Skip to main content
SpringerLink
Log in

Efficient procedures for the weighted squared tardiness permutation flowshop scheduling problem

  • Published:
Flexible Services and Manufacturing Journal Aims and scope Submit manuscript

Abstract

This paper addresses a permutation flowshop scheduling problem, with the objective of minimizing total weighted squared tardiness. The focus is on providing efficient procedures that can quickly solve medium or even large instances. Within this context, we first present multiple dispatching heuristics. These include general rules suited to various due date-related environments, heuristics developed for the problem with a linear objective function, and procedures that are suitably adapted to take the squared objective into account. Then, we describe several improvement procedures, which use one or more of three techniques. These procedures are used to improve the solution obtained by the best dispatching rule. Computational results show that the quadratic rules greatly outperform the linear counterparts, and that one of the quadratic rules is the overall best performing dispatching heuristic. The computational tests also show that all procedures significantly improve upon the initial solution. The non-dominated procedures, when considering both solution quality and runtime, are identified. The best dispatching rule, and two of the non-dominated improvement procedures, are quite efficient, and can be applied to even very large-sized problems. The remaining non-dominated improvement method can provide somewhat higher quality solutions, but it may need excessive time for extremely large instances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alidaee B, Ramakrishnan KR (1996) A computational experiment of COVERT-AU class of rules for single machine tardiness scheduling problem. Comput Ind Eng 30:201–209

    Article  Google Scholar 

  • Baker KR, Bertrand JWM (1982) A dynamic priority rule for scheduling against due-dates. J Op Manage 3:37–42

    Article  Google Scholar 

  • Dalfard VM, Ardakani A, Banihashemi TN (2011) Hybrid genetic algorithm for assembly flow-shop scheduling problem with sequence-dependent setup and transportation times. Tehnicki Vjesnik 18:467–504

    Google Scholar 

  • Fernandez-Viagas V, Framinan JM (2015a) NEH-based heuristics for the permutation flowshop scheduling problem to minimise total tardiness. Comput Op Res 60:27–36

    Article  MathSciNet  Google Scholar 

  • Fernandez-Viagas V, Framinan JM (2015b) A new set of high-performing heuristics to minimise flowtime in permutation flowshops. Comput Op Res 53:68–80

    Article  Google Scholar 

  • Fernandez-Viagas V, Leisten R, Framinan JM (2016) A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimise total flowtime. Expert Syst Appl 61:290–301

    Article  Google Scholar 

  • Fernandez-Viagas V, Ruiz R, Framinan JM (2017) A new vision of approximate methods for the permutation flowshop to minimise makespan: state-of-the-art and computational evaluation. Eur J Op Res 257:707–721

    Article  MathSciNet  Google Scholar 

  • Fernandez-Viagas V, Valente JMS, Framinan JM (2018) Iterated-greedy-based algorithms with beam search initialization for the permutation flowshop to minimise total tardiness. Expert Syst Appl 94:58–69

    Article  Google Scholar 

  • Framinan JM, Gupta JND, Leisten R (2004) A review and classification of heuristics for permutation flow-shop scheduling with makespan objective. J Op Res Soc 55:1243–1255

    Article  Google Scholar 

  • Gonçalves TC, Valente JMS, Schaller JE (2016) Metaheuristics for the single machine weighted quadratic tardiness scheduling problem. Comput Op Res 70:115–126

    Article  MathSciNet  Google Scholar 

  • Hasija S, Rajendran C (2004) Scheduling in flowshops to minimize total tardiness of jobs. Int J Prod Res 42:2289–2301

    Article  Google Scholar 

  • Hoitomt DJ, Luh PB, Max E, Pattipati KR (1990) Scheduling jobs with simple precedence constraints on parallel machines. IEEE Control Syst Mag 10:34–40

    Article  Google Scholar 

  • Holsenback JE, Russell RM, Markland RE, Philipoom PR (1999) An improved heuristic for the single-machine, weighted-tardiness problem. Omega 27:485–495

    Article  Google Scholar 

  • Jackson JR (1955) Scheduling a production line to minimize maximum tardiness, Management Science Research Project, Research Report 43. University of California, Los Angeles

    Google Scholar 

  • Kanet JJ, Li XM (2004) A weighted modified due date rule for sequencing to minimize weighted tardiness. J Sched 7:261–276

    Article  MathSciNet  Google Scholar 

  • Karabulut K (2016) A hybrid iterated greedy algorithm for total tardiness minimization in permutation flowshops. Comput Ind Eng 98:300–307

    Article  Google Scholar 

  • Luh PB, Hoitomt DJ (1993) Scheduling of manufacturing systems using the Lagrangian relaxation technique. IEEE Trans Autom Control 38:1066–1079

    Article  MathSciNet  Google Scholar 

  • Nawaz M, Enscore EE Jr, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega 11:91–95

    Article  Google Scholar 

  • Neufeld JS, Gupta JND, Buscher U (2016) A comprehensive review of flowshop group scheduling literature. Comput Op Res 70:56–74

