Exact exponential algorithms for 3-machine flowshop scheduling problems

In this paper, we focus on the design of an exact exponential time algorithm with a proved worst-case running time for 3-machine flowshop scheduling problems considering worst-case scenarios. For the minimization of the makespan criterion, a Dynamic Programming algorithm running in O ∗ ( 3 n ) is pr...

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Bibliographic Details
Published in:Journal of scheduling Vol. 21; no. 2; pp. 227 - 233
Main Authors: Shang, Lei, Lenté, Christophe, Liedloff, Mathieu, T’Kindt, Vincent
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2018
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Artificial Intelligence
Business and Management
Calculus of Variations and Optimal Control; Optimization
Computational Complexity
Computer Science
Data Structures and Algorithms
Dynamic programming
Job shops
Mathematics
Operations Research
Operations Research/Decision Theory
Optimization
Optimization and Control
Production scheduling
Run time (computers)
Scheduling
Supply Chain Management
Moderately exponential algorithms
Dynamic programming
Flowshop
Moderately exponential algorithms Dynamic programming Flowshop
ISSN:1094-6136, 1099-1425
Online Access:Get full text
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Summary:In this paper, we focus on the design of an exact exponential time algorithm with a proved worst-case running time for 3-machine flowshop scheduling problems considering worst-case scenarios. For the minimization of the makespan criterion, a Dynamic Programming algorithm running in O ∗ ( 3 n ) is proposed, which improves the current best-known time complexity 2 O ( n ) × ‖ I ‖ O ( 1 ) in the literature. The idea is based on a dominance condition and the consideration of the Pareto Front in the criteria space. The algorithm can be easily generalized to other problems that have similar structures. The generalization on two problems, namely the F 3 ‖ f max and F 3 ‖ ∑ f i problems, is discussed.
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-017-0524-2