Mathematica教學：Simplex method in tableau form

simplexmethod[c_,A_,B_,b_,xnb_,xb_,cp_,Ap_,Bp_,bp_]:=
Block[{cB,nA,nB,mysymbol,pivotCol,AB,leaveVarpos,Bnew,xbnew,
xnbnew,Anew,cnew,znew,z},

(*初始化變數*)
nA=Length[xnb];
nB=Length[xb];

(*建立符號變數*)
mysymbol=ToExpression[Flatten[{"x"<>ToString[#]&/@Range[nA],
"s"<>ToString[#]&/@Range[nB]}]];

(*找出進入變數（最負的檢驗數）*)
pivotCol=PositionSmallest[-c][[1]];

(*合併A和B矩陣*)
AB=Flatten/@Transpose[{A,B}];

(*找出離開變數（最小比率測試）*)
leaveVarpos=PositionSmallest[
b/(If[#<=0,10^-6,#]&/@
Map[Flatten,Transpose[{A,B}]][[All,pivotCol]])/.x_/;x<=0->10^6][[1]];

(*更新基變數和非基變數*)
xbnew=xb/.xb[[leaveVarpos]]->xnb[[pivotCol]];
xnbnew=xnb/.xnb[[pivotCol]]->xb[[leaveVarpos]];

(*建立新的基矩陣*)
Bnew=Map[Flatten,Transpose[{Ap,Bp}]][[All,
Flatten[Position[mysymbol,#]&/@xbnew]]];

(*計算基變數的成本係數*)
cB=cp[[Flatten[Position[mysymbol,#]&/@xbnew]]];

(*計算新的檢驗數和目標函數值*)
znew=
Flatten[{cB.Inverse[Bnew].Ap-cp[[1;;nA]],
cB.Inverse[Bnew],cB.Inverse[Bnew].bp}];

(*顯示單形法表格*)
Print[Grid[
Insert[Flatten/@Transpose[{Flatten[{z,xbnew}],
Insert[Map[Flatten,Transpose[{Inverse[Bnew].Ap,Inverse[Bnew],
Inverse[Bnew].bp}]],znew,1]}],Flatten[{Item["BasicVariable",
Background->Lighter[Yellow,0.9]],mysymbol,"Solution"}],
1],Frame->All,
Background->{{Lighter[Gray,0.8]},{Lighter[Yellow,0.9],
Lighter[Pink,0.9]}},ItemStyle->Directive[FontSize->16],
Spacings->{Table[5,{Length[mysymbol]+3}],2}]];

(*返回更新後的參數*)
{-Flatten@{cB.Inverse[Bnew].Ap-cp[[1;;nA]],
cB.Inverse[Bnew]},Inverse[Bnew].Ap,Inverse[Bnew],
Inverse[Bnew].bp,xnbnew,xbnew,cp,Ap,Bp,bp}]

Nest[simplexmethod@@#&,{
{3,5,0,0,0},
{{1,0},{0,2},{3,2}},
{{1,0,0},{0,1,0},{0,0,1}},{4,12,18},
{x1,x2},{s1,s2,s3},
{3,5,0,0,0},
{{1,0},{0,2},{3,2}},
{{1,0,0},{0,1,0},{0,0,1}},{4,12,18}},
2]

Tags: Mathematica, Mathematica 教學, Mathematica 教學 程式, Mathematica 教學講義

• 編輯文章
• 此文章網址
• 轉寄此文章
• 目前有0 意見