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.