We consider mixed-integer sets of the type MIX TU = {x : Ax amp;#8805; b; xi integer, i amp;#8712; 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 MIX TU is NP-complete...

We consider here the mixing set with flows: s + xt amp;#8805; bt, xt amp;#8804; yt for 1 amp;#8804; t amp;#8804; n; s E IR, x E IR, y E Z. It models the flow version of the basic mixing set introduced and studied by Guuml;nluuml;k and Pochet, as well as the most simple stochastic lot-sizing problem with...

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...