建議 - 結論與建議 - Delivery Problem with Time Windows

第五章結論與建議

5.2 建議

一、問題規模簡化策略、關連式旅行網絡結構表、AACS 演算法、與 GAACS 演算法為本研究所提出，其延伸應用範圍相當廣泛，研究中無法一一完成，建議後續研究可朝下列三個方向進行。

(一) 本研究為克服時窗分割策略缺失所設計的問題規模簡化策略，除了可以將PDPTW 問題轉換為無時窗限制的 SPDP 問題，亦可應用於其他有時間窗限制的路徑規劃問題。

(二) 研究中為了提升演算法績效所設計的關連式旅行網絡結構表，除了可應用於ACO 演算法中，也可以應用於其他啟發式演算法中。

(三) 本研究所設計的 AACS 啟發式演算法，求解 TSP 問題的績效確實優於 ACS 演算法，而以 AACS 為基礎，配合 GLS 所設計的

GAACS 啟發式演算法，求解 PDPTW 問題時，亦可在 25.95 分鐘的平均時間下，求出與標桿解間平均差異僅 1.47%的近似最佳解。

但是 AACS 與 GAACS 兩啟發式演算法求解其他路徑規劃問題的適用性與求解績效尚屬未知。

二、ACO 是近年新興的演算法，已陸續成功地應用於求解多種複雜組合最佳化問題，本研究亦應用 ACO 中的 ACS 為基礎設計 GAACS 求解 SPDP 問題，然而 ACO 本身屬於需要較長求解時間的演算法，PDPTW 問題的複雜度亦較高，相對所需的求解時間也較長，即使轉換為 SPDP 問題後每隻螞蟻求得可行解的時間已大幅降低，但由於 ACO 需要足夠的求解回合與螞蟻數量，因此求解時間卻又相對增加，建議後續學者應用ACO 演算法求解 SPDP 問題時可配合平行處理技術，降低求解時間。

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附錄一求解 SPDP 例題的 LINGO 程式碼

model:

Sets:

Jobs/@FILE('LGP02q.txt')/:ID,Carry,Loaded;

SubJobs/@FILE('LGP02q.txt')/:JobID,LT;

Car/ c1,c2,c3,c4 /;

ZZ(Car,SubJobs):Zki;

T(SubJobs,SubJobs):tij;

TT(T)|tij(&1,&2) #ne# -10: Cij;

RR(Car,TT):Xkij;

endsets Data:

ID=@FILE('LGP02q.txt');

Carry=@FILE('LGP02q.txt');

JobID=@FILE('LGP02q.txt');

LT=@FILE('LGP02q.txt');

tij=@FILE('LGP02q.txt');

Cij=@FILE('LGP02q.txt');

Enddata

!隨問題資料修改數據值：

n=(@size(Jobs)-1)/2; !訂單數量;

Q=10; !車容量限制;

cost=1000; !使用車輛的固定成本;

!目標式 ;

min=@sum(Car(K):@sum(TT(I,J):Cij(I,J)*Xkij(K,I,J)))

@sum(Car(K):

@sum(TT(I,J)| JobID(I) # eq# 0 # and# JobID(J) #le# n: cost*Xkij(K,I,J)));

!(作業點)限制式;

!(1)每個訂單的收送貨需同一車;

@for(Car(K): @for(Jobs(I)|ID(I) #gt# 0 #and# ID(I) #le# n:

@sum(SubJobs(J)|JobID #eq# ID(I):Zki(K,J))=@sum(SubJobs(L)|JobID

#eq# ID(I)+n:Zki(K,L)); ));

!(2)每一個Job必定會被1車服務僅1次;

@for(Jobs(J)| ID #ne# 0: @sum(Car(K):@sum(SubJobs(I)|JobID #eq# ID(J):

Zki(K,I)))=1; );

!(3)Depote的輛車數;

@sum(Car(K): @sum(SubJobs(I)|JobID #eq# 0: Zki(K,I)))=@size(Car);

!(4)服務順序;

@for(Jobs(I)|ID(I) #gt# 0 #and# ID(I) #le# n: @sum(SubJobs(J)|JobID #eq#

ID(I):@sum(Car(K):Zki(K,J)*LT(J)))<@sum(SubJobs(L)|JobID #eq#

ID(I)+n:@sum(Car(K):Zki(K,L)*LT(L))); );

