A Note on Professor Manne's "Dominance" Theorem

Professor Manne's paper recently appearing in this Journal (Manne, A. S. 1958. Programming of economic lot sizes. Management Sci. 4 (2, January).) is an ingenious application of linear programming technique to what may have hitherto been regarded as an intractable non linear situation. The excellences of the paper are, however, marred by a gap in the proof of the "Dominance" theorem. It is the aim of this communication to point out that, although the constructive proof offered by Manne is vulnerable to counter-example, an alternative, fairly simple, proof can be given. The theorem being true, the important results of the paper are not weakend.