The multi-level lot sizing problem with flexible production sequences

This paper considers a multi-level/multi-machine lot sizing problem with flexible production sequences, where the quantity and combination of items required to produce another item need not be unique. The problem is formulated as a mixed-integer linear program and the notion of echelon inventory is used to construct a new class of valid inequalities, which are called echelon cuts. Numerical results show the computational power of the echelon cuts in a branch-and-cut algorithm. These inequalities are compared to known cutting planes from the literature and it is found that, in addition to being strong and valid for the flexible production case, echelon cuts are at least as strong as certain classes of known cuts in the restricted fixed production setting.