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Group theory is used to integrate a wide variety of integer programming methods into a common computational process. Included are group optimization algorithms, Lagrangian methods, the cutting plane method, and the method of surrogate constraints. These methods are controlled by a supervisor which performs four main functions: set-up, directed search, subproblem analysis, and prognosis. Some computational experience is given. One appendix contains an algorithm for dynamically solving unconstrained group problems. A second appendix gives an algorithm for solving zero-one group problems. [ABSTRACT FROM AUTHOR]
The application of Kuhn's Hungarian Method to the problem of matrix reduction as needed in Gotlieb's method for timetable generation is described. The method is suited to both hand and computer calculation. Devices to improve the efficiency of the basic algorithm are discussed. [ABSTRACT FROM AUTHOR]
A theory of equivalent integer programs is developed that shows that every all-integer integer programming problem is equivalent to infinitely many other integer programming problems. The equivalence is such that the solution to any one problem in the equivalence class determines the solution to every other problem in the class. Procedures to construct certain canonical problems in each equivalence class are described. The relationship of this theory to computational algorithms is discussed. [ABSTRACT FROM AUTHOR]
LINEAR programming, INTEGER programming, MATHEMATICAL programming, DYNAMIC programming, MATHEMATICAL optimization, ALGORITHMS, MATHEMATICAL models in business, PROBLEM solving, COMPUTER programming, COMPUTER simulation, SIMULATION methods & models, MATHEMATICAL models
Abstract
In this report, twenty-nine integer linear programming problems, ranging from very simple to apparently rather difficult, are introduced. The results of running these problems on four different computer codes, involving five distinct algorithms, are presented as both time and iteration data. A brief description of the codes used is also included. [ABSTRACT FROM AUTHOR]