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...

We consider here the mixing set with flows: s + xt = bt, xt = yt for 1 = t = n; s [belongs] R+exp.1+, ˙ [belongs] R+exp.n, y [belongs] Z+exp.n. It models the "flow version" of the basic mixing set introduced and studied by Gunluk and Pochet, as well as the most simple stochastic lot-sizing...

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...

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....