This paper addresses a new performance measure for scheduling problems, entitled “biased tardiness penalty.” We study the approximability of minimum biased tardiness on a single machine, provided that all the due dates are equal. Two heuristic algorithms are developed for this problem, and it is shown that one of them has a worst-case ratio bound of 2. Then, we propose a dynamic programming algorithm and use it to design an FPTAS. The FPTAS is generated by cleaning up some states in the dynamic programming algorithm, and it requires time.
"Approximation Algorithms and an FPTAS for the Single Machine Problem with Biased Tardiness Penalty." J. Appl. Math. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/679702