Yet Another Note on "An Efficient Zero-One Formulation of the Multilevel Lot-Sizing Problem"

In "An Efficient Zero-One Formulation of the Multilevel Lot-Sizing Problem" [8] MCKNEW, SAYDAM, and COLEMAN claim the polynomial solvability of this particular production planning problem. Both, the proof given by MCKNEW et al. and a statement of its incorrectness by RAJAGOPALAN [10] contain errors, and the question remains whether the approach leads to a polyomial time algorithm. We show by means of an example that solving the linear program is not sufficient