Application of Incomplete Analytic Hierarchy Process and Choquet Integral to Select the best Supplier and Order Allocation in Petroleum Industry

Document Type : Original Article


School of Industrial Engineering, Iran University of Science and Technology (IUST), Tehran, Iran


In a powerful industry, supplier selection is one of the complex processes that can increase productivity and competitive advantages. Supplier selection includes different quantitative, qualitative, and also interactive criteria. In addition, the selection process has always faced with inadequate and incomplete data. Multi-criteria decision making (MCDM) is a useful approach that can be applied, for addressing the opting problems of a supplierconsidering mentioned issues. In this approach, the interaction between criteria can be considered with several methods, such as Choquet integral, which is a practical method for decision ranking. Also, incomplete data can be covered with incomplete analytic hierarchy process (AHP) method. Therefore, in this study, an application of Choquet integral along with incomplete AHP method is provided for supplier selection problem at the petroleum industry. After achieving the ranking rate of suppliers, requested orders are assigned to preferred suppliers by using multi-objective linear programming(MOLP) model and ɛ-constraint method to generate the Pareto optimal points. As a result, supplier 3 with weight 0.8274 was the most preferred supplier in which 50% of total orders was assigned to this supplier as the best selection.


  1. Wood. D.A, “Supplier selection for development of petroleum industry facilities, applying multi-criteria decision making techniques including fuzzy and intuitionistic fuzzy TOPSIS with flexible entropy weighting”, Journal of Natural Gas Science and Engineering,Vol. 28, (2015), 594-612, doi: 10.1016/j.jngse.2015.12.021.
  2. Li. S, and Zeng. W, “Risk analysis for the supplier selection problem using failure modes and effects analysis (FMEA)”, Journal of Intelligent Manufacturing,Vol. 27, No. 6, (2016), 1309-1321, doi: 10.1007/s10845-014-0953-0.
  3. Ho. W, Xu. X, and Dey. PK, “Multi-criteria decision making approaches for supplier evaluation and selection: A literature review”, European Journal of operational research,Vol. 202, No. 1, (2010),16-24, doi: 10.1016/j.ejor.2009.05.009.
  4. Tzeng. G-H, and Huang. J-J, “Multiple attribute decision making: methods and applications”, CRC press, (2011).
  5. Choquet. G, “Theory of capacities”, in Annales de l'institut Fourier, Vol. 5, (1954), 131-295, doi: 10.5802/aif.53.
  6. Grabisch. M, “The application of fuzzy integrals in multicriteria decision making”, European journal of operational research,Vol. 89, No. 3, (1996), 445-456, doi: 10.1016/0377-2217(95)00176-X.
  7. Bottero. M, Ferretti. V, Figueira.  J.R, Greco. S, and Roy. B, “On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application”, European Journal of Operational Research,Vol. 271, No. 1, (2018),120-140, doi: 10.1016/j.ejor.2018.04.022.
  8. Zegordi. S, Hosseinzadeh. A, Nahavandi. N, and Sadeghi Rad. R, “An integrated closed-loop supply chain configuration model and supplier selection based on offered discount policies”, International Journal of Engineering, Transactions C: Aspects,Vol. 31, No. 3, (2018), 440-449, doi: 10.5829/ije.2018.31.03c.06.
  9. Amiri. M.P, “Project selection for oil-fields development by using the AHP and fuzzy TOPSIS methods”, Expert Systems with Applications,Vol. 37, No. 9, (2010), 6218-6224, doi: 10.1016/j.eswa.2010.02.103.
  10. Wang. C-N, Huang. Y-F, Cheng. I, and Nguyen. V.T, “A multi-criteria decision-making (MCDM) approach using hybrid SCOR metrics, AHP, and TOPSIS for supplier evaluation and selection in the gas and oil industry”, Processes,Vol. 6, No. 12, (2018), 252, doi: 10.3390/pr6120252.
