Instances of the multi-item capacitated lot-sizing problem with setup times (MCL) often appear in practice, either in standard form or with additional constraints, but they have generally been difficult to solve to optimality. In MCL demand for multiple items must be met over a time horizon,...

We present and study a mixed integer programing model that arises as a sub-structure in any industrial applications. This model provides a relaxation of various capacitated production planning problems, more general fixed charge network flow problems, and other structured mixed integer programs....