Skip to main content
SpringerLink
Log in

An intelligent water drop algorithm to identical parallel machine scheduling with controllable processing times: a just-in-time approach

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

Identical parallel machine scheduling problem with controllable processing times is investigated in this research. In such an area, our focus is mostly motivated by the adoption of just-in-time (JIT) philosophy with the objective of minimizing total weighted tardiness and earliness as well as job compressions/expansion cost simultaneously. Also the optimal set amounts of job compressions/expansion plus the job sequence are determined on each machine. It is assumed that the jobs processing times can vary within a given interval, i.e., it is permitted to compress or expand in return for compression/expansion cost. A mixed integer linear programming (MILP) model for the considered problem is firstly proposed and thereafter the optimal jobs set amounts of compression and expansion processing times in a known sequence are determined via parallel net benefit compression–net benefit expansion called PNBC–NBE heuristic. An intelligent water drop (IWD) algorithm, as a new swarm-based nature-inspired optimization one, is also adopted to solve this multi-criteria problem. A heuristic method besides three meta-heuristic algorithms is then employed to solve small- and medium- to large-size sample-generated instances. Computational results reveal that the proposed IWDNN outperforms the other techniques and is a trustable one which can solve such complicated problems with satisfactory consequences.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Abbasy A, Hosseini SH (2008) Ant colony optimization-based approach to optimal reactive power dispatch: a comparison of various ant systems. IEEE, Piscataway

    Google Scholar 

  • Alidaee B, Ahmadian A (1993) Two parallel machine sequencing problems involving controllable job processing times. Eur J Oper Res 70(3):335–341

    Article  MATH  Google Scholar 

  • Baker KR, Scudder GD (1990) Sequencing with earliness and tardiness penalties: a review. Oper Res 38:22–36

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Chen ZL, Li CL (1996) Parallel-machine scheduling with controllable processing times. IIE Trans 28:177–180

    Article  Google Scholar 

  • Dariane AB, Sarani S (2013) Application of intelligent water drops algorithm in reservoir operation. Water Resour Manag 27(14):4827–4843

    Article  Google Scholar 

  • Drobouchevitch IG, Sidney JB (2011) Minimization of earliness, tardiness and due date penalties on uniform parallel machines with identical jobs. Comput Oper Res 39(9):1919–1926

    Article  MathSciNet  MATH  Google Scholar 

  • Duan H, Liu S, Lei X (2008) Air robot path planning based on Intelligent Water Drops optimization. In: Neural networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence). IEEE international joint conference on 1397–1401

  • Duan H, Liu S, Wu J (2009) Novel intelligent water drops optimization approach to single ucav smooth trajectory planning. Aerosp Sci Technol 13(8):442–449

    Article  Google Scholar 

  • Gürel S, Akturk MS (2007) Scheduling parallel CNC machines with time/cost trade-off considerations. Comput Oper Res 34(9):2774–2789

    Article  MATH  Google Scholar 

  • Gürel S, Körpeoğlu E, Aktürk MS (2010) An anticipative scheduling approach with controllable processing times. Comput Oper Res 37(6):1002–1013

    Article  MATH  Google Scholar 

  • Hall NG, Posner ME (1991) Earliness–tardiness scheduling problems. I: weighted deviation of completion times about a common due date. Oper Res 39:836–846

    Article  MathSciNet  MATH  Google Scholar 

  • Hall NG, Posner ME (2001) Generating experimental date for computational testing with machine scheduling applications. Oper Res 49:854–865

    Article  MathSciNet  MATH  Google Scholar 

  • Hendrawan Y, Murase H (2011) Neural-intelligent water drops algorithm to select relevant textural features for developing precision irrigation system using machine vision. Comput Electron Agric 77:214–228

    Article  Google Scholar 

  • Jansen K, Mastrolilli M (2004) Approximation schemes for parallel machine scheduling problems with controllable processing times. Comput Oper Res 31(10):1565–1581

    Article  MathSciNet  MATH  Google Scholar 

  • Kamkar I, Akbarzadeh-T MR, Yaghoobi M (2010) Intelligent water drops a new optimization algorithm for solving the vehicle routing problem. In: 2010 IEEE international conference on systems, man and cybernetics (SMC2010), 10–13 October 2010. IEEE, Piscataway, pp 4142–4146

  • Kayvanfar V, Komaki GHM, Aalaei A, Zandieh M (2014) Minimizing total tardiness and earliness on unrelated parallel machines with controllable processing times. Comput Oper Res 41:31–43

    Article  MathSciNet  MATH  Google Scholar 

  • Kayvanfar V, Mahdavi I, Komaki GHM (2013) Single machine scheduling with controllable processing times to minimize total tardiness and earliness. Comput Ind Eng 65(1):166–175

    Article  Google Scholar 

  • Kedad-Sidhoum S, Solis YR, Sourd F (2008) Lower bounds for the earliness–tardiness scheduling problem on parallel machines with distinct due dates. Eur J Oper Res 189(3):1305–1316

    Article  MathSciNet  MATH  Google Scholar 

  • Leyvand Y, Shabtay D, Steiner G, Yedidsion L (2010) Just-in-time scheduling with controllable processing times on parallel machines. J Comb Optim 19(3):347–368

    Article  MathSciNet  MATH  Google Scholar 

  • Li K, Shi Y, Yang SL, Cheng BY (2011) Parallel machine scheduling problem to minimize the makespan with resource dependent processing times. Appl Soft Comput 11(8):5551–5557

