Issue No. 09 - September (1982 vol. 31)
J. Weglarz , Institute of Control Engineering, Technical University of Poznan
V. A. Signaevskn is right that Theorem 4 holds only for concave p and that its proof may then be simplified (the thesis is not trivial). However, the practical meaning of this observation is rather not of very great importance. This follows from the fact that in practice the functions ei(si) are convex (in particular linear) or have a concave part for small si, and thus pi(si) are concave (see Corollary 1) or may be replaced by qi(si) which are concave as shown in Fig. 2. This last operation generally leads, of course, to approximate results; it should be noticed however, that the assumption concerning identical tasks (in the sense of pi(si) and vi) is in fact also an approximation of a real world situation.
J. Weglarz, "Author's Reply<sup>2</sup>," in IEEE Transactions on Computers, vol. 31, no. , pp. 898, 1982.