!(行駛路徑)限制式;

!(5)每一個作業(a)必僅有一輛車駛離(行駛到其他作業或回場站(a為送貨點時));

!a為收貨作業時;

@for(Jobs(a)|ID(a) #gt# 0 #and# ID(a) #le# n: @sum(Jobs(c)|ID(c) #ne# 0

#and# ID(c) #ne# ID(a): @sum(Car(K): @sum(RR(K,I,J)|JobID(I)

#eq# ID(a) #and# JobID(J) #eq# ID(c): Xkij)))=1;);

!a為送貨作業時;

@for(Jobs(a)|ID(a) #gt# n: @sum(Jobs(c)|ID(c) #ne# ID(a)-n #and# ID(c)

#ne# ID(a): @sum(Car(K): @sum(RR(K,I,J)|JobID(I) #eq# ID(a)

#and# JobID(J) #eq# ID(c): Xkij)))=1;);

!(5')每一個作業(c)必僅有一輛車到達;

!c為收貨作業時;

@for(Jobs(c)|ID(c) #gt# 0 #and# ID(c) #le# n: @sum(Jobs(a)|ID(a) #ne#

ID(c)+n #and# ID(a) #ne# ID(c): @sum(Car(K):

@sum(RR(K,I,J)|JobID(I) #eq# ID(a) #and# JobID(J) #eq# ID(c):

Xkij)))=1;);

!c為送貨作業時;

@for(Jobs(c)|ID(c) #gt# n: @sum(Jobs(a)|ID(a) #ne# 0 #and# ID(a) #ne#

ID(c): @sum(Car(K): @sum(RR(K,I,J)|JobID(I) #eq# ID(a) #and#

JobID(J) #eq# ID(c): Xkij)))=1;);

!(5'')駛離Depote的車輛數;

@sum(Car(K): @sum(Jobs(c)|ID(c) #gt# 0 #and# ID(c) #le# n:

@sum(RR(K,I,J)|JobID(I) #eq# 0 #and# JobID(J) #eq# ID(c):

Xkij)))<=@size(Car);

!(5''')到達Depote的車輛數;

@sum(Car(K): @sum(Jobs(c)|ID(c) #gt# n: @sum(RR(K,I,J)|JobID(I) #eq# ID(c)

#and# JobID(J) #eq# 0: Xkij)))<=@size(Car);

!(6)(作業點與路徑間的關係)流量守恆限制式(針對每一項子作業與 Depote);

!(6')(屬於收貨作業點的)每一項子作業;

@for(Car(K): @for(SubJobs(c)|JobID(c) #ne# 0 #and# JobID(c) #le# n:

@sum(RR(K,a,c)|JobID(a) #ne# JobID(c) #and# JobID(a) #ne#

JobID(c)+n:Xkij(K,a,c))=@sum(RR(K,c,e)|JobID(e) #gt# 0 #and# JobID(e)

#ne# JobID(c):Xkij(K,c,e)); ));

@for(Car(K): @for(SubJobs(c)|JobID(c) #ne# 0 #and# JobID(c) #le# n:

@sum(RR(K,a,c)|JobID(a) #ne# JobID(c) #and# JobID(a) #ne#

JobID(c)+n:Xkij(K,a,c))=Zki(K,c); ));

!(6'')(屬於送貨作業點的)每一項子作業;

@for(Car(K): @for(SubJobs(c)|JobID(c) #gt# n: @sum(RR(K,a,c)|JobID(a) #ne#

JobID(c) #and# JobID(a) #ne# 0:Xkij(K,a,c))=@sum(RR(K,c,e)|JobID(e)

#ne# JobID(c)-n #and# JobID(e) #ne# JobID(c):Xkij(K,c,e)); ));

@for(Car(K): @for(SubJobs(c)|JobID(c) #gt# n: @sum(RR(K,a,c)|JobID(a) #ne#

JobID(c) #and# JobID(a) #ne# 0:Xkij(K,a,c))=Zki(K,c); ));

!(6''')Depote;

