Abstract
Traditional mathematical models for supplier evaluation and selection have primarily focused on cost-oriented perspectives, neglecting non-cost factors such as strategic and relational measures. However, such models have often compromised the optimality of solutions. Additionally, the use of genetic algorithms in these models has resulted in similar objective function outputs with minimal differences, making it challenging to differentiate between potential suppliers. To address these limitations, this study proposes a novel approach that employs multi-criteria decision-making (MCDM) techniques to evaluate suppliers without sacrificing optimality or imposing additional constraints. The proposed model utilizes hybrid algorithms and incorporates the weighted criteria obtained through the Best–Worst Method and the ranking and selection of alternatives using the Technique for Order of Preference by Similarity to Ideal Solution. By applying MCDM methods in the post-evaluation phase, this research introduces a unique approach that preserves solution optimality. The findings highlight that while the objective function outputs from the genetic algorithm implementations may be nearly identical, they can vary significantly across other criteria. This study demonstrates the strength of multi-criteria evaluation in overcoming the limitations of genetic algorithms without compromising solution optimality.

(Source: IMF; Statista ID: 268,750)





Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Availability of data and material
Not applicable.
Code availability
MATLAB—code files.
References
Abdel-Basset M, Manogaran G, Gamal A, Smarandache F (2018) A hybrid approach of neutrosophic sets and DEMATEL method for developing supplier selection criteria. Des Autom Embed Syst 22:1–22
Aksen D (2007) Loss of customer goodwill in the uncapacitated lot-sizing problem. Comput Oper Res 9:2805–2823
Aksen D, Altınkemer K, Chand S (2003) The single-item lot-sizing problem with immediate lost sales. Eur J Oper Res 147(3):558–566
Ali BJ, Anwar G (2021) Marketing strategy: pricing strategies and its influence on consumer purchasing decision. Int J Rural Dev Environ Health Res 5(2):26–39
Assari A, Assari E (2012) Role of public participation in sustainability of historical city: usage of TOPSIS method. Indian J Sci Technol 5(3):2289–2294
Bahadori-Chinibelagh S, Fathollahi-Fard AM, Hajiaghaei-Keshteli M (2022) Two constructive algorithms to address a multi-depot home healthcare routing problem. IETE J Res 68(2):1108–1114
Cascone A, Manzo R, Piccoli B, Rarità L (2008) Optimization versus randomness for car traffic regulation. Phys Rev E 78(2):026113
Chen Z, Su S-II (2021) Omnichannel consignment supply chain cooperation: a comparative analysis of game-theoretical models. Int J Manag Sci Eng Manag 16:1–14
Cheraghalipour A, Paydar MM, Hajiaghaei-Keshteli M (2018) Applying a hybrid BWM-VIKOR approach to supplier selection: a case study in the Iranian agricultural implements industry. Int J Appl Decis Sci 11(3):274–301
Chouhan VK, Khan SH, Hajiaghaei-Keshteli M (2021) Metaheuristic approaches to design and address multi-echelon sugarcane closed-loop supply chain network. Soft Comput 25(16):11377–11404
Chowdhury NT, Baki MF, Azab A (2018) Dynamic economic lot-sizing problem: a new O (T) algorithm for the Wagner–Whitin model. Comput Ind Eng 117:6–18
D’Apice C, Manzo R, Piccoli B (2012) Optimal input flows for a PDE–ODE model of supply chains. Commun Math Sci 10(4):1225–1240
de Falco M, Gaeta M, Loia V, Rarita L, Tomasiello S (2016) Differential quadrature-based numerical solutions of a fluid dynamic model for supply chains. Commun Math Sci 14(5):1467–1476
Dehghan Nayeri M, Khazaei M, Alinasab-Imani F (2020) The critical heuristics of iranian banking credit system: analysis of the antithetical opinions of the beneficiaries. Syst Pract Action Res 33:363–392
Dokeroglu T, Sevinc E, Kucukyilmaz T, Cosar A (2019) A survey on new generation metaheuristic algorithms. Comput Ind Eng 137:106040
Ehsanifar M, Dekamini F, Spulbar C, Birau R, Khazaei M, Bărbăcioru IC (2023) A sustainable pattern of waste management and energy efficiency in smart homes using the internet of things (IoT). Sustainability 15(6):5081
Fasihi M, Tavakkoli-Moghaddam R, Najafi SE, Hajiaghaei-Keshteli M (2021) Developing a bi-objective mathematical model to design the fish closed-loop supply chain. Int J Eng 34(5):1257–1268
Foerstl K, Schleper MC, Henke M (2017) Purchasing and supply management: from efficiency to effectiveness in an integrated supply chain. J Purchas Supply Manag 23(4):223–228
Gharaei A, Karimi M, Hoseini Shekarabi SA (2020) Joint economic lot-sizing in multi-product multi-level integrated supply chains: generalized benders decomposition. Int J Syst Sci Oper Log 7(4):309–325
