Single machine earliness/tardiness scheduling problem with grey processing times and the grey common due date
Grey Systems: Theory and Application
ISSN: 2043-9377
Article publication date: 19 June 2020
Issue publication date: 13 January 2021
Abstract
Purpose
This paper presents a mixed-integer programming model for a single machine earliness/tardiness scheduling problem where the objective is to minimize total earliness/tardiness duration when the uncertainty of parameters such as processing times and due date is coded with grey numbers.
Design/methodology/approach
Grey theory and grey numbers are used for illustrating the uncertainty of parameters in processing times and common due date, where the objective is to minimize the total earliness/tardiness duration. The paper proposes a 0–1 mathematical model for the problem and an effective heuristic method for the problem by using expected processing times for ordering jobs.
Findings
The uncertainty of the processing times and common due date are encoded with grey numbers and a position-dependent mixed-integer mathematical programming model is proposed for the problem in order to minimize total grey earliness/tardiness duration of jobs having grey processing times and a common due date. By using expected processing times for ranking grey processing times, V-shaped property of the problem and an efficient heuristic method for the problem are proposed. Solutions obtained from the heuristic method show that the heuristic is effective. The experimental study also reveals that while differences between upper and lower bounds of grey processing times decrease, the proposed heuristic's performance decreases.
Originality/value
The grey theory and grey numbers have been rarely used as machine scheduling problems. Therefore, this study provides an important contribution to the literature.
Keywords
Acknowledgements
Conflict of interest: The author declared that there is no conflict of interest.
Citation
Arık, O.A. (2021), "Single machine earliness/tardiness scheduling problem with grey processing times and the grey common due date", Grey Systems: Theory and Application, Vol. 11 No. 1, pp. 95-109. https://doi.org/10.1108/GS-01-2020-0010
Publisher
:Emerald Publishing Limited
Copyright © 2020, Emerald Publishing Limited