A note on “Fully polynomial time approximation scheme for the total weighted tardiness minimization with a common due date” - Kianfar, K.; Moslehi, G. (Discrete Applied Mathematics, 2013)
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.