@for(Car(K): @sum(RR(K,I,J)|JobID(I) #eq# 0 #and# JobID(J) #gt# 0 #and#

JobID(J) #le# n:Xkij(K,I,J))=@sum(RR(K,L,I)|JobID(I) #eq# 0 #and#

JobID(L) #gt# n: Xkij(K,L,I)););

@for(Car(K): @sum(RR(K,I,J)|JobID(I) #eq# 0 #and# JobID(J) #gt# 0 #and#

JobID(J) #le# n:Xkij(K,I,J))<=1; );

!(7)車容量限制Carry(u)作業點u的運載量，Loaded(u)車輛離開作業點u時的負載量;

@for(Car(K): @for(Jobs(uu) | ID(uu) #ne# 0 #and# ID(uu) #le# n: @for(Jobs(u) |

ID(u) #ne# ID(uu) #and# ID(u) #ne# ID(uu)+n:

Loaded(uu)=(Loaded(uu)*(1-@sum(RR(K,I,J)|JobID(I) #eq# ID(uu) #and#

JobID(J) #eq# ID(u):Xkij(K,I,J))))+ (@sum(RR(K,I,J)|JobID(I) #eq# ID(uu)

#and# JobID(J) #eq# ID(u):Xkij(K,I,J))*(Carry(uu)+Loaded(u)));)));

@for(Car(K): @for(Jobs(uu) | ID(uu) #gt# n : @for(Jobs(u) | ID(u) #ne# ID(uu)

#and# ID(u) #ne# 0: Loaded(uu)=(Loaded(uu)*(1-@sum(RR(K,I,J)|JobID(I)

#eq# ID(uu) #and# JobID(J) #eq# ID(u):Xkij(K,I,J))))+

(@sum(RR(K,I,J)|JobID(I) #eq# ID(uu) #and# JobID(J) #eq#

ID(u):Xkij(K,I,J))*(Carry(uu)+Loaded(u))); ) ) );

!決策變數限制;

@for(Car(K): @for(SubJobs(I)|JobID #gt# 0: @bin(Zki(K,I));));

@for(Car(K): @for(RR(K,I,J):@bin(Xkij(K,I,J));));

@for(Jobs(u) | ID(u) #gt# 0: Loaded(u)>=0; );

@for(Jobs(u) | ID(u) #gt# 0: Loaded(u)<=Q; );

@sum(Jobs(u)| ID(u) #eq# 0: Loaded(u))=0 ;

End

附錄二 GAACS 演算法參數測試結果總表

測試的參數組合總共有 96 種。求解反覆回合數 100 次，每回合使用之螞蟻數量 10 隻，求解時間以 30 分鐘為上限，每一問題皆測試 30 次取平均值，表中數值為近似最佳解的平均值與標竿解間的差異百分比。

編號

參數測試例題平

α β λ W(t) R103_1 R103_2 R103_3 R112_1 R112_2 R112_3 R208_1 R208_2 R208_3 R210_1 R210_2 R210_3 RC204_1 RC204_2 RC204_3 RC205_1 RC205_2 RC205_3

均

1 0.2~0.01 1 0.01 5 0.789% 0.811%0.504% 2.660%2.722%2.935%1.269%1.230%1.238%3.804%4.026%2.767%4.082% 3.276%3.432%1.396%0.402% 1.111%2.136%

2 0.2~0.01 1 0.01 7 0.747%0.769%0.428% 2.661%2.682%2.915%1.257%1.134%1.331%3.655%3.776%2.814%3.619% 3.201%3.206%1.235%0.371% 1.149%2.053%

3 0.2~0.01 1 0.01 9 0.716%0.731%0.357% 2.659%2.682%2.936%1.269%1.238%1.122%3.639%3.832%2.719%3.556% 3.278%3.181%1.247%0.402% 1.109%2.037%

4 0.2~0.01 1 0.01 11 0.758%0.773%0.434% 2.658%2.722%2.956%1.282%1.327%1.144%3.788%4.082%2.671%4.020% 3.353%3.407%1.408%0.433% 1.071%2.127%

5 0.2~0.01 1 0.3 5 0.809%0.844%0.615% 2.951%2.626%2.809%1.269%1.155%1.238%3.663%3.909%2.828%3.909% 3.300%3.416%1.679%0.471% 1.129%2.146%

