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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Veröffentlicht in:Journal of scheduling Jg. 21; H. 2; S. 227 - 233
Hauptverfasser: Shang, Lei, Lenté, Christophe, Liedloff, Mathieu, T’Kindt, Vincent
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2018
Springer Nature B.V
Springer Verlag
Schlagworte:
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
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Abstract 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.
AbstractList 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∗(3n)O∗(3n) is proposed, which improves the current best-known time complexity 2O(n)×∥I∥O(1)2O(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 F3∥fmaxF3‖fmax and F3∥∑fiF3‖∑fi problems, is discussed.
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∗(3n) is proposed, which improves the current best-known time complexity 2O(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 F3‖fmax and F3‖∑fi problems, is discussed.
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.
Author Liedloff, Mathieu
T’Kindt, Vincent
Shang, Lei
Lenté, Christophe
Author_xml – sequence: 1
  givenname: Lei
  orcidid: 0000-0003-4395-3226
  surname: Shang
  fullname: Shang, Lei
  email: shang@univ-tours.fr
  organization: Laboratoire d’Informatique (EA 6300), ERL CNRS OC 6305, Université François-Rabelais de Tours
– sequence: 2
  givenname: Christophe
  surname: Lenté
  fullname: Lenté, Christophe
  organization: Laboratoire d’Informatique (EA 6300), ERL CNRS OC 6305, Université François-Rabelais de Tours
– sequence: 3
  givenname: Mathieu
  surname: Liedloff
  fullname: Liedloff, Mathieu
  organization: INSA Centre Val de Loire, LIFO EA 4022, Université d’Orléans
– sequence: 4
  givenname: Vincent
  surname: T’Kindt
  fullname: T’Kindt, Vincent
  organization: Laboratoire d’Informatique (EA 6300), ERL CNRS OC 6305, Université François-Rabelais de Tours
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Issue 2
Keywords Moderately exponential algorithms
Dynamic programming
Flowshop
Moderately exponential algorithms Dynamic programming Flowshop
Language English
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Snippet 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...
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SubjectTerms 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
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Title Exact exponential algorithms for 3-machine flowshop scheduling problems
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