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

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.