6 0.2~0.01 1 0.3 7 0.693%0.881%0.612% 2.955%2.468%2.787%1.257% 1.111%1.152%3.637%3.891%2.796%4.057% 3.102%3.503%1.590%0.429% 1.138% 2.114%

7 0.2~0.01 1 0.3 9 0.705%0.724%0.397% 2.948%2.585%2.832%1.138%1.120%1.109%3.482%3.771%2.650%3.321% 3.379%3.141%1.541%0.502% 1.089%2.024%

8 0.2~0.01 1 0.3 11 0.840%0.882%0.685% 2.954%2.626%2.787%1.257%1.109%1.331%3.679%3.854%2.923%3.972% 3.224%3.441%1.667%0.441% 1.169%2.158%

9 0.2~0.01 1 0.1 5 0.397%0.483%0.506% 2.413%2.447%2.633%1.269%1.313%1.238%3.661%3.573%2.871%3.072% 3.276%3.414%1.729%0.402% 0.462%1.953%

10 0.2~0.01 1 0.1 7 0.252%0.470%0.417% 2.414%2.293%2.627%1.265%1.186%1.100%3.579%3.531%2.770%3.010% 3.144%3.403%1.612%0.383% 0.446%1.884%

11 0.2~0.01 1 0.1 9 0.136%0.508%0.414% 2.418%2.251%2.606%1.253%1.100%1.100%3.553%3.513%2.738%3.158% 2.946%3.490%1.524%0.389% 0.454%1.864%

12 0.2~0.01 1 0.1 11 0.428%0.522%0.577% 2.415%2.447%2.612%1.257%1.217%1.331%3.677%3.517%2.967%3.135% 3.200%3.439%1.718%0.371% 0.501%1.963%

13 0.2~0.01 1 0.5 5 0.497%0.781%0.636% 2.518%2.673%2.384%1.269%1.230%1.238%3.661%3.954%2.830%2.917% 3.245%3.434%0.978%0.402% 0.527%1.954%

14 0.2~0.01 1 0.5 7 0.338%0.734%0.492% 2.518%2.534%2.398%1.277%1.203%1.100%3.573%3.967%2.653%2.804% 3.195%3.401%0.883%0.412% 0.477%1.887%

15 0.2~0.01 1 0.5 9 0.289%0.838%0.616% 2.525%2.392%2.340%1.244%1.100%1.100%3.578%3.850%2.797%3.050% 2.878%3.524%0.782%0.350% 0.556%1.878%

16 0.2~0.01 1 0.5 11 0.580%0.885%0.826% 2.524%2.673%2.326%1.236%1.100%1.490%3.704%3.803%3.089%3.086% 3.038%3.502%0.945%0.350% 0.633%1.988%

17 0.2~0.01 2 0.01 5 0.547%0.653%0.680% 2.642%2.452%2.648%1.269%1.313%1.238%3.536%3.959%2.880%2.987% 3.300%3.465%1.754%0.471% 0.661%2.025%

18 0.2~0.01 2 0.01 7 0.448%0.805%0.849% 2.653%2.208%2.557%1.216%1.100%1.100%3.515%3.745%3.093%3.302% 2.788%3.626%1.565%0.350% 0.784%1.984%

19 0.2~0.01 2 0.01 9 0.411%0.830%0.867% 2.656%2.200%2.537%1.204%1.100%1.100%3.491%3.678%3.128%3.320% 2.669%3.638%1.504%0.350% 0.809%1.972%

20 0.2~0.01 2 0.01 11 0.591%0.559%0.568% 2.636%2.579%2.700%1.299%1.635%1.417%3.531%4.065%2.751%4.222% 3.221%3.354%1.845%0.556% 0.591% 2.118%

21 0.2~0.01 2 0.3 5 0.665%0.425%0.616% 2.570%2.530%2.725%1.269%1.313%1.238%3.446%3.961%2.767%2.964% 3.273%3.416%1.262%0.474% 0.601%1.973%

22 0.2~0.01 2 0.3 7 0.585%0.350%0.535% 2.560%2.399%2.633%1.269%1.313%1.238%3.426%3.907%2.682%2.724% 3.209%3.291%1.166%0.376% 0.556%1.901%

