Originally posted by: sandeepsinghchauhan

I have this sparsity model and here i include one boolean variable which makes my objective quadratic. so what are the changes i need to do to handle this Z variable

{string} Cities = ...;
{string} Products = ...;
float Capacity = ...;

tuple route {
  string p;
  string o;
  string d;
}
{route} Routes = ...;

tuple supply {
  string p;
  string o;
}
{supply} Supplies = { <p,o> | <p,o,d> in Routes };
float Supply[Supplies] = ...;

tuple customer {
  string p;
  string d;
}
{customer} Customers = { <p,d> | <p,o,d> in Routes };
float Demand[Customers] = ...;
float Cost[Routes] = ...;

{string} Orig[p in Products] = { o | <p,o,d> in Routes };
{string} Dest[p in Products] = { d | <p,o,d> in Routes };

assert forall(p in Products)
  sum(o in Orig[p])
    Supply[<p,o>] == sum( d in Dest[p] ) Demand[<p,d>];

dvar float+ Trans[Routes];
dvar boolean Z[Routes];  
constraint ctSupply[Products][Cities];
constraint ctDemand[Products][Cities];

minimize
  sum(l in Routes) Cost[l] * Trans[l] * Z[l];
   
subject to {
  forall( p in Products , o in Orig[p] )

    ctSupply[p][o]:
      sum( d in Dest[p] )
        Trans[< p,o,d >] == Supply[<p,o>];
  forall( p in Products , d in Dest[p] )
    ctDemand[p][d]:  
      sum( o in Orig[p] )
        Trans[< p,o,d >] == Demand[<p,d>];
  ctCapacity:  forall( o , d in Cities )
                 sum( <p,o,d> in Routes )
                   Trans[<p,o,d>] <= Capacity;
                   
  active:
     forall( l in Routes)
                               
                   Z[l] == minl(1,Trans[l]);
              
}

Error

CPLEX Error 5002: Q in objective is not positive semi-definite.   

please help

Hi,

Why not using logical constraints ?

you could try to rewrite

sum(l in Routes) Cost[l] * Trans[l] * Z[l];

into

sum(l in Routes) Cost[l] * ZTrans[l];

and add in the constraints that for all I

(ZTrans[i]==0) == (Z[I]==0);

(ZTrans[i]==Trans[I]) == (Z[i]==1);

regards