Approximation Algorithms and an FPTAS for the Single Machine Problem with Biased Tardiness Penalty

Abstract EN

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 On3/ε time.