I'm studying the example of GAMS library: Enumerate all Feasible Basic Solutions of the Transportation Problem (ALLBASES,SEQ=396)

In the description they mention this statement:

**We reformulate in standard form use binary variables to determine if a variable belongs to the basis or not.**

I don't quite understand what belongs to the basis means... I do understand the formulation but I don't get the purpose of it...

May someone give me a hand on this doubt ...

This is the formulation of the "Basis" :

* Basis definition

Variables

xind(i,j) x basis indicator

sslind(i) sslack basis indicator

dslind(j) dslack basis indicator

Binary Variable xind, sslind, dslind;

Equations

defbasis basis definition

defximp(i,j) xind=0 => x=0

defsslimp(i) sslind=0 => ssl=0

defdslimp(j) dslind=0 => dsl=0;

defbasis .. card(i) + card(j) =e=

sum((i,j), xind(i,j)) + sum(i, sslind(i)) + sum(j, dslind(j));

defximp(i,j) .. x(i,j) =l= min(a(i),b(j))*xind(i,j);

defsslimp(i) .. sslack(i) =l= a(i)*sslind(i);

defdslimp(j) .. dslack(j) =l= b(j)*dslind(j);

Thank you for your helping..

Juan D