Skip to main content
Springer Nature Link
Log in

A sustainable uncertain integrated supply chain network design and assembly line balancing problem with U-shaped assembly lines and multi-mode demand

  • Optimization
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Supply chain network design (SCND) problems are essential in formulating strategic decisions on the number of facilities, network facility location, and plant capacity, to ensure the optimal delivery of products from manufacturers to end consumers. On the other hand, assembly line balancing (ALB) problems provide details on operational decisions which encompass production levels and inventories and therefore should be flexible enough to react when changes in resource availability and product demands occur. This study develops a novel combination of these independent problems as a multi-objective SCND-ALB problem which considers economic, environmental, and social objectives in determining the optimal design and operational conditions of the supply chain which consists of U-shaped assembly lines. Furthermore, the normal type belief degree-based uncertainty is considered to reflect the uncertainty of the parameters of the problem. The uncertain formulation is crisped using two different approaches. Then, two multi-objective solution approaches of the literature such as TH and GCM approaches are considered to simultaneously account for the three sustainability objectives of the obtained crisp multi-objective formulations. Finally, a numerical example is used to demonstrate the capabilities of the problem in detail. Furthermore, several test problems are used to compare the performance of the solution approaches. Based on the obtained results, the TH approach performs better in 100% of the experiments.

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
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

Enquiries about data availability should be directed to the authors.

References

  • Alavidoost MH, Tarimoradi M, Fazel Zarandi MH (2015) Fuzzy adaptive genetic algorithm for multi-objective assembly line balancing problems. Appl Soft Comput 34:655–677

    Article  Google Scholar 

  • Alavidoost MH, Babazadeh H, Sayyari ST (2016) An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem. Appl Soft Comput 40:221–235

    Article  Google Scholar 

  • Asl AJ, Solimanpur M, Shankar R (2019) Multi-objective multi-model assembly line balancing problem: a quantitative study in engine manufacturing industry. Opsearch 56(3):603–627

    Article  MathSciNet  Google Scholar 

  • Battini D, Delorme X, Dolgui A, Sgarbossa S (2015) Assembly line balancing with ergonomics paradigms: two alternative methods. IFAC-PapersOnLine 48(3):586–591

    Article  Google Scholar 

  • Baybars I (1986) A survey of exact algorithms for the simple assembly line balancing problem. Manag Sci 32:909–932

    Article  MathSciNet  Google Scholar 

  • Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):B141

    Article  MathSciNet  Google Scholar 

  • Chen L, Peng J, Zhang B (2017) Uncertain goal programming models for bicriteria solid transportation problem. Appl Soft Comput 51:49–59

    Article  Google Scholar 

  • Dalman H (2016) Uncertain programming model for multi-item solid transportation problem. Int J Mach Learn Cybern 9:1–9

    Google Scholar 

  • Ding S (2015) The α-maximum flow model with uncertain capacities. Appl Math Model 39(7):2056–2063

    Article  MathSciNet  Google Scholar 

  • Ding S, Gao Y (2014) The (σ, S) policy for uncertain multi-product newsboy problem. Expert Syst Appl 41(8):3769–3776

    Article  Google Scholar 

  • Fattahi A, Turkay M (2015) On the MILP model for the U-shaped assembly line balancing problems. Eur J Oper Res 242(1):343–346

    Article  MathSciNet  Google Scholar 

  • Gao Y (2012) Uncertain models for single facility location problems on networks. Appl Math Model 36:2592–2599

    Article  MathSciNet  Google Scholar 

  • Gao Y, Kar S (2017) Uncertain solid transportation problem with product blending. Int J Fuzzy Syst 19(6):1916–1926

    Article  MathSciNet  Google Scholar 

  • Hamta N, Akbarpour Shirazi M, Fatemi Ghomi SMT, Behdad S (2015) Supply chain network optimization considering assembly line balancing and demand uncertainty. Int J Prod Res 53(10):2970–2994