Ghorabaee MK, Zavadskas EK, Amiri M, Esmaeili A (2016) Multi-criteria evaluation of green suppliers using an extended WASPAS method with interval type-2 fuzzy sets. J Clean Prod 137:213–229
Ghosh S, Mandal MC, Ray A (2022) Green supply chain management framework for supplier selection: an integrated multi-criteria decision-making approach. Int J Manag Sci Eng Manag 17(3):205–219
Glock CH, Grosse EH, Jaber MY, Smunt TL (2019) Applications of learning curves in production and operations management: a systematic literature review. Comput Ind Eng 131:422–441
Goodarzian F, Wamba SF, Mathiyazhagan K, Taghipour A (2021) A new bi-objective green medicine supply chain network design under fuzzy environment: hybrid metaheuristic algorithms. Comput Ind Eng 160:107535
Govindan K, Mina H, Esmaeili A, Gholami-Zanjani SM (2020) An integrated hybrid approach for circular supplier selection and closed loop supply chain network design under uncertainty. J Clean prod 242:118317
Hajiaghaei-Keshteli M, Sajadifar SM (2010) Deriving the cost function for a class of three-echelon inventory system with N-retailers and one-for-one ordering policy. Int J Adv Manuf Technol 50:343–351
Ho W, Xu X, Dey PK (2010) Multi-criteria decision making approaches for supplier evaluation and selection: a literature review. Eur J Oper Res 202(1):16–24
Hosseini SM, Paydar MM, Hajiaghaei-Keshteli M (2021) Recovery solutions for ecotourism centers during the Covid-19 pandemic: utilizing fuzzy DEMATEL and fuzzy VIKOR methods. Expert Syst Appl 185:115594
Hu SJ, Ko J, Weyand L, ElMaraghy H, Lien T, Koren Y et al (2011) Assembly system design and operations for product variety. CIRP Ann 60(2):715–733
Kasemsap K (2020) The role of strategic outsourcing in global business. In: Foreign direct investments: concepts, methodologies, tools, and applications. IGI Global, pp 236–268
Katoch S, Chauhan SS, Kumar V (2021) A review on genetic algorithm: past, present, and future. Multimedia Tools Appl 80(5):8091–8126
Khazaei M, Ramezani M, Padash A, DeTombe D (2021a) Creating shared value to redesigning IT-service products using SYRCS; Diagnosing and tackling complex problems. Inf Syst e-Bus Manag 19:1–36
Khazaei M, Ramezani M, Padash A, DeTombe D (2021b) The quantification role of BWM in problem structuring methods: SYRCS methodology. Paper presented at the the international workshop on best-worst method
Luan J, Yao Z, Zhao F, Song X (2019) A novel method to solve supplier selection problem: hybrid algorithm of genetic algorithm and ant colony optimization. Math Comput Simul 156:294–309
Mirhosseini SS, Ramezani M, Khazaei M, Azar A (2021) Exploring and analysing the risks and challenges of implementing ERP systems: critical system thinking. Int J Inf Syst Change Manag 12(3):234–258
Moghadam MRS, Afsar A, Sohrabi B (2008) Inventory lot-sizing with supplier selection using hybrid intelligent algorithm. Appl Soft Comput 8(4):1523–1529
Mosallanezhad B, Gholian-Jouybari F, Cárdenas-Barrón LE, Hajiaghaei-Keshteli M (2023a) The IoT-enabled sustainable reverse supply chain for COVID-19 pandemic wastes (CPW). Eng Appl Artif Intell 120:105903
Mosallanezhad B, Arjomandi MA, Hashemi-Amiri O, Gholian-Jouybari F, Dibaj M, Akrami M, Hajiaghaei-Keshteli M (2023b) Metaheuristic optimizers to solve multi-echelon sustainable fresh seafood supply chain network design problem: a case of shrimp products. Alexandria Eng J 68:491–515
Mousavi R, Salehi-Amiri A, Zahedi A, Hajiaghaei-Keshteli M (2021) Designing a supply chain network for blood decomposition by utilizing social and environmental factor. Comput Ind Eng 160:107501
Mukhametzyanov I, Pamucar D (2018) A sensitivity analysis in MCDM problems: a statistical approach. Decis Mak Appl Manag Eng 1(2):51–80
Muneeb SM, Asim Z, Hajiaghaei-Keshteli M, Abbas H (2023) A multi-objective integrated supplier selection-production-distribution model for re-furbished products: Towards a circular economy. Renew Sustain Energy Rev 175:113156
Nasr AK, Tavana M, Alavi B, Mina H (2021) A novel fuzzy multi-objective circular supplier selection and order allocation model for sustainable closed-loop supply chains. J Clean Prod 287:124994
Nayeri MD, Khazaei M, Abdolahbeigi D (2022) The drivers of success in new-service development: rough set theory approach. Int J Serv Oper Manag 43(4):421–439
Nezhadroshan AM, Fathollahi-Fard AM, Hajiaghaei-Keshteli M (2021) A scenario-based possibilistic-stochastic programming approach to address resilient humanitarian logistics considering travel time and resilience levels of facilities. Int J Syst Sci Oper Log 8(4):321–347
