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Towards Data Science0 Hot0 comments34 min read
How Benders Decomposition Works Part I: Optimality Cuts
Benders decomposition is a powerful optimization technique that splits mixed-integer programs into a master problem (handling strategic/binary decisions) and a subproblem (handling operational decisions). The master iteratively proposes solutions, the subproblem evaluates them via LP duality, and optimality cuts are added to progressively tighten the master's cost estimate until lower and upper bounds converge. The post walks through the algorithm's history, derives optimality cuts from LP duality theory, solves a toy example by hand step-by-step, then applies the method to the uncapacitated facility location problem. A full Python implementation using Pyomo and the open-source HiGHS solver is provided, converging in 9 iterations on a 5-facility, 20-customer instance.
Source: https://towardsdatascience.com/how-benders-decomposition-works-part-i-optimality-cuts. 8sync News only summarizes and links out; content copyright belongs to the authors and original sources.
