Is it possible to solve a 2d bin packing problem or nesting problem with Cplex? The solution should present the $x$ and $y$ coordinates of each item.

  • 1
    $\begingroup$ please accept the answer that solved your problem rather than changing the question to "solved". $\endgroup$
    – EhsanK
    Commented Feb 3, 2021 at 16:49
  • $\begingroup$ @Mathew, beside of the interested answer of Alex, you might want to take a look into the ABS models to solve floor layout problems. :) $\endgroup$
    – A.Omidi
    Commented Feb 4, 2021 at 8:14

1 Answer 1


you could start with

//using CP;

int n=25; // nb of rectangles

 int sizeBigSquare=10000;
 int l[i in 1..n]=rand(100);
 int w[i in 1..n]=rand(100);
 dvar int x[i in 1..n]in 0..sizeBigSquare;
 dvar int y[i in 1..n] in 0..sizeBigSquare;
 dvar boolean rota[i in 1..n]; // do we rotate?
 dexpr int x2[i in 1..n]=x[i]+(rota[i]==1)*w[i]+(rota[i]==0)*l[i];
 dexpr int y2[i in 1..n]=y[i]+(rota[i]==1)*l[i]+(rota[i]==0)*w[i];
 dexpr int Mx=max(i in 1..n) x2[i];
 dexpr int My=max(i in 1..n) y2[i];
 minimize My;
 subject to
   forall(ordered i,j in 1..n)
     (x2[i]<=x[j]) || (x2[j]<=x[i]) || (y2[i]<=y[j]) || (y2[j]<=y[i]);
 float rate=sum(i in 1..n) w[i]*l[i]/My/Mx; 

that is relying on MIP within CPLEX

And if you comment // in //using CP; then this model will use constraint programming

  • $\begingroup$ Thanks for your interesting solution. Would you please, add some details in your answer to clarify decision variables and constraints notation? $\endgroup$
    – A.Omidi
    Commented Feb 4, 2021 at 8:18

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