Integer linear programming - auxillary binary range constraint variable
- Thread starter Akcope
- Start date
Looks like the forum downsized it. Here is a direct link: < link to objectionable page removed>
Last edited by a moderator:
- Joined
- Feb 4, 2004
- Messages
- 16,582
I'd put the image here, but it's way too wide. Whoever typed it up didn't wrap the text in a helpful manner. So, for other viewers, here's the text at the link:
I have two matrices of 1*n of variables:
. . . . .\(\displaystyle s_i,\, x_i\)
I would like to create a matrix of new variables (dimension n*k, where k is an arbitrary natural number). Using constraints, I would like the variables to have the following function:
. . . . .\(\displaystyle z_{ij}\, =\, \begin{cases}1&\mbox{ if }\, j\, \geq\, s_i\, \mbox{ and }\, j\, \leq\, x_i \\ 0&\mbox{ otherwise} \end{cases}\)
For example:
. . . . .\(\displaystyle s_i\, =\, 4\)
. . . . .\(\displaystyle x_i\, =\, 8\)
. . . . .\(\displaystyle z_{i5}\, =\, 1\)
My question is, how would I formulate the constraints of
. . . . .\(\displaystyle z_{ij}\)
?
If I have typoed something in the above, please reply with corrections. Thank you!
I have two matrices of 1*n of variables:
. . . . .\(\displaystyle s_i,\, x_i\)
I would like to create a matrix of new variables (dimension n*k, where k is an arbitrary natural number). Using constraints, I would like the variables to have the following function:
. . . . .\(\displaystyle z_{ij}\, =\, \begin{cases}1&\mbox{ if }\, j\, \geq\, s_i\, \mbox{ and }\, j\, \leq\, x_i \\ 0&\mbox{ otherwise} \end{cases}\)
For example:
. . . . .\(\displaystyle s_i\, =\, 4\)
. . . . .\(\displaystyle x_i\, =\, 8\)
. . . . .\(\displaystyle z_{i5}\, =\, 1\)
My question is, how would I formulate the constraints of
. . . . .\(\displaystyle z_{ij}\)
?
If I have typoed something in the above, please reply with corrections. Thank you!