  11. Sivapornpunlerd. N, and Setamanit. S-o, “Supplier performance evaluation: a case study of thai offshore oil & gas exploration and production company”, ASBBS Proceedings,Vol. 21, No. 1, (2014), 647.
  12. Gholamian. K, Vakilifard. H, Talebnia. G, and Hejazi. R, “Conceptual Design of Sustainable Outsourcing with Balanced Scorecard Using Analytic Hierarchy Process: A Case Study for Fajr Jam Gas Refining Company”, International Journal of Engineering, Transactions A: Basics,Vol. 33, No. 1, (2020),112-123, doi: 10.5829/ije.2020.33.01a.13.
  13. Arabzad. S.M, Ghorbani. M, Razmi. J, and Shirouyehzad. H, “Employing fuzzy TOPSIS and SWOT for supplier selection and order allocation problem”, The International Journal of Advanced Manufacturing Technology,Vol. 76, No. 5-8, (2015), 803-818, doi: /10.1007/s00170-014-6288-3.
  14. Yildiz. A, and Yayla. A, “Application of fuzzy TOPSIS and generalized Choquet integral methods to select the best supplier”, Decision Science Letters,Vol. 6, No. 2, (2017), 137-150, doi: 10.5267/j.dsl.2016.11.001.
  15. Hernadewita. H, Saleh. B. I, “Identifying Tools and Methods for Risk Identification and Assessment in Construction Supply Chain”, International Journal of Engineering, Transactions A: Basics, Vol. 33, No. 7, (2020), 1311-1320, doi: 10.5829/ije.2020.33.07a.18.
  16. Hamdan. S, and Cheaitou. A, “Supplier selection and order allocation with green criteria: An MCDM and multi-objective optimization approach”, Computers & Operations Research,Vol. 81, (2017), 282-304, doi: 10.1016/j.cor.2016.11.005.
  17. Çebi. F, and Otay, İ, “A two-stage fuzzy approach for supplier evaluation and order allocation problem with quantity discounts and lead time”, Information Sciences,Vol. 339, (2016),143-157, doi: 10.1016/j.ins.2015.12.032
  18. Hamdan. S, and Cheaitou. A, “Dynamic green supplier selection and order allocation with quantity discounts and varying supplier availability”, Computers & Industrial Engineering,Vol. 110, (2017), 573-589, doi: 10.1016/j.cie.2017.03.028.
  19. Harker. P.T, “Incomplete pairwise comparisons in the analytic hierarchy process”, Mathematical Modelling,Vol. 9, No. 11, (1987), 837-848, doi: 10.1016/0270-0255(87)90503-3.
  20. Chen. K, Kou. G, Tarn. J. M, and Song. Y, “Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices” Annals of Operations Research,Vol. 235, No. 1, (2015), 155-175, doi: 10.1007/s10479-016-2396-9.
  21. Ergu. D, Kou. G, Peng. Y, and Zhang. M, “Estimating the missing values for the incomplete decision matrix and consistency optimization in emergency management”, Applied Mathematical Modelling,Vol. 40, No. 1, (2016), 254-267,doi: 10.1016/j.apm.2015.04.047.
  22. Gao. S, Zhang. Z, and Cao. C, “Calculating Weights Methods in Complete Matrices and Incomplete Matrices”, Journal of Software, Vol. 5, No. 3, (2010), 304-311, doi: 10.4304/jsw.5.3.304-311.
  23. Kaoru. T, "A Logarithmic Least Squares Method for Incomplete Pairwise Comparisons in the Analytic Hierarchy Process”, Institute for Policy Science Research Report, Vol. 94, No. 2, (1993).
  24. Bozóki. S, Csató. L, and Temesi. J, “An application of incomplete pairwise comparison matrices for ranking top tennis players”, European Journal of Operational Research,Vol. 248, No. 1, (2016), 211-218, doi: 10.1016/j.ejor.2015.06.069.
