (2006), A goal programming approach to simple U-line balancing problem, European Journal of Operational Research, 171, pp.577-585.

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Warshall, S.(1962), A theorem on boolean matrices, Journal of ACM, 9(1), pp.11-12.

@sum(di1(K)|D(h) #eq# 1:G*X(H,G,K))))+(@sum(station(g):

@sum(di2(K)|D(h) #eq# 2:G*X(H,G,K))))+(@sum(station(g):

@sum(direction(K)|D(h) #eq# 3:G*X(H,G,K))))<=(@sum(station(j):@sum(di1(K)|D(I) #EQ# 1 :j*X(I,J,K))))+

(@sum(station(j):@sum(di2(K)|D(I) #EQ# 2 :j*X(I,J,K)))+(@sum(station(j):@sum(direction(K)|D(I) #EQ# 3 :j*X(I,J,K)))))));

!任務的優先順序;

@for(task(I):TiF(I)<=cyctime);

!任務結束時間小於等於週期時間;

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 1 #and# D(I) #eq# 1: TiF(I)-TiF(H)+9999*(1-@sum(di1(K):X(H,J,K)))+9999*(1-@sum(di1(k):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 1 #and# D(I) #eq# 2: TiF(I)-TiF(H)+9999*(1-@sum(di1(K):X(H,J,K)))+9999*(1-@sum(di2(k):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 1 #and# D(I) #eq# 3: TiF(I)-TiF(H)+9999*(1-@sum(di1(K):X(H,J,K)))+9999*(1-@sum(direction(K):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 2 #and# D(I) #eq# 1: TiF(I)-TiF(H)+9999*(1-@sum(di2(K):X(H,J,K)))+9999*(1-@sum(di1(k):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 2 #and# D(I) #eq# 2: TiF(I)-TiF(H)+9999*(1-@sum(di2(K):X(H,J,K)))+9999*(1-@sum(di2(k):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 2 #and# D(I) #eq# 3: TiF(I)-TiF(H)+9999*(1-@sum(di2(K):X(H,J,K)))+9999*(1-@sum(direction(K):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 3 #and# D(I) #eq# 1: TiF(I)-TiF(H)+9999*(1-@sum(direction(K):X(H,J,K)))+9999*(1-@sum(di1(k):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 3 #and# D(I) #eq# 2: TiF(I)-TiF(H)+9999*(1-@sum(direction(K):X(H,J,K)))+9999*(1-@sum(di2(k):X(i,J,K)))>=T(I))));

@for(task(I):@for(task(H)|y1(H,I) #EQ# 1:@for(station(J)|D(H)#EQ# 3 #and# D(I) #eq# 3: TiF(I)-TiF(H)+9999*(1-@sum(direction(K):X(H,J,K)))+9999*(1-@sum(direction(K):X(i,J,K)))>=T(I))));

!限制式;

@for(task(I):@for(task(J)|y(I,J) #EQ# 1 :@for(di1(A)|kip(i,j) #eq# 1:@for(station(k):TiF(J)-TiF(I)+(9999*(1-X(J,K,A)))+(9999*(1-X(I,K,A)))+(9999*(1-Z(i,j)))>=T(J)))));

@for(task(I):@for(task(J)|y(I,J) #EQ# 1 :@for(di2(A)|kip(i,j) #eq# 2:@for(station(k):TiF(J)-TiF(I)+(9999*(1-X(J,K,A)))+(9999*(1-X(I,K,A)))+(9999*(1-Z(i,j)))>=T(J)))));

@for(task(I):@for(task(J)|y(I,J) #EQ# 1 :@for(direction(A)|kip(i,j) #eq# 3:@for(station(k):TiF(J)-TiF(I)+(9999*(1-X(J,K,A)))+(9999*(1-X(I,K,A)))+(9999*(1-Z(i,j)))>=T(J)))));

!限制式;

@for(task(I):@for(task(J)|y(I,J) #EQ# 1 :@for(di1(A)|kip(i,j) #eq# 1:@for(station(k):TiF(I)-TiF(J)+(9999*(1-X(J,K,A)))+(9999*(1-X(I,K,A)))+(9999*Z(i,j))>=T(I)))));

@for(task(I):@for(task(J)|y(I,J) #EQ# 1 :@for(di2(A)|kip(i,j) #eq# 2:@for(station(k):TiF(I)-TiF(J)+(9999*(1-X(J,K,A)))+(9999*(1-X(I,K,A)))+(9999*Z(i,j))>=T(I)))));

@for(task(I):@for(task(J)|y(I,J) #EQ# 1 :@for(direction(A)|kip(i,j) #eq# 3:@for(station(k):TiF(I)-TiF(J)+(9999*(1-X(J,K,A)))+(9999*(1-X(I,K,A)))+(9999*Z(i,j))>=T(I)))));

!限制式;

@for(station(j):@sum(left(I):@sum(di1(K)|D(I) #EQ# 1:(X(I,J,K)-9999*Yj(j))))<=0);

@for(station(j):@sum(right(I):@sum(di2(K)|D(I) #EQ# 2:(X(I,J,K)-9999*Yj(j))))<=0);

@for(station(j):@sum(either(I):@sum(direction(K)|D(I) #EQ# 3:(X(I,J,K)-9999*Yj(j))))<=0);

@for(task(I):TiF(I)>=T(I));

2.型二問題