計(jì)劃網(wǎng)絡(luò)優(yōu)化模型

計(jì)劃網(wǎng)絡(luò)優(yōu)化模型10103471410（C）（G）（D）（F）（E）（B）（A）3為方便建立模型，將上圖轉(zhuǎn)化會(huì)下圖：E35BA12FCDG467模型的建立與求解模型Ⅰ：設(shè)是事件i的開(kāi)始時(shí)間，是時(shí)間j的開(kāi)始時(shí)間，設(shè)是作業(yè)（i，j）的計(jì)劃時(shí)間，為了得到最早開(kāi)工時(shí)間和作業(yè)關(guān)鍵路徑，目標(biāo)函數(shù)為：。即作業(yè)開(kāi)始時(shí)間盡量早，這樣得到最早開(kāi)工時(shí)間。再引入作業(yè)對(duì)應(yīng)弧上的當(dāng)然松弛變量，且。V是事件集合，A是所有事件集合。這樣可得到作業(yè)最早開(kāi)工時(shí)間，當(dāng)最早開(kāi)工時(shí)間與最遲開(kāi)工時(shí)間相同時(shí)就得到項(xiàng)目的關(guān)鍵路徑。程序：model:sets:events/1..7/:x;operate(events,events)/1,22,32,43,43,54,65,66,7/:s,t;endsetsdata:t=10143073410;enddatamin=@sum(events:x);@for(operate(i,j):s(i,j)=x(j)-x(i)-t(i,j));End結(jié)果：Globaloptimalsolutionfound.Objectivevalue:169.0000Totalsolveriterations:0VariableValueReducedCostX(1)0.0000007.000000X(2)10.000000.000000X(3)24.000000.000000X(4)24.000000.000000X(5)31.000000.000000X(6)35.000000.000000X(7)45.000000.000000S(1,2)0.0000006.000000S(2,3)0.0000005.000000S(2,4)11.000000.000000S(3,4)0.0000001.000000S(3,5)0.0000003.000000S(4,6)8.0000000.000000S(5,6)0.0000002.000000S(6,7)0.0000001.000000T(1,2)10.000000.000000T(2,3)14.000000.000000T(2,4)3.0000000.000000T(3,4)0.0000000.000000T(3,5)7.0000000.000000T(4,6)3.0000000.000000T(5,6)4.0000000.000000T(6,7)10.000000.000000（如表所示，方括號(hào)中第一個(gè)數(shù)是最早開(kāi)工時(shí)間，第二個(gè)數(shù)是最遲開(kāi)工時(shí)間。）工作開(kāi)工時(shí)間計(jì)劃時(shí)間A(1，2)[0，0]10B(2，3)[10，10]14C(2，4)[24，35]3D(4，6)[24，32]3E(3，5)[31，31]7F(5，6)[35，35]4G(6，7)[45，45]10當(dāng)最早開(kāi)工時(shí)間與最遲開(kāi)工時(shí)間相同時(shí)就得到項(xiàng)目的關(guān)鍵路徑由此可得最佳路徑為ABDEFG。最短時(shí)間為45。模型Ⅱ：設(shè)是事件i的開(kāi)始時(shí)間，是時(shí)間j的開(kāi)始時(shí)間，設(shè)是作業(yè)（i，j）的計(jì)劃時(shí)間，是完成（i，j）的最短時(shí)間，是作業(yè)（i，j）可能減少的時(shí)間，減少時(shí)間所花是費(fèi)用，因此有：程序：MODEL:sets:events/1..7/:x;operate(events,events)/1,22,32,43,43,54,65,66,7/:s,t,m,c,y;endsetsdata:t=10143037410;m=108201638;c=04102353;enddatamin=mincost+sumx;mincost=@sum(operate:c*y);sumx=@sum(events:x);@for(operate(i,j):s(i,j)=x(j)-x(i)+y(i,j)-t(i,j));n=@size(events);@for(operate:@bnd(0,y,t-m));END結(jié)果：Globaloptimalsolutionfound.Objectivevalue:151.0000Totalsolveriterations:0VariableValueReducedCostMINCOST24.000000.000000SUMX127.00000.000000N7.0000000.000000X(1)0.0000007.000000X(2)10.000000.000000X(3)18.000000.000000X(4)18.000000.000000X(5)21.000000.000000X(6)25.000000.000000X(7)35.000000.000000S(1,2)0.0000006.000000S(2,3)0.0000005.000000S(2,4)5.0000000.000000S(3,4)0.0000003.000000S(3,5)0.0000001.000000S(4,6)0.0000002.000000S(5,6)0.0000000.000000S(6,7)0.0000001.000000T(1,2)10.000000.000000T(2,3)14.000000.000000T(2,4)3.0000000.000000T(3,4)0.0000000.000000T(3,5)3.0000000.000000T(4,6)7.0000000.000000T(5,6)4.0000000.000000T(6,7)10.000000.000000M(1,2)10.000000.000000M(2,3)8.0000000.000000M(2,4)2.0000000.000000M(3,4)0.0000000.000000M(3,5)1.0000000.000000M(4,6)6.0000000.000000M(5,6)3.0000000.000000M(6,7)8.0000000.000000C(1,2)0.0000000.000000C(2,3)4.0000000.000000C(2,4)1.0000000.000000C(3,4)0.0000000.000000C(3,5)2.0000000.000000C(4,6)3.0000000.000000C(5,6)5.0000000.000000C(6,7)3.0000000.000000Y(