Sets
         i /1*20/
         alias(i,j);
     
     Parameters
         pi(i)   "Profit of item i"
         W       "Width of the container"
         H       "Height of the container"
         D       "Depth of the container"
         wi(i)   "Width of item i"
         hi(i)   "Height of item i"
         di(i)   "Depth of item i";
     
     Variables
         z       "Objective: total profit"
         si(i)   "1 if item i is selected, 0 otherwise"
         xi(i)   "X-coordinate of item i"
         yi(i)   "Y-coordinate of item i"
         zi(i)   "Z-coordinate of item i"
         lij(i,j) "1 if item i is to the left of item j"
         uij(i,j) "1 if item i is below item j"
         bij(i,j) "1 if item i is behind item j";
     
     Binary Variables si, lij, uij, bij;
     
     Positive Variables xi, yi, zi;
     
     Equations
         obj             "Objective function"
         packing1(i,j)   "Non-overlapping constraint for x"
         packing2(i,j)   "Non-overlapping constraint for y"
         packing3(i,j)   "Non-overlapping constraint for z"
         bound_x(i)      "X-bound constraint"
         bound_y(i)      "Y-bound constraint"
         bound_z(i)      "Z-bound constraint";
     
     * Objective: maximize total profit
     obj .. 
         z =e= sum(i, pi(i) * si(i));
     
     * Non-overlapping constraints
     packing1(i,j) $ (i <> j) ..
         xi(i) + wi(i) * si(i) + W * lij(i,j) =l= xi(j) + W * (1 - si(i));
     
     packing2(i,j) $ (i <> j) ..
         yi(i) + hi(i) * si(i) + H * uij(i,j) =l= yi(j) + H * (1 - si(i));
     
     packing3(i,j) $ (i <> j) ..
         zi(i) + di(i) * si(i) + D * bij(i,j) =l= zi(j) + D * (1 - si(i));
     
     * Boundary constraints
     bound_x(i) ..
         xi(i) + wi(i) * si(i) =l= W;
     
     bound_y(i) ..
         yi(i) + hi(i) * si(i) =l= H;
     
     bound_z(i) ..
         zi(i) + di(i) * si(i) =l= D;
     
     Model BinPacking /all/;
     Solve BinPacking using mip maximizing z;

I’m trying to run this code on GAMS. However, it’s giving me “Dimension different – The symbol is referenced with more/less indices as declared” error in packing1(i,j) $ (i <> j) .. I’m trying to create model for 3D bin packing for rolls. If you know better way, please write it on the comments.