Skip to main content
Springer Nature Link
Log in

Particle swarm optimization based-algorithms to solve the two-machine cross-docking flow shop problem: just in time scheduling

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

Cross-docking is an innovative logistical strategy which provides less inventory holding costs, less transportation costs and fast customer deliveries without storage in between or less than 24 hours. In this paper, we address the two-machine cross-docking scheduling problem within a Just-In-Time (JIT) context. This latter requires the punctuality and exactness of product deliveries. To satisfy this target, we aim to minimize the total earliness and tardiness, then early or tardy deliveries are discouraged. This study presents a great contribution in solving such NP-hard problem while applying different versions of the PSO (Particle Swarm Optimization) algorithm. One of them is hybridized with the Genetic Algorithm (GA). This latter is then shown to be the best one over computational experiments using different sized instances and by determining a percentage deviation from a developed lower bound.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Data availability

The authors confirm that the data supporting the findings of this study are available within the article.

References

  • Agustina D, Lee CKM, Piplani R (2011) Cross-docking scheduling with delivery time window and temporary storage. IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), Singapore, 6-9 December

  • Álvarez-Pérez GA, González-Velarde JL, Fowler JW (2009) Cross-docking JIT scheduling : an alternative solution approach. The Journal of the Operational Research Society 60:554–564

    Article  Google Scholar 

  • Amin-nayeri MR, Moslehi G (2000) Optimal algorithm for single machine sequencing to minimize early/tardy cost. Esteghlal Journal of Engineering. Isfahan Univ Technol (In Persian) 19:35–48

    Google Scholar 

  • Boloori Arabani AR, Fatemi Ghomi SMT, Zandieh M (2010) A multi-criteria cross-docking scheduling with just-in-time approach. Int J Adv Manuf Technol 49:741–756

    Article  Google Scholar 

  • Chen F, Lee CY (2009) Minimizing the makespan in a two-machine cross-docking flow shop problem. European Journal of Operational Research 193:59–72

    Article  MathSciNet  Google Scholar 

  • Chen JS, Pan JCH, Lin CM (2008) A hybrid genetic algorithm for the re-entrant flow-shop scheduling problem. Expert Syst Appl 34:570–577

    Article  Google Scholar 

  • Cheng BW, Chang CL (2007) A study on flowshop scheduling problem combining Taguchi experimental design and genetic algorithm. Expert Syst Appl 32:415–421

    Article  Google Scholar 

  • Cook RL, Gibson B, Mac Curd yD (2005) A lean approach to crossdocking. Supply Chain Management Review 9:54–63

    Google Scholar 

  • Dulebenets MA (2019) A Delayed Start Parallel Evolutionary Algorithm for just-in-time truck scheduling at a cross-docking facility. Int J Production Economics 212:236–258

    Article  Google Scholar 

  • Eberhart RC and Shi Y (2001) Tracking and Optimizing Dynamic Systems with Particle Swarms. In: Proceedings of the IEEE Congress on Evolutionary Computation, Seoul Korea, 27-30 May, pages 94–100

  • Eberhart RC, and Shi Y (2000) Comparing Inertia Weights and Constriction Factorsin Particle Swarm Optimization. In: Proceedings of the Congress on Evolutionary Computing, San Diego USA. IEEE Service Center, Piscataway NJ, pages 84–89

  • Fazel Zarandi MH, Khorshidian H, Akbarpour Shirazi M (2016) A constraint programming model for the scheduling of JIT cross-docking systems with preemption. J Intell Manuf 27:297–313

    Article  Google Scholar 

  • Golias MM, Ivey S, Haralambides H, Saharidis G (2009) Maximizing throughput and minimizing tardiness and earliness at a cross dock facility: A bi-objective formulation. Annual Meeting of the Transportation Research Board, Washington

  • Graham R, Lawler E, Lenstra JK, Rinnooy Kan AHG (1997) Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5:287–326

