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This article aims to explain the Nested Benders algorithm for the solution oflarge-scale stochastic programming problems in a way that is intelligible tosomeone coming to it for the first time. In doing so it gives an explanation ofBenders decomposition and of its application to two-stage stochasticprogramming problems (also known in this context as the L-shaped method), thenextends this to multi-stage problems as the Nested Benders algorithm. Thearticle is aimed at readers with some knowledge of linear and possiblystochastic programming but aims to develop most concepts from simple principlesin an understandable way. The focus is on intuitive understanding rather thanrigorous proofs.

Benders, Nested Benders and Stochastic Programming: An Intuitive Introduction