# Questions tagged [decomposition]

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### Is there a way to calcuate the maximum number of cuts in a Benders decomposition?

Since the benders algorithm is finite, there a maximum number of cuts that could theoretically be added. The worst case is that I add cuts for all extreme points and all extreme rays that are part of ...
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### How do you derive the Benders feasibility cuts?

starting off with a MIP that I want to solve using Benders. so in Benders Decomposition, you add feasibility cuts in the following form: $v^j (b - Ax) \geq 0$ with $j \in J$ being the set of extreme ...
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I am dealing with the following problem as follows. $$\min \sum_{i,j}( x_{i}+y_{j}+q_{ij}+w_{i})$$ $$\text{s.t.} x_{i}+y_{j}+q_{ij}+w_{i} \geq b_{ij}, \forall i,j$$ Is it possible to handle this ... 73 views

### Benders with MINLP subproblem as the pricing problem of Dantzig Wolfe

I have a convex MINLP that after a Dantzig-Wolfe reformulation, passes most of the difficulty onto the pricing problem, which becomes a convex MINLP itself. The pricing problem should be solvable with ...
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### Minimizing sum of similar functions with a dependence

Consider an objective function in the form of minimization of maximization that is the sum of $N$ similar functions $f\left(x\right)\ge 0$, $\ \forall x$. The summation of all variables is constant (e....
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### Benders Decomposition for Fixed Charge Transportation Problem

I am trying to write down the steps in Benders decomposition for the Fixed Charge Transportation Problem and was hoping someone could confirm/deny whether my understanding of it is correct. The ...
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I have a multi-stage model with both binary and continuous first-stage investment variables and continuous operational next-stage variables:  \sum_{s} \rho_{s} \left[ x_{s} + y_{s} + \sum_{t}(y^{op}...