Problem combining 2 models [closed]

Question

I'm trying to combine 2 independent linear optimization models while individually they are working combined they are not. My guess on the mistake is that the last part where I solve for the variables is not right (also suggested by Mathematica, but I don't understand what I'm doing wrong). What do I have to change in my combined model?

The latter part is:

{Flatten[Table[Subscript[X, t, z], {t, 1, 2}, {z, 1, 2}]], 
     Flatten[Table[Subscript[W, c, i], {c, 1, 2}, {i, 1, 2}]]}]

Here is the individual first model:

{Subscript[e, 1], Subscript[e, 2]} = {1, 2}; 
{Subscript[H, 1], Subscript[H, 2]} = {2, 1}; 
NMinimize[{Sum[
   Subscript[e, t]*Subscript[H, z]*Subscript[X, t, z], {t, 1, 2}, {z, 
    1, 2}], 
     And @@ 
    Flatten[Table[
      Element[Subscript[X, t, z], Integers], {t, 1, 2}, {z, 1, 2}]] && 
       And @@ 
    Flatten[Table[
      0 <= Subscript[X, t, z] <= 1, {z, 1, 2}, {t, 1, 2}]] && 
   And @@ Table[Sum[Subscript[X, t, z], {z, 1, 2}] == 1, {t, 1, 2}] && 
       And @@ 
    Table[Sum[Subscript[X, t, z], {t, 1, 2}] == 1, {z, 1, 2}]}, 
 Flatten[Table[Subscript[X, t, z], {t, 1, 2}, {z, 1, 2}]]]

Here is the individual second model:

{Subscript[d, 1], Subscript[d, 2]} = {1, 2}; 
{Subscript[A, 1], Subscript[A, 2]} = {2, 1}; 
NMinimize[{Sum[Subscript[d, c]*Subscript[A, i]*Subscript[W, c, i], 
       {c, 1, 2}, {i, 1, 2}], 
     And @@ 
    Flatten[Table[Element[Subscript[W, c, i], Integers], {c, 1, 2}, 
             {i, 1, 2}]] && 
   And @@ Flatten[Table[0 <= Subscript[W, c, i] <= 1, 
             {c, 1, 2}, {i, 1, 2}]] && 
       And @@ 
    Table[Sum[Subscript[W, c, i], {c, 1, 2}] == 1, {i, 1, 2}] && 
       And @@ 
    Table[Sum[Subscript[W, c, i], {i, 1, 2}] == 1, {c, 1, 2}]}, 
   Flatten[Table[Subscript[W, c, i], {c, 1, 2}, {i, 1, 2}]]]

Here is the combined model:

{Subscript[e, 1], Subscript[e, 2]} = {1, 2}; 
{Subscript[H, 1], Subscript[H, 2]} = {2, 1}; 
{Subscript[d, 1], Subscript[d, 2]} = {1, 2}; 
{Subscript[A, 1], Subscript[A, 2]} = {2, 1}; 
NMinimize[{Sum[Subscript[e, t]*Subscript[H, z]*Subscript[X, t, z], 
         {t, 1, 2}, {z, 1, 2}] + Sum[Subscript[d, c]*Subscript[A, i]*
           Subscript[W, c, i], {c, 1, 2}, {i, 1, 2}], 
     And @@ 
    Flatten[Table[Element[Subscript[X, t, z], Integers], {t, 1, 2}, 
             {z, 1, 2}]] && 
   And @@ Flatten[Table[0 <= Subscript[X, t, z] <= 1, 
             {z, 1, 2}, {t, 1, 2}]] && 
       And @@ Flatten[Table[Element[Subscript[W, c, i], Integers], 
             {c, 1, 2}, {i, 1, 2}]] && 
       And @@ Flatten[Table[0 <= Subscript[W, c, i] <= 1, {c, 1, 2}, 
             {i, 1, 2}]] && 
   And @@ Table[Sum[Subscript[X, t, z], {z, 1, 2}] == 
             1, {t, 1, 2}] && 
       And @@ 
    Table[Sum[Subscript[X, t, z], {t, 1, 2}] == 1, {z, 1, 2}] && 
       And @@ 
    Table[Sum[Subscript[W, c, i], {c, 1, 2}] == 1, {i, 1, 2}] && 
       And @@ 
    Table[Sum[Subscript[W, c, i], {i, 1, 2}] == 1, {c, 1, 2}]}, 
   {Flatten[Table[Subscript[X, t, z], {t, 1, 2}, {z, 1, 2}]], 
     Flatten[Table[Subscript[W, c, i], {c, 1, 2}, {i, 1, 2}]]}]

Answer 1

The error message is very clear:

NMinimize::lvar: "Variables {{Subscript[X, 1,1],Subscript[X, 1,2],Subscript[X, 2,1],Subscript[X, 2,2]},{Subscript[W, 1,1],Subscript[W, 1,2],Subscript[W, 2,1],Subscript[W, 2,2]}} should be a list of variables, with each element being a variable, or a list containing a variable and lower and upper bounds for the starting region for that variable. "

Obviously all your variables are not in one list but two. This is easily solved by using an extra flatten.

Here is the full code:

{Subscript[e, 1], Subscript[e, 2]} = {1, 2}; {Subscript[H, 1], 
  Subscript[H, 2]} = {2, 1}; {Subscript[d, 1], Subscript[d, 2]} = {1, 
  2}; {Subscript[A, 1], Subscript[A, 2]} = {2, 
  1}; NMinimize[{Sum[
    Subscript[e, t]*Subscript[H, z]*Subscript[X, t, z], {t, 1, 2}, {z,
      1, 2}] + 
   Sum[Subscript[d, c] Subscript[A, i] Subscript[W, c, i], {c, 1, 
     2}, {i, 1, 2}], 
  And @@ Flatten[
     Table[Element[Subscript[X, t, z], Integers], {t, 1, 2}, {z, 1, 
       2}]] && And @@ 
    Flatten[Table[
      0 <= Subscript[X, t, z] <= 1, {z, 1, 2}, {t, 1, 2}]] && 
   And @@ Flatten[
     Table[Element[Subscript[W, c, i], Integers], {c, 1, 2}, {i, 1, 
       2}]] && And @@ 
    Flatten[Table[
      0 <= Subscript[W, c, i] <= 1, {c, 1, 2}, {i, 1, 2}]] && 
   And @@ Table[Sum[Subscript[X, t, z], {z, 1, 2}] == 1, {t, 1, 2}] &&
    And @@ Table[Sum[Subscript[X, t, z], {t, 1, 2}] == 1, {z, 1, 2}] &&
    And @@ Table[Sum[Subscript[W, c, i], {c, 1, 2}] == 1, {i, 1, 2}] &&
    And @@ Table[Sum[Subscript[W, c, i], {i, 1, 2}] == 1, {c, 1, 2}]},
  Flatten@{Flatten[Table[Subscript[X, t, z], {t, 1, 2}, {z, 1, 2}]], 
   Flatten[Table[Subscript[W, c, i], {c, 1, 2}, {i, 1, 2}]]}]