# Questions tagged [dantzig-wolfe-decomposition]

For questions on a method that transforms a subset of the linear inequalities of a linear program into an equivalent representation by its extreme points and rays; this generally introduces a large number of new variables.

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### How to deal with the sub-problem with zero reduced cost in D-W decomposition

The specific linear programme has an optimal solution as $x_1 = 0.66$, $x_2 = 1.33$, $x_3 = 12.2$, $x_4 = 0.0$ and the objective value is $33.3$. While the problem is solved by D-W decomposition ...
235 views

### Can I apply decomposition methods for this scheduling problem

I have a centralized optimization problem for a residential area in the context of a smart grid and load flexibility. So let's say I have 10 buildings and each of them has an electric heating device. ...
52 views

### Dantzig decomposition and Column Generation for equality constraints

I was trying to apply Dantzig Decomposition followed by Column Generation. The following is how I was taught. \begin{array}{l} \text { Minimize }-10 x_1-2 x_{2}-4 x_{3} \\ \text { subject to: } x_{1}+...
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### How can I initialize the Restricted Master Problem in Dantzig-Wolfe decomposition?

I am attempting to solve a linear program via Dantzig-Wolfe decomposition. It is the first time I implement this method. Before the pricing iterations start, I need to provide an initial set of ...
148 views

### Is Dantzig-Wolfe decomposition finite if variables are unbounded?

Most descriptions of the Dantzig-Wolfe decomposition, I have seen end up with subproblems like this: $$\min_{x_j \in \mathbb{R}^n} \{ (\pi A_j - c_j)x_j \mid x_j \in P_j \}$$ They argue that $P_j$ ...
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### Column generation for TSP

For teaching purposes, I would like to solve the Travelling Salesman Problem with a column generation approach. In the academic literature, an approach is proposed (for example here), where columns ...
353 views

### What are the modern optimization methods for large systems?

I came across the preface of Optimization Theory for Large Systems (you can read it in Amazon). The author claims in the table (page v) that some of the methods such as Dantzig Wolfe decomposition, ...