Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Single machine scheduling to minimize total late work
Operations Research
Mathematics of Operations Research
An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem
INFORMS Journal on Computing
An FPTAS for the Minimum Total Weighted Tardiness Problem with a Fixed Number of Distinct Due Dates
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Non-approximability of just-in-time scheduling
Journal of Scheduling
Discrete Applied Mathematics
Theoretical Computer Science
Approximation algorithms for scheduling problems with a modified total weighted tardiness objective
Operations Research Letters
Approximation Techniques for Utilitarian Mechanism Design
SIAM Journal on Computing
An FPTAS for the minimum total weighted tardiness problem with a fixed number of distinct due dates
ACM Transactions on Algorithms (TALG)
Hi-index | 5.23 |
Given a single machine and a set of jobs with due dates, the classical NP-hard problem of scheduling to minimize total tardiness is a well-understood one. Lawler gave a fully polynomial-time approximation scheme (FPTAS) for it some 20 years ago. If the jobs have positive weights the problem of minimizing total weighted tardiness seems to be considerably more intricate, it. In this paper, we give some of the first approximation algorithms for it. We examine first the weighted problem with a fixed number of due dates and we design a pseudopolynomial algorithm for it. We show how to transform the pseudopolynomial algorithm to an FPTAS for the case where the weights are polynomially bounded.For the case with an arbitrary number of due dates and polynomially bounded processing times, we provide a quasipolynomial algorithm which produces a schedule whose value has an additive error proportional to the weighted sum of the due dates. We also investigate the performance of algorithms for minimizing the related total weighted late work objective.