    Article  MathSciNet  Google Scholar 

  • Hamdi I, Hazgui Y (2021) Exact and heuristic methods to solve the two-machine cross-docking flowshop scheduling problem. Int J Oper Res 42:464–477

    Article  MathSciNet  Google Scholar 

  • Hamdi I, Tekaya MF (2020) A genetic algorithm to minimize the makespan two-machine cross-docking flowshop problem. Journal of the Operations Research Society of China 8:457–476

    Article  MathSciNet  Google Scholar 

  • Hamdi I, Loukil T (2017) The permutation flowshop scheduling problem with exact time lags to minimize the total earliness and tardiness. Int J Oper Res 28:70–86

    Article  MathSciNet  Google Scholar 

  • Hengmeechai P, Wisittipanich W (2015) A multiple-objective differential evolution for Just-in-time door assignment and truck scheduling in multi door cross-docking problems. Industrial Engineering & Management Systems 14:299–311

    Article  Google Scholar 

  • Jayanthi SE, Anusuya S (2017) Minimization of Total Weighted Earliness and Tardiness using PSO for One Machine Scheduling. International Journal of Pure and Applied Mathematical Sciences 10:35–44

    Google Scholar 

  • Ladier AL, Alpan G (2014) Crossdock truck scheduling with time windows : Earliness, tardiness and storage policies. J Intell Manuf 29:569–583

    Article  Google Scholar 

  • Li Y, Lim A, Rodrigues B (2004) Cross-docking JIT scheduling with time windows. Int J Oper Res soc 55:1342–1351

    Article  Google Scholar 

  • M’Hallah R (2007) Minimizing total earliness and tardiness on a single machine using a hybrid heuristic. Comput Oper Res 34:3126–3142

    Article  Google Scholar 

  • Makui A, Tokhmehchi N (2015) A Hybrid Approach for Cross-Docking Scheduling. Indian Journal of Science and Technology 8:1–10

    Google Scholar 

  • Mokhtari H, Noroozi A (2018) An efficient chaotic based PSO for earliness/tardiness optimization in a batch processing flow shop scheduling problem. J Intell Manuf 29:1063–1081

    Article  Google Scholar 

  • Moslehi G, Mirzaee M, Vasei M, Modarres M, Azaronk A (2009) Two-machine flow shop scheduling to minimize the sum of maximum earliness and tardiness. Int J Production Economics 122:763–773

    Article  Google Scholar 

  • Moslehi G, Vasei M, Azaron A (2005) Tavakkoli-Moghaddam, R. : Optimal scheduling for a single machine to minimize the sum of maximum earliness and tardiness considering idle insert. Appl Math Comput 167:1430–1450

    MathSciNet  MATH  Google Scholar 

  • Napolitano M (2011) Crossdock fuels growth at Dots. Logistics Management 50:30–34

    Google Scholar 

  • Nearchou AC (2004) The effect of various operators on the genetic search for large scheduling problems 88:191–203

  • Ozcan E, Mohan CK (1999) Particleswarmoptimization : Surfing the waves, Proceedings of the 1999 congress on evolutionary computation, pp. 1939-1944

  • Qi X, Yu G, Bard JF (2002) Single machine scheduling with assignable due dates. Discrete Applied Mathematics 122:211–233

    Article  MathSciNet  Google Scholar 

  • Roston GP, Sturges RH (1996) GeneticAlgorithmsynthesis of four-bar mechanisms. Artificial Intelligence for Engineering. Design. Analysis and Manufacturing 10:371–390

    Google Scholar 

  • Schwerdfeger S, Boysen N, Briskorn D (2018) Just-in-time logistics for far-distant suppliers: scheduling truck departures from an intermediate cross-docking terminal. OR Spectrum 40:1–21

    Article  MathSciNet  Google Scholar 

  • Shabtay D (2012) The just-in-time scheduling problem in a flow-shop scheduling system. European Journal of Operational Research 216:521–532

