Showing papers by "Abraham Charnes published in 1958"
TL;DR: In this paper, an integrated series of operations research studies directed toward improvement in such scheduling methods is presented. But the focus is on essentials of the mathematical model and other phases of the OR studies are brought in only as required.
Abstract: Scheduling heating oil production is an important management problem. It is also a complex one. Weather and demand uncertainties, allocation of production between different refineries, joint-and by-product relations, storage limitations, maintenance of minimal supplies and many other factors need to be considered.
This paper is concerned with one of an integrated series of operations research studies directed toward improvement in such scheduling methods. Emphasis is on essentials of the mathematical model. Institutional features and other phases of the OR studies are brought in only as required.
632 citations
TL;DR: In this article, the optimal allocation of search effort in convex programming is formulated as a convex optimization problem, and a sketch of how extensions may also be effected to continuous distributions.
Abstract: This paper will be concerned with formulating the optimum allocation of search effort as a problem in convex programming so that their solutions may be made amenable to treatment by the adjacent extreme point methods of linear programming. Attention will be concentrated on discrete (statistical) distributions because this class of cases admits of the easiest and most straight-forward treatment. A sketch will then be given of how extensions may also be effected to continuous distributions.
118 citations
TL;DR: Since the semiradical o-(S) of a semiring S is contained in every semimaximal semimodular left ideal L, this implies that u(S)S < a (S) < L, hence a(P) < PL, and it is shown if r ¢ v(S), then there exists a semiprimitive ideal P such that r f P.
Abstract: THEOREM 8. The semiradical of a semiring is the intersection of the semiprimitive ideals. Proof: Since the semiradical o-(S) of a semiring S is contained in every semimaximal semimodular left ideal L, this implies that u(S)S < a(S) < L, hence a(S) < PLConversely, we shall show if r ¢ v(S), then there exists a semiprimitive ideal P such that r f P. By Lemma 10 (left and right interchanged) we know that rS f a(S) and thus there exists an element x of S such rx f a(S). By Theorem 7 there exists a semimaximal semimodular left ideal L such that rx f L. This implies that r f PL.
30 citations