# Questions tagged [benders-decomposition]

For questions related to Benders decomposition, a type of optimization algorithm in which certain variables are optimized in a "master problem," the values of those variables are fixed, the remaining variables are optimized in a "subproblem," cuts are generated to be added to the master problem, and the method repeats.

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### Automated Benders Using Annotations

I'm trying to solve an optimization model using Automated Benders with annotations using CPLEX library in C++. I've defined a master problem and N (number of supply nodes in my model's network) ...
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### How should I implement Benders Decomposition with annotations in C++ using CPLEX library

I'm a beginner in C++ and want to implement Benders decomposition in C++ using CPLEX. I'm gonna use it for a special case study, so I need to customize the cuts to minimize the optimality gap. However,...
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### 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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### Difference between Optimality cuts and Feasibility cuts for L shaped method in stochastic programming?

What is the difference between Optimality cuts and Feasibility cuts for L shaped method in stochastic programming? Like for the following problem they used Optimality cuts,  \begin{aligned} & z=\...
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1 vote
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### Further decomposing master problem in benders

In the benders decomposition, is it possible to decompose the master problem as follows and let the subproblem become the subproblem of the new subproblem? Let's say that we have the following problem....
441 views

### Dantzig-Wolfe vs Benders Decomposition on the dual problem - Computational differences

My question is a follow-up to this one: Relationship between Bendersā decomposition and Dantzig-Wolfe decomposition. Here what is being discussed is the relationship between the two methods, and it is ...
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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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1 vote
356 views

### Apply Benders decomposition approach in CPLEX with python while using docplex class

I am new to cplex with python. I want to solve a problem using the Benders decomposition approach. Where I want to use UserCutCallback and LazyConstraintCallback. I am writing code in script format (...
1k views

### Is Dantzig-Wolfe and Benders' Decomposition still applied in Operations Research?

A year ago, I had taken my master's degree class Optimisation Theory, and we were learning Dantzig-Wolfe Decomposition and Benders' Decomposition. I found it very challenging to use these algorithms ...
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### Benders decomposition for a dense MILP

I am trying to solve a large MILP, but it seems like dense problems can be very difficult for moderns solvers. I tried to solve the problem described below considering only constraints (1) and (2) ...
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149 views

### multi stage stochastic programming algorithm

I have a multi-stage stochastic programming model. I have 3 groups of variables: the first group takes values at the beginning of the planning horizon before the first realization and does not change ...
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### Adding cuts doesn't change the solution of master problem in Benders decomposition

From the problem Unbounded master problem in Benders decomposition, it can happen that after adding cuts the master problem is still unbounded. The answers in the post suggest adding bound for the ...
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821 views

### Unbounded master problem in Benders decomposition

After a few iterations, my master problem with optimality cuts is still unbounded. I wonder if it's possible in theory? If it's possible, how to deal with the unbounded master problem?
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### How to find extreme rays

I am applying Benders decomposition and the dual is unbounded. I need to find the extreme rays to proceed, but I am not sure how to do that. Following is an example problem, can someone explain how ...
185 views

### How to fix unbalanced multi-commodity network flow with equal supply and demand?

I have a fairly large network with eleven commodities and arc capacities that are commodity-dependent (i.e. an arc may have a higher capacity for one commodity than another). I'm solving a protection-...
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1 vote
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### How to eliminate large matrix coefficients and large RHS warning in Gurobi

I'm solving a large network flow problem using Gurobi to do Benders decomposition in Python. The imported .csvs contain values that typically fall in either zero, the range of [20,200], or with a ...
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