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Benders, Nested Benders and Stochastic Programming: An Intuitive Introduction

James Murphy(jm362***at***cam.ac.uk)

Abstract: This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of Benders decomposition and of its application to two-stage stochastic programming problems (also known in this context as the L-shaped method), then extends this to multi-stage problems as the Nested Benders algorithm. The article is aimed at readers with some knowledge of linear and possibly stochastic programming but aims to develop most concepts from simple principles in an understandable way. The focus is on intuitive understanding rather than rigorous proofs.

Keywords: Benders, Nested Benders, stochastic programming, linear programming, constrained optimization, L-shaped method, decomposition methods, cutting-plane methods

Category 1: Stochastic Programming

Citation: Cambridge University Engineering Department Technical Report, CUED/F-INFENG/TR.675, December 2013

Download: [PDF]

Entry Submitted: 12/11/2013
Entry Accepted: 12/11/2013
Entry Last Modified: 12/11/2013

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