Abstract
A single machine group scheduling problem with due date assignment and resource allocation is investigated. Based on production similarities, jobs are classified into groups and it is required that jobs within the same group are processed contiguously, in order to achieve high-volume production efficiency. Jobs in the same group are allowed to have different due dates. The job processing times are resource dependent, and both convex and bounded linear resource consumption functions are considered. The aim is minimizing an aggregate cost which takes into account earliness, tardiness, due date assignment and resource allocation costs, by finding a group schedule, due date assignment and resource allocation for all jobs. For both resource consumption functions, we present properties of the optimal solutions, and for the special case where the size of every group is the same and the minimum of the due date assignment cost and the tardiness cost for each job is identical, we present an algorithm to optimally solve the problem in \(O(n^3)\) time, where n is the total number of jobs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
References
Bajwa N, Melouk S, Bryant P (2019) A hybrid heuristic approach to minimize number of tardy jobs in group technology systems. Int Trans Oper Res 26(5):1847–1867
Chen Y, Cheng Y (2021) Optimal due date assignment without restriction and convex resource allocation in group technology scheduling. In: Du DZ, Du D, Wu C, Xu D (eds) Combinatorial optimization and applications, COCOA 2021. Lecture notes in computer science, vol 13135, Springer, Cham
Graham RL, Lawler EL, Lenstra JK et al (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326
Hardy G, Littlewood JE, Polya G (1967) Inequalities. Cambridge University Press, London
Ji M, Zhang X, Tang X et al (2016) Group scheduling with group-dependent multiple due windows assignment. Int J Prod Res 54(4):1244–1256
Keshavarz T, Savelsbergh M, Salmasi N (2015) A branch-and-bound algorithm for the single machine sequence-dependent group scheduling problem with earliness and tardiness penalties. Appl Math Model 39(20):6410–6424
Li W, Zhao C (2015) Single machine scheduling problem with multiple due windows assignment in a group technology. J Appl Math Comput 44:477–494
Li S, Ng CT, Yuan J (2011) Group scheduling and due date assignment on a single machine. Int J Prod Econ 130(2):230–235
Liu L, Xu Y, Yin N et al (2014) Single machine group scheduling problem with deteriorating jobs and release dates. Appl Mech Mater 513–517:2145–2148
Lv D, Luo S, Xue J et al (2021) A note on single machine common flow allowance group scheduling with learning effect and resource allocation. Comput Ind Eng 151:106941
Panwalkar SS, Smith ML, Seidmann A (1982) Common due date assignment to minimize total penalty for the one machine scheduling problem. Oper Res 30(2):391–399
Qin H, Zhang Z, Bai D (2016) Permutation flowshop group scheduling with position-based learning effect. Comput Ind Eng 92:1–15
Seidmann A, Panwalkar SS, Smith ML (1981) Optimal assignment of due-dates for a single processor scheduling problem. Int J Prod Res 19(4):393–399
Shabtay D (2016) Optimal restricted due date assignment in scheduling. Eur J Oper Res 252(1):79–89
Shabtay D, Itskovich Y, Yedidsion L et al (2010) Optimal due date assignment and resource allocation in a group technology scheduling environment. Comput Oper Res 37(12):2218–2228
Wang L, Liu M, Wang J et al (2021) Optimization for due-date assignment single-machine scheduling under group technology. Complexity 6656261:1–9
Yin N, Kang L, Wang X (2014) Single machine group scheduling with processing times dependent on position, starting time and allotted resource. Appl Math Model 38(19–20):4602–4613
Acknowledgements
The authors are grateful to the two anonymous referees for their helpful comments and suggestions.
Funding
This work was partially supported by the Major Program of National Natural Science Foundation of China under Grant Nos. 72192830 and 72192834, and the Key Project of National Natural Science Foundation of China under Grant No. 71732006.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflict of interest to declare that are relevant to the content of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
A preliminary version of this paper appears in Combinatorial Optimization and Applications, COCOA 2021. Lecture Notes in Computer Science, vol 13135, Springer, Cham.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Chen, Y., Ma, X., Zhang, G. et al. On optimal due date assignment without restriction and resource allocation in group technology scheduling. J Comb Optim 45, 64 (2023). https://doi.org/10.1007/s10878-023-00993-z
Accepted:
Published:
DOI: https://doi.org/10.1007/s10878-023-00993-z