Pareto optimal algorithms for minimizing total (weighted) completion time and maximum cost on a single machine

Zhimeng Liu; Shuguang Li

doi:10.3934/mbe.2022346

Pareto optimal algorithms for minimizing total (weighted) completion time and maximum cost on a single machine

Math Biosci Eng. 2022 May 18;19(7):7337-7348. doi: 10.3934/mbe.2022346.

Authors

Zhimeng Liu¹, Shuguang Li¹

Affiliation

¹ College of Computer Science and Technology, Shandong Technology and Business University, Yantai 264005, China.

PMID: 35730309
DOI: 10.3934/mbe.2022346

Abstract

This paper studies the Pareto scheduling problem of minimizing total weighted completion time and maximum cost on a single machine. It is known that the problem is strongly NP-hard. Algorithms with running time $ O(n^3) $ are presented for the following cases: arbitrary processing times, equal release dates and equal weights; equal processing times, arbitrary release dates and equal weights; equal processing times, equal release dates and arbitrary weights.

Keywords: Pareto optimization; maximum cost; scheduling; single machine; total weighted completion time.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms*
Time