Single-machine Pareto-scheduling with multiple weighting vectors for minimizing the total weighted late works

Shuen Guo; Zhichao Geng; Jinjiang Yuan

doi:10.3934/jimo.2021192

Article Contents

2023, Volume 19, Issue 1: 456-471. Doi: 10.3934/jimo.2021192

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Single-machine Pareto-scheduling with multiple weighting vectors for minimizing the total weighted late works

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China

^*Corresponding author: Jinjiang Yuan
^*Corresponding author: Jinjiang Yuan

Received: February 28, 2021

Revised: July 31, 2021

Early access: November 2021

Published: January 2023

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Abstract

In this paper, we study the single-machine Pareto-scheduling of jobs with multiple weighting vectors for minimizing the total weighted late works. Each weighting vector has its corresponding weighted late work. The goal of the problem is to find the Pareto-frontier for the weighted late works of the multiple weighting vectors. When the number of weighting vectors is arbitrary, it is implied in the literature that the problem is unary NP-hard. Then we concentrate on our research under the assumption that the number of weighting vectors is a constant. For this problem, we present a dynamic programming algorithm running in pseudo-polynomial time and a fully polynomial-time approximation scheme (FPTAS).

Keywords:

Scheduling,
multiple weights,
weighted late work,
Pareto-frontier,
fully polynomial-time approximation scheme.

Mathematics Subject Classification: Primary: 90B35; Secondary: 68M20.

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References

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