Stochastic lot-sizing problem with deterministic demands and Wagner–Whitin costs

In this paper, we consider a two-stage stochastic uncapacitated lot-sizing problem with deterministic demands and Wagner–Whitin costs. We develop an extended formulation in the higher dimensional space that provides integral solutions by showing that its constraint matrix is totally unimodular. We also provide the integral polyhedron of the problem in the original space by projecting the extended formulation to the original space.