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...

For the problem of lot-sizing on a tree with constant capacities, or stochastic lot-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 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...