Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Say I have 2 LPs, LP_1 and LP_2 which have real and integer variables and a staircase structure (i.e. the solution and feasible region of LP_2 depends on the solution of LP_1).

$LP_1$ has the form

$\min c_1 (x_1 + z_1)$
$ s.t.$
$ A_1 (x_1 + z_1) = b_1$
$ x_1, z_1 \geq 0 $
$ x_1, \in \mathbb{R^{n_1^{real}}}, z_1 \in \mathbb{Z^{n_1^{int}}}$

and the second LP $LP_2$ has the form

$\min c_2 (x_2 z_2)$
$s.t.$
$ A_2 (x_2 + z_2) + E_2 (x_1 + z_1) = b_2$
$ x_2, z_2 \geq 0 $
$ x_2, \in \mathbb{R^{n_2^{real}}}, z_2 \in \mathbb{Z^{n_2^{int}}}$

Given a trial solution $x_1, z_1$, how can I solve $LP_2$ and then generate a cutting plane using Bender's Decomposition to add to $LP_1$? Any advice is appreciated - I believe the answer involves "lifting" though I'm not sure on what it is and why it works.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.