I've been studying the Benders decomposition method to solve stochastic integer problems.

I've also stumbled across papers using a so called L-shaped-algorithm which also divides into master problem and sub problem.

Are these the same techniques? If not, what are the differences?


1 Answer 1


In the paper that proposed L-shaped method, you can find

In section 2, an algorithm which is essentially the same as the algorithm developed by Benders[3] is described and a geometric interpretation is given.

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-- Van Slyke, R. M., & Wets, R. (1969). L-shaped linear programs with applications to optimal control and stochastic programming. SIAM Journal on Applied Mathematics, 17(4), 638–663. https://doi.org/10.1137/0117061

So "Benders decomposition" and "L-shaped method" can be interchangeable.

However, when "L-shaped" is used, one implies the problem is stochastic, as you can find "stochastic programming" in the above title. While Benders decomposition is intended for a more general class of problems.

  • $\begingroup$ Thank you! Since I'm solely dealing with stochastic problems for now, I can use the methods synonymously. $\endgroup$ Commented Jul 13, 2023 at 14:31

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