# Questions tagged [cutting-planes]

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### How to redefine separation procedure to get 0-1 knapsack with odd number of items

So I have a 0-1 knapsack problem: \begin{align}\max&\quad \sum_j c_j x_j\\ \text{s.t.}&\quad \sum_j a_j x_j \leq b\\ &\quad x_j \in \{0,1\}\end{align} but it has an additional requirement ...
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### A specific case of a resource constrained project scheduling problem with partially renewable resources (RCPSP/$\pi$) - OR-Tools

I've been trying solve a specific case of the resource constrained project scheduling problem with partially renewable resources (RCPSP/$\pi$ in the literature e.g. this paper). These resources are ...
138 views

### What to do with cuts (constraints) when a fixation is contrary to a RHS in a ILP / LP relaxation?

I am trying to understand an algorithm in a paper by Crévits et al. (2012)1 (see algorithm 2, the cuts I'm referring to are from the reduced costs). It uses a series of successive cuts on a linear ...
66 views

### How to implement CPLEX user cuts using CPXaddusercuts in C API?

I am trying to use CPXaddusercuts to add cutting planes, which have not been violated yet but are likely to be violated as we go down the branch & bound tree, to the list (pool) of constraints. As ...
189 views

### Objective Integrality Cuts

Consider a mixed integer linear program with an objective function that includes only integer variables. Objective integrality cuts are known as a class of valid inequalities that can be added to ...
281 views

### Cplex : The cutting stock problem

The problem below aims to minimize the cutting leftovers from each cut : A company manufactures desks for kids gardens and primary schools, colleges and high schools. The leg of these deks all have ...
156 views

### Cutting-planes application procedure for a specific problem

Sort of following up with this question. I reformulated another model to make it convex and possibly solve it with some cut generation method. I would like to double-check whether I am doing it ...
127 views

### Improving cuts from sub-problem with problem-specific hierarchical information

I'm solving an assignment-alike problem with a Logic-based Benders decomposition-alike (LBBD) method. The master problem provides an assignment, which is checked in the sub-problem. Define the set of ...
### Why isn't $x_2+x_3+x_4\le 2$ a cutting plane?
In my textbook, to generate cutting planes, they tell you to proceed as follows: A procedure for generating cutting planes: Select a ($\le$) constraint that has only nonnegative coefficients. ...