23 0.2~0.01 2 0.3 9 0.550%0.323%0.496% 2.558%2.372%2.614%1.269%1.313%1.238%3.406%3.848%2.650%2.548% 3.169%3.197%1.147%0.360% 0.543%1.867%

24 0.2~0.01 2 0.3 11 0.693%0.446%0.647% 2.572%2.551%2.740%1.269%1.313%1.238%3.462%4.009%2.818%3.101% 3.305%3.491%1.277%0.487% 0.611%2.002%

25 0.2~0.01 2 0.1 5 0.951%1.050%0.737% 2.933%2.530%2.809%1.155%1.238%1.238%4.100%3.599%2.885%4.037% 3.299%3.383%1.396%0.497% 1.144%2.166%

26 0.2~0.01 2 0.1 7 0.910%0.952%0.637% 2.871%2.425%2.677%1.141%1.231%1.155%4.081%3.526%2.800%3.814% 3.238%3.265%1.317%0.407% 1.103%2.086%

27 0.2~0.01 2 0.1 9 0.869%0.942%0.610% 2.920%2.400%2.698%1.141%1.231%1.155%4.060%3.441%2.746%3.650% 3.195%3.165%1.296%0.383% 1.086%2.055%

28 0.2~0.01 2 0.1 11 0.988%1.060%0.762% 2.888%2.552%2.790%1.155%1.238%1.238% 4.119%3.676%2.934%4.185% 3.338%3.474%1.415%0.519% 1.160%2.194%

29 0.2~0.01 2 0.5 5 0.597%0.617% 0.711% 2.706%2.595%2.732%1.238%1.313%1.238%3.886%4.032%2.767%4.310% 3.299%3.416%1.955%0.402% 1.144%2.164%

30 0.2~0.01 2 0.5 7 0.544%0.542%0.649% 2.644%2.490%2.599%1.224%1.306%1.155%3.867%3.975%2.657%4.088% 3.218%3.298%1.857%0.350% 1.086%2.086%

31 0.2~0.01 2 0.5 9 0.516%0.517%0.584% 2.629%2.465%2.621%1.224%1.306%1.155%3.846%3.846%2.650%3.923% 3.206%3.207%1.847%0.350% 1.135%2.057%

32 0.2~0.01 2 0.5 11 0.622%0.641%0.773% 2.721%2.619% 2.711%1.238%1.313%1.238%3.906%4.155%2.795%4.467% 3.311%3.503%1.965%0.425% 1.098%2.194%

33 0.2~0.01 3 0.01 5 0.442%0.444%0.517% 2.500%2.372%2.605%1.269%1.313%1.238%3.746%3.785%2.751%2.808% 3.276%3.406%1.350%0.497% 0.787%1.950%

34 0.2~0.01 3 0.01 7 0.383%0.368%0.461% 2.435%2.287%2.486%1.257%1.306%1.163%3.665%3.719%2.650%2.608% 3.204%3.300%1.263%0.416% 0.734%1.872%

35 0.2~0.01 3 0.01 9 0.365%0.346%0.402% 2.431%2.247%2.506%1.249%1.307%1.163%3.699%3.650%2.650%2.547% 3.193%3.177%1.257%0.418% 0.740%1.852%

36 0.2~0.01 3 0.01 11 0.462%0.469%0.580% 2.485%2.416%2.584%1.278%1.312%1.238%3.709%3.861%2.827%2.996% 3.289%3.529%1.357%0.496% 0.781%1.982%

37 0.2~0.01 3 0.3 5 0.541%0.624%0.546% 2.526%2.618%2.459%1.238%1.313%1.238%3.746%3.812%2.828%3.138% 3.198%3.462%1.521%0.471% 0.833%2.006%

38 0.2~0.01 3 0.3 7 0.482%0.571%0.469% 2.445%2.534%2.343%1.224%1.306%1.155%3.677%3.735%2.723%2.946% 3.125%3.356%1.431%0.391% 0.785%1.928%

39 0.2~0.01 3 0.3 9 0.464%0.555%0.448% 2.420%2.508%2.308%1.220%1.304%1.130%3.656%3.712%2.682%2.889% 3.104%3.324%1.404%0.371% 0.767%1.904%

