Originally posted by: NaomiLearnCplex

Hello there,

Below is the coding for a binary integer minimization problem. My cost function cij is the sum of decision variables xij from i to i+9. The last 9 rows exceed the range of i. I want to express the row index as a function of i. The row index is represented as 1 plus the remainder of i divided by the number of rows (ns), where i iterates from i to i+9. (Detailed formuation is shown in below picture) By doing this, I can form a closed row sum loop by connecting the last row to the first row. However, I don't know how to write my cost function using CPLEX.

What I did is to write 

dexpr int c[i in shift, j in comb ] = x [ i] [ j ] +x [ i+1] [ j ] +x [ i+2] [ j ] +x [ i+3] [ j ] +x [ i+4] [ j ] +x [ i+5] [ j ] +x [ i+6] [ j ] +x [ i+7] [ j ] +x [ i+8] [ j ] +x [ i+9] [ j]

;

But definitely, this expression has a range problem.

Anyone could help? Many thanks in advance!

int nc=...; 
int ns=...; 


range comb=1..nc; 
range shift=1..ns; 

//define decision variables
dvar boolean x[shift][comb];

//define parameters 
int CombSF[comb]=...;
dexpr int c[i in shift, j in comb]= x[i][j]+x[i+1][j]+x[i+2][j]+x[i+3][j]+x[i+4][j]+x[i+5][j]+x[i+6][j]+x[i+7][j]+x[i+8][j]+x[i+9][j];
int dl[shift]=...;
int du[shift]=...;

//define objective function
minimize sum(i in shift, j in comb)c[i][j]*x[i][j];

//define constraints
subject to 
{ 
Con01:
forall(i in shift)
  dl[i]<=sum(j in comb)x[i][j]<=du[i];

Con02:
forall(j in comb)
  sum(i in shift)x[i][j]==CombSF[j];
}

Hi,

have you tried to turn

dexpr int c[i in shift, j in comb]=
x[i][j]+x[i+1][j]+x[i+2][j]+x[i+3][j]+x[i+4][j]+x[i+5][j]+x[i+6][j]+x[i+7][j]+x[i+8][j]+x[i+9][j];
 

into

dexpr int c[i in shift, j in comb]=
sum(k in 0..9:i+k<=ns) x[i+k][j];

in order not to have the out of range ?

int nc=10;
int ns=30;
range comb=1..nc;
range shift=1..ns;

//define decision variables
dvar boolean x[shift][comb];

//define parameters
int CombSF[i in comb]=rand(10);
dexpr int c[i in shift, j in comb]=
//x[i][j]+x[i+1][j]+x[i+2][j]+x[i+3][j]+x[i+4][j]+x[i+5][j]+x[i+6][j]+x[i+7][j]+x[i+8][j]+x[i+9][j];
sum(k in 0..9:i+k<=ns) x[i+k][j];

int dl[i in shift]=rand(10);
int du[i in shift]=rand(10)+20;

//define objective function
minimize sum(i in shift, j in comb)c[i][j]*x[i][j];

//define constraints
subject to
{
Con01a:
forall(i in shift)
dl[i]<=sum(j in comb)x[i][j];

Con01b:
forall(i in shift)
sum(j in comb)x[i][j]<=du[i];

Con02:
forall(j in comb)
sum(i in shift)x[i][j]==CombSF[j];
}

works better.

regards

https://www.linkedin.com/pulse/low-barrier-entry-optimization-through-cplex-alex-fleischer/

Originally posted by: NaomiLearnCplex

Thank you. I modified a bit to meet my needs and it works!

dexpr int c[i in shift, j in comb]= sum (k in 0..4)x[1+(i+k-1)%ns][j];