    Article  MathSciNet  Google Scholar 

  • Osman IH, Belouadah H, Fleszar K, Saffar M (2009), Hybrid of the weighted minimum slack and shortest processing time dispatching rules for the total weighted tardiness single machine scheduling problem with availability constraints. In: Paper presented at the MISTA 2009—multidisciplinary international conference on scheduling: theory and applications, Dublin, Ireland

  • Ow PS, Morton TE (1988) Filtered beam search in scheduling. Int J Prod Res 26:35–62

    Article  Google Scholar 

  • Panwalkar SS, Iskander W (1977) Survey of scheduling rules. Op Res 25:45–61

    Article  MathSciNet  Google Scholar 

  • Potts CN, van Wassenhove LN (1991) Single-machine tardiness sequencing heuristics. IIE Trans 23:346–354

    Article  Google Scholar 

  • Reza Hejazi S, Saghafian S (2005) Flowshop-scheduling problems with makespan criterion: a review. Int J Prod Res 43:2895–2929

    Article  Google Scholar 

  • Ruiz R, Maroto C (2005) A comprehensive review and evaluation of permutation flowshop heuristics. Eur J Op Res 165:479–494

    Article  Google Scholar 

  • Ruiz R, Stützle T (2008) An Iterated Greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives. Eur J Op Res 187:1143–1159

    Article  Google Scholar 

  • Schaller J, Valente JMS (2012) Minimizing the weighted sum of squared tardiness on a single machine. Comput Op Res 39:919–928

    Article  MathSciNet  Google Scholar 

  • Schaller J, Valente JMS (2018) Efficient heuristics for minimizing weighted sum of squared tardiness on identical parallel machines. Comput Ind Eng 119:146–156

    Article  Google Scholar 

  • Smith WE (1956) Various optimizers for single-stage production. Naval Res Logist Q 3:59–66

    Article  MathSciNet  Google Scholar 

  • Sun XQ, Noble JS, Klein CM (1999) Single-machine scheduling with sequence dependent setup to minimize total weighted squared tardiness. IIE Trans 31:113–124

    Google Scholar 

  • Sun Y, Zhang C, Gao L, Wang X (2011) Multi-objective optimization algorithms for flow shop scheduling problem: a review and prospects. Int J Adv Manuf Technol 55:723–739

    Article  Google Scholar 

  • Taguchi G (1986) Introduction to quality engineering: designing quality into products and processes. Asian Productivity Organization, Tokio

    Google Scholar 

  • Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Op Res 64:278–285

    Article  Google Scholar 

  • Thomalla CS (2001) Job shop scheduling with alternative process plans. Int J Prod Econ 74:125–134

    Article  Google Scholar 

  • Valente JMS, Alves RAFS (2008) Heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties. Comput Op Res 35:3696–3713

    Article  MathSciNet  Google Scholar 

  • Valente JMS, Schaller JE (2012) Dispatching heuristics for the single machine weighted quadratic tardiness scheduling problem. Comput Op Res 39:2223–2231

    Article  MathSciNet  Google Scholar 

  • Vallada E, Ruiz R (2010) Genetic algorithms with path relinking for the minimum tardiness permutation flowshop problem. Omega 38:57–67

    Article  Google Scholar 

  • Vallada E, Ruiz R, Minella G (2008) Minimising total tardiness in the m-machine flowshop problem: a review and evaluation of heuristics and metaheuristics. Comput Op Res 35:1350–1373

    Article  Google Scholar 

  • Vepsalainen APJ, Morton TE (1987) Priority rules for job shops with weighted tardiness costs. Manage Sci 33:1035–1047

    Article  Google Scholar 

  • Volgenant A, Teerhuis E (1999) Improved heuristics for the n-job single-machine weighted tardiness problem. Comput Op Res 26:35–44

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the two anonymous referees, and the associate editor, for their helpful comments and suggestions, which have improved this paper.

Author information

Authors and Affiliations

  1. Information Systems Department, NORS, Rua Manuel Pinto de Azevedo 711, 1º, 4149-010, Porto, Portugal

    Maria Raquel C. Costa

  2. LIAAD – INESC TEC, Faculdade de Economia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-464, Porto, Portugal

    Jorge M. S. Valente

  3. Department of Business Administration, Eastern Connecticut State University, 83 Windham St., Willimantic, CT, 06226-2295, USA

    Jeffrey E. Schaller

Authors
  1. Maria Raquel C. Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jorge M. S. Valente
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jeffrey E. Schaller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge M. S. Valente.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (XLSX 15 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Costa, M.R.C., Valente, J.M.S. & Schaller, J.E. Efficient procedures for the weighted squared tardiness permutation flowshop scheduling problem. Flex Serv Manuf J 32, 487–522 (2020). https://doi.org/10.1007/s10696-019-09363-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10696-019-09363-6

Keywords

Search

Navigation