Journal ArticleDOI
An Additive Algorithm for Solving Linear Programs with Zero-One Variables
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In this paper, an algorithm for solving linear programs with variables constrained to take only one of the values 0 or 1 is proposed, where the only operations required under the algorithm are additions and subtractions.Abstract:
An algorithm is proposed for solving linear programs with variables constrained to take only one of the values 0 or 1. It starts by setting all the n variables equal to 0, and consists of a systematic procedure of successively assigning to certain variables the value 1, in such a way that after trying a small part of all the 2n possible combinations, one obtains either an optimal solution, or evidence of the fact that no feasible solution exists. The only operations required under the algorithm are additions and subtractions; thus round-off errors are excluded. Problems involving up to 15 variables can be solved with this algorithm by hand in not more than 3-4 hours. An extension of the algorithm to integer linear programming and to nonlinear programming is available, but not dealt with in this article.read more
Citations
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Book
Engineering Optimization : Theory and Practice
TL;DR: This chapter discusses Optimization Techniques, which are used in Linear Programming I and II, and Nonlinear Programming II, which is concerned with One-Dimensional Minimization.
Journal ArticleDOI
Branch-and-Bound Methods: A Survey
Eugene L. Lawler,D. E. Wood +1 more
TL;DR: The essential features of the branch-and-bound approach to constrained optimization are described, and several specific applications are reviewed, including integer linear programming Land-Doig and Balas methods, nonlinear programming minimization of nonconvex objective functions, and the quadratic assignment problem Gilmore and Lawler methods.
Journal ArticleDOI
An Implicit Enumeration Algorithm to Generate Tests for Combinational Logic Circuits
TL;DR: PODEM (path-oriented decision making) is a new test generation algorithm for combinational logic circuits that uses an implicit enumeration approach analogous to that used for solving 0-1 integer programming problems and is significantly more efficient than DALG over the general spectrum of combinational Logic circuits.
Book ChapterDOI
Lagrangian Relaxation for Integer Programming
TL;DR: It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8].
Journal ArticleDOI
A survey of exact algorithms for the simple assembly line balancing problem
TL;DR: The simple assembly line balancing problem (SALBP) as discussed by the authors is a deterministic optimization problem where all input parameters are assumed to be known with certainty and all the algorithms discussed are exact.
References
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Book
Linear Programming and Extensions
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
Book ChapterDOI
An Automatic Method for Solving Discrete Programming Problems
Ailsa H. Land,Alison G. Doig +1 more
TL;DR: In the late 1950s there was a group of teachers and research assistants at the London School of Economics interested in linear programming and its extensions, in particular Helen Makower, George Morton, Ailsa Land and Alison Doig.
Journal ArticleDOI
A Linear Programming Approach to the Cutting-Stock Problem
P. C. Gilmore,Ralph E. Gomory +1 more
TL;DR: In this paper, a technique is described for overcoming the difficulty in the linear programming formulation of the cutting-stock problem, which enables one to compute always with a matrix which has no more columns than it has rows.
Book
Management Models and Industrial Applications of Linear Programming
TL;DR: In place of a survey or evaluation of industrial studies, two broad issues which are relevant to all such applications will be discussed, including the use of linear programming models as guides to data collection and analysis and prognosis of fruitful areas of additional research, especially those which appear to have been opened by industrial applications.