Much progress has been made in recent years in solving certain classes of production planning problems using mixed integer programming. One of the major challenges is how to make this expertise available and easy to use to the non-specialist and to the practitioners. Here we describe a modeling...

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...