    Article  Google Scholar 

  • Hazır Ö, Dolgui A (2015) A decomposition based solution algorithm for U-type assembly line balancing with interval data. Comput Oper Res 59:126–131

    Article  MathSciNet  Google Scholar 

  • Heydari A, Mahmoodirad A, Niroomand S (2016) An entropy-based mathematical formulation for straight assembly line balancing problem. Int J Strateg Decis Sci 7(2):57–68

    Article  Google Scholar 

  • Huang X, Di H (2016) Uncertain portfolio selection with background risk. Appl Math Comput 276:284–296

    MathSciNet  Google Scholar 

  • Jamshidi M, Saneie M, Mahmoodirad A, Hosseizadeh Lotfi F, Tohidi G (2019) Uncertain RUSSEL data envelopment analysis model: a case study in Iranian banks. J Intell Fuzzy Syst 37(2):2937–2951

    Article  Google Scholar 

  • Jamshidi M, Sanei M, Mahmoodirad A, Tohidi G, Hosseinzade Lotfi F (2021a) Uncertain SBM data envelopment analysis model: a case study in Iranian banks. Int J Financ Econ 26(2):2674–2689

    Article  Google Scholar 

  • Jamshidi M, Sanei M, Mahmoodirad A, Tohidi G, Hosseinzade Lotfi F (2021b) Uncertain BCC data envelopment analysis model with belief degree: a case study in Iranian Banks. Int J Ind Math 13(3):239–249

    Google Scholar 

  • Jamshidi M, Sanei M, Mahmoodirad A (2022) An uncertain allocation models in data envelopment analysis: a case in the Iranian Stock Market. Scientia Iranica 29(6):3434–3454

    Google Scholar 

  • Koç Ç (2017) An evolutionary algorithm for supply chain network design with assembly line balancing. Neural Comput Appl 28(11):3183–3195

    Article  Google Scholar 

  • Kovács G, Vizvári B (2018) A generalization of Hunter’s bound to hypergraphs. Ann Oper Res. https://doi.org/10.1007/s10479-018-2869-0

    Article  Google Scholar 

  • Kucukkoc I, Zhang DZ (2014) Mathematical model and agent based solution approach for the simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines. Int J Prod Econ 158:314–333

    Article  Google Scholar 

  • Kucukkoc I, Zhang DZ (2016) Mixed-model parallel two-sided assembly line balancing problem: a flexible agent-based ant colony optimization approach. Comput Ind Eng 97:58–72

    Article  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin, Heidelberg

    Google Scholar 

  • Liu L, Zhang B, Ma W (2018) Uncertain programming models for fixed charge multi-item solid transportation problem. Soft Comput 22(17):5825–5833

    Article  Google Scholar 

  • Mahmoodirad A, Niroomand S (2020a) A belief degree-based uncertain scheme for a bi-objective two-stage green supply chain network design problem with direct shipment. Soft Comput 24(24):18499–18519

    Article  Google Scholar 

  • Mahmoodirad A, Niroomand S (2020b) Uncertain location-allocation decisions for a bi-objective two-stage supply chain network design problem with environmental impacts. Expert Syst 37:e12558

    Article  Google Scholar 

  • Mahmoodirad A, Sanei M (2016) Solving a multi-stage multi-product solid supply chain network design problem by meta-heuristics. Scientia Iranica 23(3):1429–1440

    Article  Google Scholar 

  • Mahmoodirad A, Dehghan R, Niroomand S (2019) Modelling Linear fractional transportation problem in belief degree-based uncertain environment. J Exp Theor Artif Intell 31(3):393–408

    Article  Google Scholar 

  • Mahmoodirad A, Niroomand S, Shafiee M (2020) A closed loop supply chain network design problem with multi-mode demand satisfaction in fuzzy environment. J Intell Fuzzy Syst 39(1):503–524

