For the problem of lot-sizing on a tree with constant capacities, or stochastic log-sizing with a scenario tree, we present various reformulations based on mixing sets. We also show how earlier results for uncapacitated problems involving (Q, SQ) inequalities can be simplified and extended....

We consider mixed-integer sets of the type M IX T U = {x : Ax b; xi integer, i I}, where A is a totally unimodular matrix, b is an arbitrary vector and I is a nonempty subset of the column indices of A. We show that the problem of checking nonemptiness of a set M IX T U is NP-complete when A...

Here we study the discrete lot-sizing problem with an initial stock variable and an associated variable upper bound constraint. This problem is of interest in its own right, and is also a natural relaxation of the constant capacity lot-sizing problem with upper bounds and fixed charges on the...