Showing papers by "Abraham Charnes published in 1970"
TL;DR: This paper considers a distribution model with upper and lower bounds on the number of units shipped from an origin or to a destination, and generalization of the classical distribution problem makes the model more versatile from a theoretical standpoint and more usable from an applications viewpoint.
Abstract: This paper considers a distribution model with upper and lower bounds on the number of units shipped from an origin or to a destination. Our problem differs from the classical distribution model in which the node shipping amounts are, by contrast, specified exactly. This generalization of the classical distribution problem not only makes the model more versatile from a theoretical standpoint but also makes the model more usable from an applications viewpoint.
23 citations
TL;DR: These solutions are quite elementary and the decision criteria given are easily interpreted, and are not necessary for the three applications in capital budgeting, production planning, and input-output analysis given in the paper.
Abstract: This paper derives explicit solutions for a class of linear (inequality) economic models heretofore treated by linear programming. These solutions are quite elementary and the decision criteria given are easily interpreted. The explicit solutions may involve the inversion of a single matrix, but even this is not necessary for the three applications in capital budgeting, production planning, and input-output analysis given in the paper.
12 citations
10 citations
TL;DR: A certain class of distribution problems has been treated incorrectly and ambiguously in two major and widely read texts on linear programming, namely, even if all the shipping costs are nonnegative, an optimal solution may ship more than the minimum demand to a destination.
Abstract: A certain class of distribution problems has been treated incorrectly and ambiguously, respectively, in two major and widely read texts on linear programming. This note traces the nature of this mistreatment to a paradoxical solution property of this class of problems, namely, even if all the shipping costs are nonnegative, an optimal solution may ship more than the minimum demand to a destination.
5 citations
TL;DR: In this paper, the authors present models for planning the social development of a country, which are intended to provide some understanding and assessment of inter-temporal changes in social groups through industrial, educational, health, etc.
Abstract: This paper discusses models for planning the social development of a country. These models are intended to provide some understanding and assessment of inter-temporal changes in social groups through industrial, educational, health, etc. opportunities and constraints over a time horizon. They thus include constraints and goals for planning the improvement in living conditions and the upgrading of different segments of society. The models also make extensive use of various sociological factors. While these models are presented in the context of a developing nation, the concepts, attributes and formalisms are not limited to such cases.
4 citations
TL;DR: The extension of the linear approximation problem minimize subject to AX + ϵ = b to the case where the elements of b are independent random variables with known distributions is extended by the use of chance constraints.
Abstract: This paper considers the extension of the linear approximation problem minimize ‖ϵ‖ subject to AX + ϵ = b to the case where the elements of b are independent random variables with known distributions. This extension is accomplished by the use of chance constraints. An analysis of this stochastic problem shows that the problem can be solved by some of the powerful computational methods of approximation theory.
4 citations