A note on “Fully polynomial time approximation scheme for the total weighted tardiness minimization with a common due date”

In this note, through a counter-example we show that the results in a recent paper (Kacem, 2010)  [1] are incorrect. Since the proposed dynamic programming in Kacem (2010)  [1] fails to optimally solve the problem in some instances, the designed FPTAS with O(n2/ε) complexity is wrong. Then, we provi...

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Veröffentlicht in:Discrete Applied Mathematics Jg. 161; H. 13-14; S. 2205 - 2206
Hauptverfasser: Kianfar, K., Moslehi, G.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.09.2013
Schlagworte:
Approximation
Common due date
Complexity
Due dates
Dynamic programming
FPTAS
Mathematical analysis
Minimization
Optimization
Polynomials
Scheduling
Tardiness
Scheduling
Approximation
Common due date
FPTAS
Tardiness
ISSN:0166-218X, 1872-6771
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Abstract In this note, through a counter-example we show that the results in a recent paper (Kacem, 2010)  [1] are incorrect. Since the proposed dynamic programming in Kacem (2010)  [1] fails to optimally solve the problem in some instances, the designed FPTAS with O(n2/ε) complexity is wrong. Then, we provide a modified FPTAS of O(n3/ε) time complexity for the considered problem.
AbstractList In this note, through a counter-example we show that the results in a recent paper (Kacem, 2010)  [1] are incorrect. Since the proposed dynamic programming in Kacem (2010)  [1] fails to optimally solve the problem in some instances, the designed FPTAS with O(n2/ε) complexity is wrong. Then, we provide a modified FPTAS of O(n3/ε) time complexity for the considered problem.
In this note, through a counter-example we show that the results in a recent paper (Kacem, 2010) [1] are incorrect. Since the proposed dynamic programming in Kacem (2010) [1] fails to optimally solve the problem in some instances, the designed FPTAS with O(n super(2)/ epsilon )O(n2/ epsilon ) complexity is wrong. Then, we provide a modified FPTAS of O(n super(3)/ epsilon )O(n3/ epsilon ) time complexity for the considered problem.
Author Kianfar, K.
Moslehi, G.
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Keywords Scheduling
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Common due date
FPTAS
Tardiness
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References Kacem (br000005) 2010; 158
Kacem (10.1016/j.dam.2013.02.026_br000005) 2010; 158
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  article-title: Fully polynomial time approximation scheme for the total weighted tardiness minimizing with a common due date
  publication-title: Discrete Appl. Math.
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Snippet In this note, through a counter-example we show that the results in a recent paper (Kacem, 2010)  [1] are incorrect. Since the proposed dynamic programming in...
In this note, through a counter-example we show that the results in a recent paper (Kacem, 2010) [1] are incorrect. Since the proposed dynamic programming in...
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SubjectTerms Approximation
Common due date
Complexity
Due dates
Dynamic programming
FPTAS
Mathematical analysis
Minimization
Optimization
Polynomials
Scheduling
Tardiness
Title A note on “Fully polynomial time approximation scheme for the total weighted tardiness minimization with a common due date”
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