Abstract
The duality theory of programming under uncertainty is developed for the special case of proportional penalties and normal probability distributions, and from this an approximately optimal sampling plan is determined by the solution to a separable nonlinear programming problem with linear constraints. The duality theory is interesting per se; in particular, it evidences clearly the specific roles of the means and standard deviations in determining the solution. The duality theory of programming under uncertainty has been available for some time, at least in principle, by application of the general theory. It is worthwhile, however, to examine specially structured problems in finer detail, and that is the purpose of this paper.
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