    Article  Google Scholar 

  • Make MRA, Rashid MFFA, Razali MM (2017) A review of two-sided assembly line balancing problem. Int J Adv Manuf Technolgy 89(5–8):1743–1763

    Article  Google Scholar 

  • Molla-Alizadeh-Zavardehi S, Mahmoodirad A, Rahimian M (2014) Step fixed charge transportation problems via genetic algorithm. Indian J Sci Technol 7(7):949–954

    Article  Google Scholar 

  • Mosallaeipour S, Mahmoodirad A, Niroomand S, Vizvari B (2018) Simultaneous selection of material and supplier under uncertainty in carton box industries: a fuzzy possibilistic multi-criteria approach. Soft Comput 22(9):2891–2905

    Article  Google Scholar 

  • Niroomand S, Hadi-Vencheh A, Mirzaei N, Molla-Alizadeh-Zavardehi S (2016) Hybrid greedy algorithms for fuzzy tardiness/earliness minimization in a special single machine scheduling problem: case study and generalization. Int J Comput Integr Manuf 29(8):870–888

    Article  Google Scholar 

  • Niroomand S, Mosallaeipour S, Mahmoodirad A, Vizvari B (2018) A study of a robust multi-objective supplier-material selection problem. IMA J Manag Math 29(3):325–349

    MathSciNet  Google Scholar 

  • Niroomand S, Mahmoodirad A, Mosallaeipour S (2019) A hybrid solution approach for fuzzy multiobjective dual supplier and material selection problem of carton box production systems. Expert Syst 36(1):e12341

    Article  Google Scholar 

  • No RKG, Niroomand S, Didehkhani H, Mahmoodirad A (2021) Modified interval EDAS approach for the multi-criteria ranking problem in banking sector of Iran. J Ambient Intell Humaniz Comput 12:8129–8148

    Article  Google Scholar 

  • Ogan D, Azizoglu M (2015) A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements. J Manuf Syst 36:46–54

    Article  Google Scholar 

  • Oksuz MK, Buyukozkan K, Satoglu SI (2017) U-shaped assembly line worker assignment and balancing problem: a mathematical model and two meta-heuristics. Comput Ind Eng 112:246–263

    Article  Google Scholar 

  • Özcan U (2019) Balancing and scheduling tasks in parallel assembly lines with sequence-dependent setup times. Int J Prod Econ 213:81–96

    Article  Google Scholar 

  • Özçelik G, Faruk Yılmaz Ö, Betül Yeni F (2021) Robust optimisation for ripple effect on reverse supply chain: an industrial case study. Int J Prod Res 59(1):245–264

    Article  Google Scholar 

  • Paksoy T, Özceylan E (2012) Supply chain optimisation with U-type assembly line balancing. Int J Prod Res 50(18):5085–5105

    Article  Google Scholar 

  • Paksoy T, Özceylan E, Gökçen H (2012) Supply chain optimisation with assembly line balancing. Int J Prod Res 50(11):3115–3136

    Article  Google Scholar 

  • Pereira J, Vilà M (2016) A new model for supply chain network design with integrated assembly line balancing decisions. Int J Prod Res 54(9):2653–2669

    Article  Google Scholar 

  • Pishvaee MS, Farahani RZ, Dullaert W (2010) A memetic algorithm for bi-objective integrated forward/reverse logistics network design. Comput Oper Res 37(6):1100–1112

    Article  Google Scholar 

  • Ramezanian R, Khalesi S (2019) Integration of multi-product supply chain network design and assembly line balancing. Oper Res. https://doi.org/10.1007/s12351-019-00453-9

    Article  Google Scholar 

  • Razali MM, Kamarudin NH, Ab-Rashid MFF, Mohd Rose AN (2019) Recent trend in mixed-model assembly line balancing optimization using soft computing approaches. Eng Comput 36(2):622–645

    Article  Google Scholar 

  • Salehi M, Maleki HR, Niroomand S (2018) A multi-objective assembly line balancing problem with worker’s skill and qualification considerations in fuzzy environment. Appl Intell 48(8):2137–2156

