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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Bibliographic Details
Published in:Discrete Applied Mathematics 2013-09, Vol.161 (13-14), p.2205-2206
Main Authors: Kianfar, K., Moslehi, G.
Format: Article
Language:English
Subjects:
Approximation
Common due date
Complexity
Due dates
Dynamic programming
FPTAS
Mathematical analysis
Minimization
Optimization
Polynomials
Scheduling
Tardiness
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2013.02.026