    Article  Google Scholar 

  • M’Hallah R, Al-Khamis T (2012) Minimising total weighted earliness and tardiness on parallel machines using a hybrid heuristic. Int J Prod Res 50(10):2639–2664

    Article  Google Scholar 

  • Niu SH, Ong SK, Nee AYC (2012) An improved intelligent water drops algorithm for achieving optimal job-shop scheduling solutions. Int J Prod Res 50(15):4192–4205

    Article  Google Scholar 

  • Niu SH, Ong SK, Nee AYC (2013) An improved intelligent water drops algorithm for solving multi-objective job shop scheduling. Eng Appl Artif Intell 26(10):2431–2442

    Article  Google Scholar 

  • Nowicki E, Zdrzalka S (1990) A survey of results for sequencing problems with controllable processing times. Discrete Appl Math 26:271–287

    Article  MathSciNet  MATH  Google Scholar 

  • Nowicki E, Zdrzałka S (1995) A bicriterion approach to preemptive scheduling of parallel machines with controllable job processing times. Discrete Appl Math 63(3):237–256

    Article  MathSciNet  MATH  Google Scholar 

  • Omar MK, Teo SC (2006) Minimizing the sum of earliness/tardiness in identical parallel machines schedule with incompatible job families: An improved MIP approach. Appl Math Comput 181(2):1008–1017

    MathSciNet  MATH  Google Scholar 

  • Pinedo M (2008) Scheduling theory, algorithms, and systems, 3rd edn. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

  • Polyakovskiy S, M’Hallah R (2014) A multi-agent system for the weighted earliness tardiness parallel machine problem. Comput Oper Res 44:115–136

    Article  MathSciNet  MATH  Google Scholar 

  • Shabtay D, Steiner G (2007) A survey of scheduling with controllable processing times. Discrete Appl Math 155:1643–1666

    Article  MathSciNet  MATH  Google Scholar 

  • Shah-Hosseini H (2007) Problem solving by intelligent water drops. In: Proceedings of IEEE congress on evolutionary computation, CEC 2007. Institute of Electrical and Electronic Engineers Computer Society, Singapore, pp 3226–3231

  • Shah-Hosseini H (2008) Intelligent water drops algorithm: a new optimization method for solving the multiple knapsack problem. Int J Intell Comput Cybern 1(2):193–212

    Article  MathSciNet  MATH  Google Scholar 

  • Shah-Hosseini H (2009) The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm. Int J Bio-Ins Comput 1(1–2):71–79

    Article  Google Scholar 

  • Shah-Hosseini H (2012) An approach to continuous optimization by the intelligent water drops algorithm. Proc Soc Behav Sci 32:224–229

    Article  Google Scholar 

  • Shakhlevich N, Strusevich V (2008) Preemptive scheduling on uniform parallel machines with controllable job processing times. Algorithmica 51(4):451–473

    Article  MathSciNet  MATH  Google Scholar 

  • Sivrikaya F, Ulusoy G (1999) Parallel machine scheduling with earliness and tardiness penalties. Comput Oper Res 26:773–787

    Article  MathSciNet  MATH  Google Scholar 

  • Sorensen K, Glover F (2013) Metaheuristics. In: Gass SI, Harris CM (eds) Encyclopedia of operations research and management science, 3rd edn. Springer, New York

    Google Scholar 

  • Su LH (2009) Minimizing earliness and tardiness subject to total completion time in an identical parallel machine system. Comput Oper Res 36(2):461–471

    Article  MathSciNet  MATH  Google Scholar 

  • Sun H, Wang G (2003) Parallel machine earliness and tardiness scheduling with proportional weights. Comput Oper Res 30(5):801–808

    Article  MATH  Google Scholar 

  • Turkcan A, Akturk MS, Storer RH (2009) Predictive/reactive scheduling with controllable processing times and earliness–tardiness penalties. IIE Trans 41(12):1080–1095

    Article  Google Scholar 

  • Vickson RG (1980) Two single machine sequencing problems involving controllable job processing times. AIIE Trans 12:258–262

    Article  MathSciNet  Google Scholar 

  • Wan G (2007) Single machine common due window scheduling with controllable job processing times. Lect Notes Comput Sci 4616:279–290

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JB (2006) Single machine scheduling with common due date and controllable processing times. Appl Math Comput 174:1245–1254

    MathSciNet  MATH  Google Scholar 

  • Yang DL, Cheng TCE, Yang SJ (2014) Parallel-machine scheduling with controllable processing times and rate-modifying activities to minimise total cost involving total completion time and job compressions. Int J Prod Res 52(4):1133–1141

    Article  Google Scholar 

  • Yi Y, Wang DW (2003) Soft computing for scheduling with batch setup times and earliness–tardiness penalties on parallel machines. J Intell Manuf 14(3–4):311–322

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Ave., 15875-4413, Tehran, Iran

    Vahid Kayvanfar

  2. Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, G.C., Tehran, Iran

    M. Zandieh

  3. Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran

    Ehsan Teymourian

Authors
  1. Vahid Kayvanfar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Zandieh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ehsan Teymourian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Zandieh.

Additional information

Communicated by José Mario Martínez.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kayvanfar, V., Zandieh, M. & Teymourian, E. An intelligent water drop algorithm to identical parallel machine scheduling with controllable processing times: a just-in-time approach. Comp. Appl. Math. 36, 159–184 (2017). https://doi.org/10.1007/s40314-015-0218-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40314-015-0218-3

Keywords

Mathematics Subject Classification

Search

Navigation