Approximation algorithms and an FPTAS for the single machine problem with biased tardiness penalty

Abstract

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 O n 3 / ε time. © 2014 G. Moslehi and K. Kianfar.