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Optimization - production in two categories

0

$begingroup$

I ran in to this idea in a homework assignment, but here's the general idea which I'm having trouble formulating.

Imagine you have two producers $x_1$ and $x_2$ which can produce in two different categories (call them $y_1$ and $y_2$). Let's say $x_1$ can make $M$ in $y_1$ and $N-M$ in $y_2$. $x_2$ has a similar constraint of making $T$ in $y_1$ and $N-T$ in $y_2$. And you have some requirements for $y_1$ and $y_2$ production. This roughly gives something like:

Minimize $textcost_x_1 cdot x_2 + textcost_x_2 cdot x_2$
such that
beginalign
M cdot x_1 + T cdot x_2 &geq y_1_textproduction_requirement \
(N-M) cdot x1 + (N-T) cdot x_2 &geq y_2_textproduction_requirement \
x_1, x_2 &text are integers.
endalign
This is incorrect though, because not all $x_1$ or $x_2$ need to produce the same number of $y_1$ or $y_2$. Thoughts on formulating this? Concepts that will help with this? Another thing, though I don't think it really matters here, is that $x_1$ and $x_2$ are integers.

optimization integer-programming

share|cite|improve this question

edited Apr 2 at 2:14

Brian

1,499416

asked Apr 2 at 1:38

AlexAlex

1014

$endgroup$

add a comment | 

0

$begingroup$

I ran in to this idea in a homework assignment, but here's the general idea which I'm having trouble formulating.

Imagine you have two producers $x_1$ and $x_2$ which can produce in two different categories (call them $y_1$ and $y_2$). Let's say $x_1$ can make $M$ in $y_1$ and $N-M$ in $y_2$. $x_2$ has a similar constraint of making $T$ in $y_1$ and $N-T$ in $y_2$. And you have some requirements for $y_1$ and $y_2$ production. This roughly gives something like:

Minimize $textcost_x_1 cdot x_2 + textcost_x_2 cdot x_2$
such that
beginalign
M cdot x_1 + T cdot x_2 &geq y_1_textproduction_requirement \
(N-M) cdot x1 + (N-T) cdot x_2 &geq y_2_textproduction_requirement \
x_1, x_2 &text are integers.
endalign
This is incorrect though, because not all $x_1$ or $x_2$ need to produce the same number of $y_1$ or $y_2$. Thoughts on formulating this? Concepts that will help with this? Another thing, though I don't think it really matters here, is that $x_1$ and $x_2$ are integers.

optimization integer-programming

share|cite|improve this question

edited Apr 2 at 2:14

Brian

1,499416

asked Apr 2 at 1:38

AlexAlex

1014

$endgroup$

add a comment | 

$begingroup$

I ran in to this idea in a homework assignment, but here's the general idea which I'm having trouble formulating.

Imagine you have two producers $x_1$ and $x_2$ which can produce in two different categories (call them $y_1$ and $y_2$). Let's say $x_1$ can make $M$ in $y_1$ and $N-M$ in $y_2$. $x_2$ has a similar constraint of making $T$ in $y_1$ and $N-T$ in $y_2$. And you have some requirements for $y_1$ and $y_2$ production. This roughly gives something like:

Minimize $textcost_x_1 cdot x_2 + textcost_x_2 cdot x_2$
such that
beginalign
M cdot x_1 + T cdot x_2 &geq y_1_textproduction_requirement \
(N-M) cdot x1 + (N-T) cdot x_2 &geq y_2_textproduction_requirement \
x_1, x_2 &text are integers.
endalign
This is incorrect though, because not all $x_1$ or $x_2$ need to produce the same number of $y_1$ or $y_2$. Thoughts on formulating this? Concepts that will help with this? Another thing, though I don't think it really matters here, is that $x_1$ and $x_2$ are integers.

optimization integer-programming

share|cite|improve this question

edited Apr 2 at 2:14

Brian

1,499416

asked Apr 2 at 1:38

AlexAlex

1014

$endgroup$

share|cite|improve this question

edited Apr 2 at 2:14

Brian

1,499416

asked Apr 2 at 1:38

AlexAlex

1014

share|cite|improve this question

edited Apr 2 at 2:14

Brian

1,499416

asked Apr 2 at 1:38

AlexAlex

1014

edited Apr 2 at 2:14

Brian

1,499416

edited Apr 2 at 2:14

Brian

1,499416

asked Apr 2 at 1:38

AlexAlex

1014

asked Apr 2 at 1:38

AlexAlex

1014