40 0.2~0.01 3 0.3 11 0.558%0.650%0.568% 2.551%2.643%2.494%1.279%1.315%1.306%3.766%3.835%2.869%3.195% 3.215%3.494%1.552%0.491% 0.852%2.035%

41 0.2~0.01 3 0.1 5 0.522%0.894%0.809% 2.919%2.701%2.613%1.269%1.313%1.238%3.536%3.509%2.767%3.103% 3.245%3.433%1.865%0.497% 1.124%2.075%

42 0.2~0.01 3 0.1 7 0.463%0.830%0.744% 2.850%2.623%2.495%1.255%1.306%1.155%3.431%3.442%2.698%2.853% 3.173%3.333%1.784%0.407% 1.069%1.995%

43 0.2~0.01 3 0.1 9 0.451%0.817%0.731% 2.836%2.572%2.460%1.200%1.299%1.100%3.410%3.429%2.652%2.803% 3.159%3.301%1.768%0.378% 1.057%1.968%

44 0.2~0.01 3 0.1 11 0.533%0.907%0.821% 2.932%2.747%2.644%1.338%1.320%1.320%3.565%3.526%2.808%3.148% 3.258%3.468%1.903%0.524% 1.150%2.106%

45 0.2~0.01 3 0.5 5 0.618%0.857%0.815% 2.962%2.793%2.776%1.269%1.313%1.238%3.723%3.570%2.827%4.037% 3.276%3.416%1.689%0.444% 1.111%2.152%

46 0.2~0.01 3 0.5 7 0.548%0.782%0.726% 2.880%2.715%2.658%1.200%1.382%1.155%3.618%3.513%2.772%3.662% 3.205%3.316%1.596%0.365% 1.043%2.063%

47 0.2~0.01 3 0.5 9 0.524%0.770%0.705% 2.860%2.697%2.630%1.184%1.398%1.135%3.593%3.502%2.757%3.572% 3.188%3.292%1.605%0.350% 0.996%2.042%

48 0.2~0.01 3 0.5 11 0.645%0.869%0.842% 2.982%2.813%2.807%1.286%1.382%1.257%3.749%3.582%2.843%4.127% 3.293%3.441%1.700%0.463% 1.158%2.180%

49 2~ 0.01 2 0.01 5 0.664%0.315%0.648% 2.750% 2.811%3.061%1.286%1.382%1.257%3.682%3.998%3.556%3.062% 3.305%3.434%1.158%0.402% 0.815%2.088%

50 2~ 0.01 2 0.01 7 0.598%0.276%0.534% 2.669%2.735%2.984%1.148%1.244%1.120%3.600%3.947%3.502%2.812% 3.234%3.335%1.086%0.350% 0.748%1.996%

51 2~ 0.01 2 0.01 9 0.584%0.268% 0.511% 2.648%2.720%2.969%1.121%1.217%1.100%3.584%3.937%3.492%2.762% 3.219%3.309%1.060%0.350% 0.723%1.976%

52 2~ 0.01 2 0.01 11 0.683%0.325%0.680% 2.779%2.833%3.082%1.324%1.420%1.296%3.704%4.012%3.571%3.133% 3.325%3.471%1.194%0.440% 0.851% 2.118%

53 2~ 0.01 2 0.3 5 0.456%0.637%0.508% 2.534%2.370%2.694%1.269%1.344%1.357%3.173%3.457%2.767%2.549% 3.382%3.314%1.292%0.771% 0.737%1.923%

54 2~ 0.01 2 0.3 7 0.400%0.580%0.453% 2.488%2.323%2.646% 1.118%1.138%1.233%3.049%3.299%2.650%2.548% 3.348%3.246%1.232%0.713% 0.677%1.841%

55 2~ 0.01 2 0.3 9 0.395%0.575%0.448% 2.478%2.309%2.622%1.100%1.100%1.100%3.012%3.252%2.650%2.545% 3.338%3.226%1.214%0.695% 0.659%1.818%

56 2~ 0.01 2 0.3 11 0.461%0.642%0.513% 2.544%2.384%2.718%1.407%1.406%1.632%3.210%3.504%2.803%2.553% 3.392%3.334% 1.311%0.789% 0.755%1.964%

