We study two continuous knapsack sets Y≥ and Y≤ with n integer, one unbounded continuous and m bounded continuous variables in either ≥ or ≤ form. When the coefficients of the integer variables are integer and divisible, we show in both cases that the convex hull is the intersection of...

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...

We study the convex hull of the continuous knapsack set which consists of a single inequality constraint with n non-negative integer and m non-negative bounded continuous variables. When n = 1, this set is a slight generalization of the single arc flow set studied by Magnanti, Mirchandani, and...

We explore one method for finding the convex hull of certain mixed integer sets. The approach is to break up the original set into a small number of subsets, find a compact polyhedral description of the convex hull of each subset, and then take the convex hull of the union of these polyhedra....

We consider a multi-item lot-sizing problem in which there are demands, and unit production and storage costs. In addition production of any mix of items is measured in batches of fixed size, and there is a fixed set-up cost per batch in each period. Suppose that the unit production costs are...

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...