A NOTE ON AN EFFICIENT ZERO-ONE FORMULATION OF THE MULTILEVEL LOT-SIZING PROBLEM

In a recent paper, McKnew, Saydam, and Coleman [3] presented a novel zero-one integer programming formulation of the multilevel dynamic, deterministic lot-sizing problem in assembly systems. they stated that "the relaxed linear programming solution to this formulation will always be integer" [3, p. 280] since the constraint matrix is totally unimodular. In this note, we point out that the constraint matrix is not totally unimodular and therefore the authors' claim that a linear relaxation of the zero-one integer formulation always yields an integer solution is not true.