Nourmohamadi Shalke P, Paydar MM, Hajiaghaei-Keshteli M (2018) Sustainable supplier selection and order allocation through quantity discounts. Int J Manag Sci Eng Manag 13(1):20–32
Ramezani M, Azar A, Khazaei M (2021) Gap analysis through a hybrid method: critical systems heuristics and best worst method. Paper presented at the the international workshop on best-worst method
Rarità L, Stamova I, Tomasiello S (2021) Numerical schemes and genetic algorithms for the optimal control of a continuous model of supply chains. Appl Math Comput 388:125464
Rezaei J (2015) Best-worst multi-criteria decision-making method. Omega 53:49–57
Rezaei J (2016) Best-worst multi-criteria decision-making method: some properties and a linear model. Omega 64:126–130
Rezaei J, Davoodi M (2011) Multi-objective models for lot-sizing with supplier selection. Int J Prod Econ 130(1):77–86
Saaty TL (2001) Deriving the AHP 1–9 scale from first principles. In: ISAHP 2001 proceedings, Bern, Switzerland
Sahebjamnia N, Goodarzian F, Hajiaghaei-Keshteli M (2020) Optimization of multi-period three-echelon citrus supply chain problem. J Optim Ind Eng 13(1):39-53
Sarwani MZ, Rahmi A, Mahmudy WF (2017) An adaptive genetic algorithm for cost optimization of multi-stage supply chain. J Telecommun Electron Comput Eng 9(2–7):155–160
Selvachandran G, Peng X (2019) A modified TOPSIS method based on vague parameterized vague soft sets and its application to supplier selection problems. Neural Comput Appl 31(10):5901–5916
Svahn S, Westerlund M (2009) Purchasing strategies in supply relationships. J Bus 24(3/4):173–181
Taghipour A, Khazaei M, Azar A, Rajabzadeh Ghatari A, Hajiaghaei-Keshteli M, Ramezani M (2022) Creating shared value and strategic corporate social responsibility through outsourcing within supply chain management. Sustainability 14(4):1940
Taghipour A, Ramezani M, Khazaei M, Roohparvar V, Hassannayebi E (2023) Smart transportation behavior through the COVID-19 pandemic: a ride-hailing system in Iran. Sustainability 15(5):4178
Tchokogué A, Merminod N (2021) The purchasing department’s leadership role in developing and maintaining a preferred customer status. J Purch Supply Manag 27(2):100686
Vadde S, Zeid A, Kamarthi SV (2011) Pricing decisions in a multi-criteria setting for product recovery facilities. Omega 39(2):186–193
Yan J (2022) The evolution and governance of online rumors during the public health emergency: taking COVID-19 pandemic related rumors as an example. Int J Manag Sci Eng Manag 17(1):1–9
Acknowledgements
We would like to express our heartfelt acknowledgement to the late Professor Adel Azar for his invaluable contributions to this paper. Professor Azar's expertise, guidance, and mentorship have greatly influenced the development and quality of our research. His profound knowledge, dedication, and passion for science, have been instrumental in shaping the ideas and direction of this study. Professor Adel Azar's untimely passing in August 2022 has left a void in the academic community, and we deeply mourn the loss of such a remarkable scholar and mentor. We will always cherish the memories of working with him, his insightful discussions, and his unwavering support throughout the research process. We extend our sincere gratitude to Professor Adel Azar for his significant contributions and lasting impact on this paper. His passion for knowledge and commitment to excellence will continue to inspire us in our future research endeavors. May his soul rest in peace.
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
MK and AA contributed to conceptualization; MK and MH-K helped in methodology; MK done software; MR, ARG, and AA helped in validation; MH-K and MR contributed to formal analysis; AA and MK helped in investigation; MK, MH-K, and AA contributed to resources; MK helped in data curation; AA and MK contributed to writing—original draft preparation; MK, MH-K, AF, and MR contributed to writing; MK, AF, and MR helped in visualization; AA helped in supervision; AF and MK contributed to project administration and ARG revision. All authors have read and agreed to the published version of the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
There is no conflict of interest.
Ethical approval
Not applicable, because this article does not contain any studies with human or animal subjects.
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.
About this article
Cite this article
Khazaei, M., Hajiaghaei-Keshteli, M., Rajabzadeh Ghatari, A. et al. A multi-criteria supplier evaluation and selection model without reducing the level of optimality. Soft Comput 27, 17175–17188 (2023). https://doi.org/10.1007/s00500-023-08954-8
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-023-08954-8