    Article  Google Scholar 

  • Samizadeh R, Vatankhah S, Aghagoli S (2017) Introducing a bi-level model to optimise the distribution network design and assembly line balancing. Int J Adv Oper Manag 9(2):106–121

    Google Scholar 

  • Samouei P, Fattahi P, Ashayeri J, Ghazinoory S (2016) Bottleneck easing-based assignment of work and product mixture determination: fuzzy assembly line balancing approach. Appl Math Model 40(7–8):4323–4340

    Article  MathSciNet  Google Scholar 

  • Sun BQ, Wang L (2019) A decomposition-based matheuristic for supply chain network design with assembly line balancing. Comput Ind Eng 131:408–417

    Article  Google Scholar 

  • Torabi SA, Hassini E (2008) An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets Syst 159:193–214

    Article  MathSciNet  Google Scholar 

  • Wen M, Guo L, Kang R, Yang Y (2014) Data envelopment analysis with uncertain inputs and outputs. J Appl Math. https://doi.org/10.1155/2014/307108

    Article  Google Scholar 

  • Yılmaz ÖF (2020a) Robust optimization for U-shaped assembly line worker assignment and balancing problem with uncertain task times. Croat Oper Res Rev 11:229–239

    Article  Google Scholar 

  • Yılmaz ÖF (2020b) Examining additive manufacturing in supply chain context through an optimization model. Comput Ind Eng 142:106335

    Article  Google Scholar 

  • Yılmaz ÖF (2022) An integrated bi-objective U-shaped assembly line balancing and parts feeding problem: optimization model and exact solution method. Ann Math Artif Intell 90(7–9):679–696

    Article  MathSciNet  Google Scholar 

  • Yılmaz ÖF, Pardalos PM (2017) Minimizing average lead time for the coordinated scheduling problem in a two-stage supply chain with multiple customers and multiple manufacturers. Comput Ind Eng 114:244–257

    Article  Google Scholar 

  • Yolmeh A, Salehi N (2015) An outer approximation method for an integration of supply chain network designing and assembly line balancing under uncertainty. Comput Ind Eng 83:297–306

    Article  Google Scholar 

  • Yuguang Z, Bo A, Yong Z (2016) A PSO algorithm for multi-objective hull assembly line balancing using the stratified optimization strategy. Comput Ind Eng 98:53–62

    Article  Google Scholar 

  • Zacharia PTh, Nearchou AC (2016) A population-based algorithm for the bi-objective assembly line worker assignment and balancing problem. Eng Appl Artif Intell 49:1–9

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the editors and anonymous reviewers of the journal for their constructive comments that helped to improve the paper.

Funding

This study was not funded by any organization.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Nahid Farzan, Sadegh Niroomand & Saber Molla-Alizadeh-Zavardehi

  2. Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

    Ali Mahmoodirad

  3. Department of Industrial Engineering, Firouzabad Higher Education Center, Shiraz University of Technology, Shiraz, Iran

    Sadegh Niroomand

Authors
  1. Nahid Farzan
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Ali Mahmoodirad
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Sadegh Niroomand
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Saber Molla-Alizadeh-Zavardehi
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Ali Mahmoodirad.

Ethics declarations

Conflict of interest

Author Nahid Farzan declares that he has no conflict of interest. Author Ali Mahmoodirad declares that he has no conflict of interest. Author Sadegh Niroomand declares that he has no conflict of interest. Author Saber Molla-Alizadeh-Zavardehi declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

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

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Farzan, N., Mahmoodirad, A., Niroomand, S. et al. A sustainable uncertain integrated supply chain network design and assembly line balancing problem with U-shaped assembly lines and multi-mode demand. Soft Comput 28, 2967–2986 (2024). https://doi.org/10.1007/s00500-023-09227-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-09227-0

Keywords