Journal ArticleDOI
The Complexity of Flowshop and Jobshop Scheduling
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TLDR
The results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of thetask lengths.Abstract:
NP-complete problems form an extensive equivalence class of combinatorial problems for which no nonenumerative algorithms are known. Our first result shows that determining a shortest-length schedule in an m-machine flowshop is NP-complete for m ≥ 3. For m = 2, there is an efficient algorithm for finding such schedules. The second result shows that determining a minimum mean-flow-time schedule in an m-machine flowshop is NP-complete for every m ≥ 2. Finally we show that the shortest-length schedule problem for an m-machine jobshop is NP-complete for every m ≥ 2. Our results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of the task lengths.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
Ant algorithms for discrete optimization
TL;DR: An overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies' foraging behavior, and the ant colony optimization (ACO) metaheuristic is presented.
Book ChapterDOI
Complexity of machine scheduling problems
TL;DR: In this paper, the authors survey and extend the results on the complexity of machine scheduling problems and give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity.
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 genetic algorithm for the Flexible Job-shop Scheduling Problem
TL;DR: A genetic algorithm for the Flexible Job-shop Scheduling Problem (FJSP) integrates different strategies for generating the initial population, selecting the individuals for reproduction and reproducing new individuals to prove that genetic algorithms are effective for solving FJSP.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
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
Theory of scheduling
TL;DR: Reading theory of scheduling as one of the reading material to finish quickly to increase the knowledge and happiness in your lonely time.
Book ChapterDOI
Complexity of machine scheduling problems
TL;DR: In this paper, the authors survey and extend the results on the complexity of machine scheduling problems and give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity.