Showing papers in "International Journal of Computer Mathematics in 1964"
TL;DR: The decomposition algorithm of Dantzig and Wolfe is a procedure for the solution of linear programs using a generalized extension of the simplex method and a worked numerical example given.
Abstract: The decomposition algorithm of Dantzig and Wolfe is a procedure for the solution of linear programs using a generalized extension of the simplex method. In this paper the algorithm is described and a worked numerical example given. No new results are presented. The paper is intended to further publicise the method. The terminology used is that agreed upon by the participants at a workshop on the decomposition algorithm held by Mathematica in February, 1962 under the sponsorship of the Special Interest Group of Mathematical Programming of the Association of Computing Machinery.
82 citations
TL;DR: In this article, the authors present a competitive strategy model for the construction industry, which is based on the competitive strategy models for the game theory problem of game theory, and apply it to the real world.
Abstract: (1964). Competitive strategy models for the construction industry. International Journal of Computer Mathematics: Vol. 1, No. 1-4, pp. 251-272.
9 citations
5 citations
TL;DR: In this article, the problem of finding an optimal control program for transits in a transportation system is formulated as a problem in discrete-variable linear programming and a solution method is proposed.
Abstract: The problem of finding an optimal control program for transits in a transportation system is discussed. The problem is formulated as a problem in discrete-variable linear programming and a solution method is proposed.
2 citations
TL;DR: In this paper, a search procedure for fitting experimental observations to a nonlinear function of several variables or optimizing a function having several independent parameters is described, where the objective is to minimize the least square of the error between experimental measurements and values of the function.
Abstract: In many engineering problems involving optimization of a function or fitting experimental data to a function of several variables, analytical procedures fail, either due to the complexity of the problem or difficulties involved in obtaining analytical form for partial derivatives. When the number of independent variables of the function to be optimized gets large, and if the function has many nonlinearities and local optima, the well-known optimization methods1′3′4 fail to guarantee a global optimum for the function. This is often encountered in functional-fit problems where one tries to minimize the least square of the error between experimental measurements and values of the function. In such cases one invariably has to resort to a search procedure.In this note we describe a search procedure to be used on a digital computer for either fitting experimental observations to a nonlinear function of several variables or optimizing a function having several independent parameters.
1 citations
1 citations
1 citations
TL;DR: In this article, an application of the Monte Carlo technique employed in calculating reflected radiation from a broad beam of gamma radiation normally incident on a plane and smooth surface is presented, where the reflecting medium is infinitely thick and homogeneous.
Abstract: The method presented in this paper is an application of the Monte Carlo technique employed in calculating reflected radiation from a broad beam of gamma radiation normally incident on a plane and smooth surface. The reflecting medium is infinitely thick and homogeneous. It should be noted that the results of the calculation are almost 100 per cent accurate for thicknesses over 20 mean free paths † and for engineering purposes are useful between 10 and 20 mean free paths within a few per cent of accuracy. The incident radiation considered here is mono-energetic. In case of a spectrum of energies of the incident radiation the beam first has to be lumped in discrete energy bins and for each bin the mean energy must be evaluated, after which each is used as a mono-energetic radiation. In order to be able to reuse calculated values without repetition of the computer work it is planned to perform calculations for energies from 0.5 Mev to 10 Mev in 0.5 Mev energy increments and to print the results as a set of t...
1 citations
TL;DR: In this article, a conditioned system of linear algebraic equations is presented. But this system is not a deterministic system, and it cannot be expressed in terms of a set of equations.
Abstract: (1964). III Conditioned systems of linear algebraic equations. International Journal of Computer Mathematics: Vol. 1, No. 1-4, pp. 36-50.
1 citations
TL;DR: The application of methods from queueing theory to the analysis of centralized supervisory systems for industrial processes is discussed and a method is given for determining the percent of information lost or the probability of structural information losses for complex telemetering systems.
Abstract: The application of methods from queueing theory to the analysis of centralized supervisory systems for industrial processes is discussed. When information transmittal is sporadic, one of the quality criteria for operation of complex telemetering systems is the percent of information lost or the probability of structural information losses. A method is given for determining this criterion for a system which has one or more common receivers at a central point and has a single traffic queue in the storage devices (single-stage systems).
TL;DR: The basic application of analog computer methods to the solution (modelling) of dynamic economic problems is discussed and the necessity and feasibility of utilizing the built-in expansion equipment available in modern analog computers are considered.
Abstract: The basic application of analog computer methods to the solution (modelling) of dynamic economic problems is discussed. Consideration is given, especially, to both the necessity and feasibility of utilizing for this purpose the built-in expansion equipment available in modern analog computers. In addition, the solution to several fundamental problems of economic modelling are presented and discussed in their relation to dynamic computation in the broad area of economic analysis
TL;DR: This chapter discusses how to simulate a random process on a computer to obtain independent realizations of it and the mathematical expectation of this random variable M{(x, y, . . . ) will be a function of the parameters.
Abstract: Suppose we are given a random process depending on one or more parameters x, y, . . . . and that we can simulate this process on a computer to obtain independent realizations of it. Suppose further that some function, whose value for each realization is a random variable {(x, y, . . . , ) depending on the parameters of the process, is associated with the random process. The mathematical expectation of this random variable M{(x, y, . . . ) will be a function of the parameters: