# 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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### How to determine if a given problem seems to be a good fit to be solved using combinatorial Benders decomposition

Combinatorial Benders decomposition is a mathematical programming technique consisting into dividing a problem into a master problem and a sub problem. The master problem is solved to optimality (or ...
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### Textbook recommendation for linear programming decomposition fundamentals

I am looking for a textbook on linear programming decomposition fundamentals. The book should be clear and easy-to-follow for self study and should include examples to illustrate the concepts.
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### Stochastic Facility Location Model

I am solving a stochastic facility location model using Benders decomposition (L-shaped algorithm). In each scenario, I want to allocate demands from origin to a fixed number of closest open ...
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### Stochastic programming MIP solvers

I am aware that Benders Decomposition is readily available in CPLEX and in SCIP; but are there any (free) solvers that provide off the shelf stochastic programming MIP algorithms or a nice to work ...
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### Relationship between Benders decomposition and Dantzig-Wolfe decomposition

It’s often said that “Benders decomposition is Dantzig-Wolfe applied to the dual”. How can this statement be made precise? I know that in Dantzig-Wolfe, cuts are added in one-to-one correspondence ...
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### How to handle an IP sub-problem with an objective function in Benders Decomposition

I have a question on Benders Decomposition (BD). Suppose I have an MILP model which can be decomposed into a master problem (MP) including integer and continuous variables and a subproblem (SP) ...
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### 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 do I check convergence in stochastic Benders?

So in the deterministic version of Benders, the main process works like this: I initialize my x-vector (Integer variables from the master problem) and solve the dual subproblem (SP). I add an ...
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1 vote