  25. Bozóki. S, “A method for solving LSM problems of small size in the AHP”, Central European Journal of Operations Research,Vol. 11, No. 1, (2003), 17-33.
  26. Bozóki. S, “Solution of the least squares method problem of pairwise comparison matrices”, Central European Journal of Operations Research,Vol. 16, No. 4, (2008), 345,doi: 10.1007/s10100-008-0063-1.
  27. Faramondi. L, Oliva. G, and Bozóki. S, “Incomplete Analytic Hierarchy Process with Minimum Ordinal Violations”, IEEE Transactions on Automatic Control,(2020), doi: 10.1109/TAC.2020.3004788.
  28. Foroozesh. N, and Tavakkoli-Moghaddam. R, “Sustainable Supplier Selection by a New Hybrid Support Vector-model based on the Cuckoo Optimization Algorithm”, International Journal of Engineering, Transactions C: Aspects,Vol. 30, No. 6, (2017), 867-875, doi: 10.5829/ije.2017.30.06c.07.
  29. Xu. Y, Patnayakuni. R, and Wang. H, “Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations”, Applied Mathematical Modelling,Vol. 37, No. 4, (2013), 2139-2152, doi: 10.1016/j.apm.2012.05.010.
  30. Gomez-Ruiz. J.A, Karanik. M, and Peláez. J.I, “Estimation of missing judgments in AHP pairwise matrices using a neural network-based model”, Applied Mathematics and Computation,Vol. 216, No. 10, (2010), 2959-2975, doi: 10.1016/j.amc.2010.04.009.
  31. Zhou. X, Hu. Y, Deng. Y, Chan. F.T, and Ishizaka. A, “A DEMATEL-based completion method for incomplete pairwise comparison matrix in AHP”, Annals of Operations Research,Vol. 271, No. 2, (2018), 1045-1066, doi: 10.1007/s10479-018-2769-3.
  32. Saaty. T.L, “Decision making—the analytic hierarchy and network processes (AHP/ANP)”, Journal of Systems Science and Systems Engineering,Vol. 13, No. 1, (2004), 1-35, doi: 10.1007/s11518-006-0151-5.
  33. Ghayoomi. M, Abooei.  M. H, Vahdatzad.  M. A, and Ebrahimi.  A, “Designing a Model for Creation of Export Consortiain Business Cluster”, International Journal of Engineering, Transactions C: Aspects, Vol. 33, No. 3, (2020), 459-467, doi: 10.5829/ije.2020.33.03c.10.
  34. Sugeno. M, “Theory of fuzzy integrals and its applications”, Doct. Thesis, Tokyo Institute of technology,(1974).
  35. Mavrotas. G, “Effective implementation of the ε-constraint method in multi-objective mathematical programming problems”, Applied Mathematics and Computation, Vol. 213, No. 2, (2009), 455-465, doi: 10.1016/j.amc.2009.03.037.
  36. Rao. C, Xiao. X, Goh. M, Zheng. J, and Wen. J, “Compound mechanism design of supplier selection based on multi-attribute auction and risk management of supply chain”, Computers & Industrial Engineering,Vol. 105, (2017), 63-75, doi: 10.1016/j.cie.2016.12.042.
  37. Banaeian. N, Nielsen. I.E, Mobli. H, and Omid. M, “Green supplier selection in edible oil production by a hybrid model using Delphi method and Green Data Envelopment Analysis (GDEA)”, Management and Production Engineering Review,Vol. 5, No. 4, (2014), 3-8, doi: 10.2478/mper-2014-0030.
  38. Kaviani. M.A, Yazdi. A.K, Ocampo. L, and Kusi-Sarpong. S, “An integrated grey-based multi-criteria decision-making approach for supplier evaluation and selection in the oil and gas industry”, Kybernetes,(2019), doi: 10.1108/K-05-2018-0265.