    Article  MathSciNet  Google Scholar 

  • Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization, Evolutionary Computation, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406)

  • Shi Y, Eberhart R (1998) A modified particle swarm optimizer. Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence, The 1998 IEEE International Conference

  • Tasgetiren MF, Liang YC, Sevkli M, Gencyilmaz G (2007) A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem. European Journal of Operational Research 177:1930–1947

    Article  Google Scholar 

  • Tasgetiren T, Sakarya MF, Sevkli M, Liang YC, Cencylmaz G (2004) Particle swarm optimization algorithm for single machine total weighted tardiness problem. In: Proceeding of the 2004 congress on evolutionary computation, Portland, 1412–1419

  • Tavakkoli-Moghaddam R, Moslehi G, Vasei M, Azaron A (2006) A branch-and-bound algorithm for a single machine sequencing to minimize the sum of maximum earliness and tardiness with idle insert. Appl Math Comput 174:388–408

    MathSciNet  MATH  Google Scholar 

  • Tyagi N, Tripathi RP, Chandramouli AB (2016) Single Machine Scheduling Model with Total Tardiness Problem. Indian Journal of Science and Technology 9:1–14

    Google Scholar 

  • Van den Bergh F, Engelbrecht A (2010) A Convergence Proof for the Particle Swarm Optimiser. Fundamenta Informaticae 105:341–374

    Article  MathSciNet  Google Scholar 

  • Van den Bergh F (2001) An analysis of particle swarm optimizers. Ph.D.dissertation, University of Pretoria, Pretoria, South Africa

  • Van den Bergh F and Engelbrecht AP (2001) Training Product Unit Networks using Cooperative Particle Swarm Optimisers. In: Proceedings of the International Joint Conference on Neural Networks (IJCNN), Washington DC, USA, pages 126–132

  • Vinoj K, Jose T (2016) Flow shop scheduling using genetic algorithm. International journal of latest trends in engineering and technology 7:231–239

    Google Scholar 

  • Wisittipanich W, Irohara T, Hengmeecha P (2020) Particle swarm optimisation for truck scheduling problem in cross docking network. International Journal of Industrial and Systems Engineering 35:345–371

    Article  Google Scholar 

  • Witt CE (1998) Crossdocking: concepts demand choice. Material Handling Engineering 53:44–9

    Google Scholar 

  • Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver Press, 2nd ed

  • Ye Y, Li J, Li K, Fu H (2018) Cross-docking truck scheduling with product unloading/loading constraints based on an improved particle swarm optimisation algorithm. Int J Prod Res 56:5365–5385

    Article  Google Scholar 

  • Yea Y, Li JF, Fung RYK, Li K, Fu H (2018) Optimizing truck scheduling in a cross-docking system with preemption and unloading/loading sequence constraint. 27-29 March 2018 IEEE 15th International Conference on Networking, Sensing and Control (ICNSC), Zhuhai, China

  • Zhao H, Chen L (2015) Hybrid Particle Swarm Optimization for Two-stage Cross Docking Scheduling. International Journal of Hybrid Information Technology 8:249–266

    Article  Google Scholar 

Download references

Funding

The authors declare that no funds were received during the preparation of this manuscript.

Author information

Authors and Affiliations

  1. High Institute of Transport and Logistics, University of Sousse, Sousse, Tunisia

    Imen Hamdi & Imen Boujneh

  2. MODILS lab, Faculty of Economics and Management, University of Sfax, Sfax, Tunisia

    Imen Hamdi

Authors
  1. Imen Hamdi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Imen Boujneh
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Imen Hamdi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hamdi, I., Boujneh, I. Particle swarm optimization based-algorithms to solve the two-machine cross-docking flow shop problem: just in time scheduling. J Comb Optim 44, 947–969 (2022). https://doi.org/10.1007/s10878-022-00871-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-022-00871-0

Keywords