57 2~ 0.01 2 0.1 5 0.365%0.662%0.636% 2.382%2.622%2.615%1.155%1.155%1.155%3.374%3.325%2.823%3.219% 3.156%3.440%1.283%0.484% 0.591%1.913%

58 2~ 0.01 2 0.1 7 0.327%0.621%0.591% 2.342%2.582% 2.611%1.100%1.100%1.100%3.269%3.226%2.738%2.924% 3.078%3.267%1.193%0.413% 0.505%1.833%

59 2~ 0.01 2 0.1 9 0.308%0.600%0.569% 2.322%2.561%2.609%1.100%1.100%1.100%3.217%3.176%2.696%2.776% 3.039%3.180%1.187%0.385% 0.481%1.800%

60 2~ 0.01 2 0.1 11 0.379%0.678%0.653% 2.397%2.637%2.616%1.176%1.180%1.176%3.413%3.363%2.855%3.330% 3.185%3.504%1.259%0.499% 0.594%1.939%

61 2~ 0.01 2 0.5 5 0.628%1.160%0.793% 2.945%2.674%2.847%1.137%1.156%1.131%3.852%3.615%2.976%4.077% 3.512%3.416%0.620%0.373% 0.512%2.079%

62 2~ 0.01 2 0.5 7 0.577%1.106%0.738% 2.873%2.601%2.772%1.100%1.100%1.100%3.768%3.529%2.892%3.782% 3.435%3.256%0.564%0.350% 0.451%2.000%

63 2~ 0.01 2 0.5 9 0.558%1.086%0.720% 2.844%2.576%2.753%1.100%1.100%1.100%3.743%3.504%2.860%3.664% 3.408%3.216%0.535%0.350% 0.427%1.975%

64 2~ 0.01 2 0.5 11 0.648%1.179% 0.811% 2.965%2.698%2.876%1.170%1.189%1.165%3.876%3.641%3.008%4.170% 3.539%3.455%0.642%0.397% 0.532%2.109%

65 2~ 0.1 2 0.01 5 0.700%0.853%0.750% 2.888%2.742%2.772%1.235%1.344%1.155%3.792%4.096%2.956%3.962% 3.357%3.406%1.462%0.402% 1.146%2.168%

66 2~ 0.1 2 0.01 7 0.650%0.808%0.705% 2.828%2.681%2.712%1.217%1.313%1.189%3.693%3.996%2.856%3.667% 3.282%3.259%1.387%0.350% 1.072%2.092%

67 2~ 0.1 2 0.01 9 0.642%0.795%0.690% 2.822%2.675%2.692%1.203%1.291%1.175%3.655%3.961%2.827%3.563% 3.256%3.194%1.369%0.350% 1.047%2.067%

68 2~ 0.1 2 0.01 11 0.717%0.879%0.766% 2.876%2.754%2.760%1.313%1.426%1.285%3.870%4.165%3.014%4.270% 3.414%3.547%1.513%0.444% 1.197%2.234%

69 2~ 0.1 2 0.3 5 0.767%1.176%0.918% 2.848%2.694%2.790%1.267%1.155%1.357%3.865%3.625%3.141%4.529% 3.273%3.488%1.675%0.471% 1.208%2.236%

70 2~ 0.1 2 0.3 7 0.722%1.132%0.873% 2.785%2.637%2.733%1.198%1.100%1.288%3.790%3.543%3.070%4.208% 3.198%3.328%1.598%0.396% 1.132%2.152%

71 2~ 0.1 2 0.3 9 0.708% 1.119%0.859% 2.764%2.619%2.710%1.171%1.100%1.260%3.759%3.516%3.036%4.080% 3.167%3.264%1.567%0.366% 1.101%2.120%

72 2~ 0.1 2 0.3 11 0.780%1.188%0.930% 2.867% 2.711% 2.811%1.292%1.180%1.381%3.892%3.650%3.172%4.644% 3.300%3.546%1.703%0.499% 1.235%2.266%

在文檔中 Delivery Problem with Time Windows (頁 97-114)

建議

第五章 結論與建議

5.2 建議

參考文獻

Lecture Notes in Computer Science, Vol. 840, Springer Berlin / Heidelberg.

