Journal ArticleDOI
Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems
Edward Ignall,Linus Schrage +1 more
TLDR
In this paper, the branch-and-bound technique was applied to two flow-shop scheduling problems, i.e., 2-machine and 3-machine, with the objective of minimizing the makespan.Abstract:
The branch-and-bound technique of Little, et al. and Land and Doig is presented and then applied to two flow-shop scheduling problems. Computational results for up to 9 jobs are given for the 2-machine problem when the objective is minimizing the mean completion time. This problem was previously untreated. Results for up to 10 jobs, including comparisons with other techniques, are given for the 3-machine problem when the objective is minimizing the makespan.read more
Citations
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Book ChapterDOI
Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey
TL;DR: In this article, the authors survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory, and indicate some problems for future research and include a selective bibliography.
Journal ArticleDOI
A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem
TL;DR: A simple algorithm is presented in this paper, which produces very good sequences in comparison with existing heuristics, and performs especially well on large flow-shop problems in both the static and dynamic sequencing environments.
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.
Sequencing and scheduling: algorithms and complexity
TL;DR: This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.
Journal ArticleDOI
A Heuristic Algorithm for the n Job, m Machine Sequencing Problem
TL;DR: A simple algorithm for the solution of very large sequence problems without the use of a computer that produces approximate solutions to the n job, m machine sequencing problem where no passing is considered and the criterion is minimum total elapsed time.
References
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Journal ArticleDOI
Optimal two- and three-stage production schedules with setup times included
TL;DR: A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum.
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.
Book
An Algorithm for the Traveling Salesman Problem
TL;DR: A “branch and bound” algorithm is presented for solving the traveling salesman problem, where the set of all tours feasible solutions is broken up into increasingly small subsets by a procedure called branching.
Journal ArticleDOI
Development of M-Stage Decision Rule for Scheduling N Jobs Through M Machines
TL;DR: This paper describes an algorithm that will yield an optimum sequence for n jobs requiring processing through M machines when no passing is allowed and an example problem.
Journal ArticleDOI
Approximate Solutions to the Three-Machine Scheduling Problem
TL;DR: In this article, the authors present experimental results from applying several computational methods for solving the classic three-machine scheduling model, where the objective function employed is the total amount of processing time elapsing for the completion of all n items on three machines.