Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints

Péter Györgyi, T. Kis

Research output: Contribution to journalArticle

Abstract

In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the resource consumptions are arbitrary.

Original languageEnglish
JournalJournal of Scheduling
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Approximation algorithms
Polynomials
Processing
Scheduling
Non-renewable resources
Resource constraints
Single machine

Keywords

  • Approximation algorithms
  • Non-renewable resources
  • Single-machine scheduling

ASJC Scopus subject areas

  • Software
  • Engineering(all)
  • Management Science and Operations Research
  • Artificial Intelligence

Cite this

@article{f9742931c108451aac18a864c8aadff6,
title = "Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints",
abstract = "In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the resource consumptions are arbitrary.",
keywords = "Approximation algorithms, Non-renewable resources, Single-machine scheduling",
author = "P{\'e}ter Gy{\"o}rgyi and T. Kis",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s10951-019-00601-1",
language = "English",
journal = "Journal of Scheduling",
issn = "1094-6136",
publisher = "Springer New York",

}

TY - JOUR

T1 - Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints

AU - Györgyi, Péter

AU - Kis, T.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the resource consumptions are arbitrary.

AB - In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the resource consumptions are arbitrary.

KW - Approximation algorithms

KW - Non-renewable resources

KW - Single-machine scheduling

UR - http://www.scopus.com/inward/record.url?scp=85061234155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061234155&partnerID=8YFLogxK

U2 - 10.1007/s10951-019-00601-1

DO - 10.1007/s10951-019-00601-1

M3 - Article

AN - SCOPUS:85061234155

JO - Journal of Scheduling

JF - Journal of Scheduling

SN - 1094-6136

ER -