附錄一 求解 SPDP 例題的 LINGO 程式碼

model:

Sets:

endsets Data:

Enddata

min=@sum(Car(K):@sum(TT(I,J):Cij(I,J)*Xkij(K,I,J)))

@sum(Car(K):

@sum(TT(I,J)| JobID(I) # eq# 0 # and# JobID(J) #le# n: cost*Xkij(K,I,J)));

@for(Car(K): @for(Jobs(I)|ID(I) #gt# 0 #and# ID(I) #le# n:

@sum(SubJobs(J)|JobID #eq# ID(I):Zki(K,J))=@sum(SubJobs(L)|JobID

@for(Jobs(J)| ID #ne# 0: @sum(Car(K):@sum(SubJobs(I)|JobID #eq# ID(J):

@sum(Car(K): @sum(SubJobs(I)|JobID #eq# 0: Zki(K,I)))=@size(Car);

@for(Jobs(I)|ID(I) #gt# 0 #and# ID(I) #le# n: @sum(SubJobs(J)|JobID #eq#

@for(Jobs(a)|ID(a) #gt# 0 #and# ID(a) #le# n: @sum(Jobs(c)|ID(c) #ne# 0

@for(Jobs(a)|ID(a) #gt# n: @sum(Jobs(c)|ID(c) #ne# ID(a)-n #and# ID(c)

@for(Jobs(c)|ID(c) #gt# 0 #and# ID(c) #le# n: @sum(Jobs(a)|ID(a) #ne#

@sum(RR(K,I,J)|JobID(I) #eq# ID(a) #and# JobID(J) #eq# ID(c):

@for(Jobs(c)|ID(c) #gt# n: @sum(Jobs(a)|ID(a) #ne# 0 #and# ID(a) #ne#

@sum(Car(K): @sum(Jobs(c)|ID(c) #gt# 0 #and# ID(c) #le# n:

@sum(RR(K,I,J)|JobID(I) #eq# 0 #and# JobID(J) #eq# ID(c):

@sum(Car(K): @sum(Jobs(c)|ID(c) #gt# n: @sum(RR(K,I,J)|JobID(I) #eq# ID(c)

@for(Car(K): @for(SubJobs(c)|JobID(c) #ne# 0 #and# JobID(c) #le# n:

@sum(RR(K,a,c)|JobID(a) #ne# JobID(c) #and# JobID(a) #ne#

@for(Car(K): @for(SubJobs(c)|JobID(c) #ne# 0 #and# JobID(c) #le# n:

@sum(RR(K,a,c)|JobID(a) #ne# JobID(c) #and# JobID(a) #ne#

@for(Car(K): @for(SubJobs(c)|JobID(c) #gt# n: @sum(RR(K,a,c)|JobID(a) #ne#

@for(Car(K): @for(SubJobs(c)|JobID(c) #gt# n: @sum(RR(K,a,c)|JobID(a) #ne#

@for(Car(K): @sum(RR(K,I,J)|JobID(I) #eq# 0 #and# JobID(J) #gt# 0 #and#

@for(Car(K): @sum(RR(K,I,J)|JobID(I) #eq# 0 #and# JobID(J) #gt# 0 #and#

@for(Car(K): @for(Jobs(uu) | ID(uu) #ne# 0 #and# ID(uu) #le# n: @for(Jobs(u) |

@for(Car(K): @for(Jobs(uu) | ID(uu) #gt# n : @for(Jobs(u) | ID(u) #ne# ID(uu)

@for(Car(K): @for(SubJobs(I)|JobID #gt# 0: @bin(Zki(K,I));));

@for(Car(K): @for(RR(K,I,J):@bin(Xkij(K,I,J));));

@for(Jobs(u) | ID(u) #gt# 0: Loaded(u)>=0; );

@for(Jobs(u) | ID(u) #gt# 0: Loaded(u)<=Q; );

@sum(Jobs(u)| ID(u) #eq# 0: Loaded(u))=0 ;

End

附錄二 GAACS 演算法參數測試結果總表

編 號

參數 測 試 例 題 平

均

第五章結論與建議

附錄一求解 SPDP 例題的 LINGO 程式碼

編號

參數測試例題平