Search

This paper presents a general model to be used in adjusting cash flows which occur over future time intervals to reflect the effects of continuous compounding and/or discounting. The method is illustrated by means of a hypothetical example. The framework of analysis employed here may be extended to other systems having similar characteristics of growth and decay. In the physical and biological sciences, it often happens that the rate of change in the quantity of a substance is proportional to the amount of the substance present at the time. In such cases, the associated system is said to be subject to "exponential growth" or "exponential decay." A classic example of this phenomenon is the continous decomposition of radioactive materials. In this instance, the rate of decomposition at any given time is proportional to the amount of material remaining at that time. Similarly, the reproduction of bacteria is a familiar process which, under certain conditions, involves exponential growth. Exponential models have been used to describe a wide variety of systems in the social sciences and medicine. For example, human populations under certain conditions are subject to exponential growth. Isard [10] cites several studies involving the use of an exponential form to predict changes in city population. This same methodolgy may be extended to analyses involving wildlife and marine population patterns, migration, disease epidemics, and other analogous economic and sociological systems. In this paper, the primary concern is with cash flow systems. It should be noted however, that the model developed here may be extended to other applications. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to determining the optimal facility locations for uncapacitated location problems in two stages. First, it is shown that a subset of all solutions to the uncapacitated public facility location problem can be obtained by considering a closely related private location problem. The exact nature of the problem is established using the Generalised Lagrange Multiplier results given by Everett. In the second section of the paper a particularly efficient parametric decomposition algorithm, which is based on the results of the first section, is presented. Computational results are given which summarize the current level of experience with the algorithm. [ABSTRACT FROM AUTHOR]

David P. Rutenberg [1] provided a method to solve separable nonlinear objective functions with large-scale linear constraints by using W. I. Zangwill's Convex Simplex Method [2]. However, here seem to be several errors in §4.3 [1, p. 397]. Two counterexamples to his conclusions are given in this paper. A revised definition of subproblem, therefore, an optimal criterion of the large-sealed program, is also given. [ABSTRACT FROM AUTHOR]

In a previous paper, APPELGREN (1969), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and- bound algorithm, where the branching is performed on one of the `essential' fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the DANTZIG-WOLFE decomposition, since the constraints generated in the master program have to be taken into account in the solution of the subprograms. The success in this case is due to the simple structure of the master LP problem. [ABSTRACT FROM AUTHOR]

This paper presents a decomposition procedure for extending the size of problems that can be solved using dynamic programming. It essentially consists of decomposing the tabular arrays of data into blocks of data, and then performing the dynamic programming calculations over the whole tabular array by calculating on each block separately. [ABSTRACT FROM AUTHOR]

This paper presents two versions of a method for solving large linear programs through decomposition. In both versions the problem is decomposed into subprograms as in the DANTZIG-WOLFE model, but each version uses a different type of linking program. The subprograms are first solved, and then the infeasibility of the resulting solution for the linking program is used to generate a price-adjustment process (much like a market mechanism), which gradually corrects the objective functions of the subprograms, until either some optimal solutions to the latter yield a feasible solution to the linking program (then the problem is solved), or evidence is obtained that the problem has no feasible solution. [ABSTRACT FROM AUTHOR]

In this tutorial the author shows how graph theory can be used to model the structural relationships in a behavioral theory. The basic elements of a graph and its related matrices are defined and illustrated. A survey of applications of graph theory in behavioral science is followed by an extensive bibliography. [ABSTRACT FROM AUTHOR]

Describes a technique for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs. Generalization of the duality theorem for linear programming; Decentralized decision process.

A unifying framework is developed to facilitate the understanding of most known computational approaches to integer programming. A number of currently operational algorithms are related to this framework, and prospects for future progress are assessed. [ABSTRACT FROM AUTHOR]