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/?) O ( n 2 / ? ) complexity is wrong. Then, we provide a modified FPTAS of O(n3/?) O ( n 3 / ? ) time complexity for the considered problem.
approximation tardiness common due date fptas scheduling