# Problem combining 2 models [closed]

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}]]}]

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## closed as too localized by Ajasja, tkott, Mr.Wizard♦Dec 11 '12 at 21:07

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@gert Welcome to the Mathematica Stackexchange! Please format your code using four indents or back-ticks (), so that people will find it easier to read your code. For more info check out the FAQ: mathematica.stackexchange.com/faq –  Ajasja Dec 11 '12 at 15:54

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}]]}]

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