Showing papers by "Abraham Charnes published in 1974"
TL;DR: This paper presents an algorithm for solving interval linear programming (IP) problems that is a finite iterative method that solves a full row rank, ( IP) problem with only one additional constraint.
Abstract: This paper presents an algorithm for solving interval linear programming (IP) problems. The algorithm is a finite iterative method. At each iteration it solves a full row rank, (IP) problem with only one additional constraint.
23 citations
TL;DR: A theoretical justification and an Illustrative implementation of a method for generating linear programming test problems with known solutions that permits the generation of test problems that are of arbitrary size and have a wide range of numerical characteristics are presented.
Abstract: Users of linear programming computer codes have realized the necessity of evaluating the capacity, effectiveness, and accuracy of the solutions provided by such codes. Large scale linear programming codes at most installations are assumed to be generating correct solutions without ever having been “bench-marked” by test problems with known solutions. The reason for this failure to adequately test the codes is that rarely are there large problems with known solutions readily available. This paper presents a theoretical justification and an Illustrative implementation of a method for generating linear programming test problems with known solutions. The method permits the generation of test problems that are of arbitrary size and have a wide range of numerical characteristics.
21 citations
TL;DR: In this article, a linear programming method for the calculation of the optimal strategies and the value of a two-person zero-sum game is presented. But the characteristic function for a constrainedn-person game may not satisfy properties, such as superadditivity, usually associated with a characteristic function.
Abstract: The usual properties of a characteristic function game were derived byvon Neumann andMorgenstern from the properties of a game in normal form. In this paper we give a linear programming principle for the calculation of the characteristic function. The principle is a direct application ofCharnes' linear programming method for the calculation of the optimal strategies and the value of a two-person zero-sum game. The linear programming principle gives another method for proving the standard properties of a characteristic function when it is derived from a game in normal form. Using an idea originated byCharnes for two person games, we develop the concept of a constrainedn-person game as a simple, practical extension of ann-person game. However the characteristic function for a constrainedn-person game may not satisfy properties, such as superadditivity, usually associated with a characteristic function.
18 citations