(*Input: A=Cost matrix, B=Position of basic cells, IA=Shipping amount corresponding to the postion in B*)
(*Output:matrix of M1=z_{ij}-c_{ij},S=Matrix of Shipping plan*)
TObj[A_,B_,IA_]:=Module[{M1,m,n,M,b,i,j,S},
m=Dimensions[A][[1]];n=Dimensions[A][[2]];
M1=Table[0,m,n];
S=M1;
M=Table[0,m+n-1,m+n];
b=Table[0,m+n-1];
For[i=1,i<=m+n-1,i++,M[[i,B[[i,1]]]]=1;M[[i,m+B[[i,2]]]]=1;b[[i]]=Extract[A,B[[i]]]; (*A[[B[[i]][[1]],B[[i]][[2]]]]*)];
V=LinearSolve[M,b];
For[i=1,i<=m,i++,
For[j=1,j<=n,j++,
If[MemberQ[B,{i,j}],M1[[i,j]]=bp;S[[i,j]]=IA[[Flatten[Position[B,{i,j}]][[1]]]],
M1[[i,j]]= V[[i]]+V[[m+j]]-A[[i,j]];
]
]
];
{M1//MatrixForm, S//MatrixForm}]

(*Lp=cells along loops, Bp=Basic cells, Ia=Shipping amount, Mv=Cost matrix*)
(*Output:Bp2=basic position after pivoting, Ia2=new shipping amount, Tc=Shipping cost*)
TPivot[Lp_,Bp_,Ia_,Mv_]:=Module[{ll,lpp,elia,pma,ma,Bp2,Ia2,Tc},
ll=Length[Lp];
lpp=Flatten[Table[Position[Bp,Lp[[i]]],{i,2,Length[Lp]}]]; (*Position in of LP(i) in BP*)
elia=Table[Ia[[  lpp[[2i-1]]   ]],{i,1,ll/2}]; (*removing the entering var, extract the odd position amount*)
pma=PositionSmallest[elia][[1]]; (*find the position of smallest amount which is the departing var*)
ma=Min[elia]; (*the smallest amount*)
Bp2=ReplaceAll[Bp,Lp[[2*pma]]->Lp[[1]]] ;(*replacing the even departing position by the entering position*)
lpp=Join[lpp,Position[Bp,Lp[[2*pma]]][[1]]];
Ia2=Ia;
For[i=1,i<=ll/2,i++,
Ia2[[lpp[[2i-1]]]]=Ia[[lpp[[2i-1]]]]-ma;
Ia2[[lpp[[2i]]]]=Ia2[[lpp[[2i]]]]+ma;
];
Tc=Sum[Extract[Mv,Bp2[[i]]]*Ia2[[i]],{i,1,Length[Ia2]}];
{Bp2,Ia2,Tc}
]