An extended grey relational analysis based on COPRAS method for sustainable supplier selection in project procurement problems

Document Type : Research Paper


1 Shahed University

2 University of Tehran



The sustainable supplier selection (SSS) problem is an integral part of project procurement management. In this paper, a new extended grey relational analysis (GRA) based on the complex proportional assessment (COPRAS) is applied for SSS problems for using the merits of these two methods simultaneously. Furthermore, a new multi-objective optimization model (MOOM) is developed to obtain the objective weights of criteria. Moreover, to illustrate the uncertainty of real SSS problems and derived uncertainty of experts’ judgments, grey numbers are employed. To reduce the reliance on the experts, a new MOOM is developed for criteria’ weights determination. Finally, the performance of the introduced method is demonstrated by solving a numerical example.


Baudry, G., Macharis, C., & Vallee, T. (2018). Range-based Multi-Actor Multi-Criteria Analysis: A combined method of Multi-Actor Multi-Criteria Analysis and Monte Carlo simulation to support participatory decision making under uncertainty. European Journal of Operational Research264(1), 257-269.
Chatterjee, P., Athawale, V. M., & Chakraborty, S. (2011). Materials selection using complex proportional assessment and evaluation of mixed data methods. Materials & Design32(2), 851-860.
Chen, C. H. (2019). A New Multi-Criteria Assessment Model Combining GRA Techniques with Intuitionistic Fuzzy Entropy-Based TOPSIS Method for Sustainable Building Materials Supplier Selection. Sustainability11(8), 2265.
Chen, Z., Ming, X., Zhou, T., & Chang, Y. (2019). Sustainable supplier selection for smart supply chain considering internal and external uncertainty: An integrated rough-fuzzy approach. Applied Soft Computing, 106004.
Deng, J. L. (1982). Control problems of grey systems. Sys. & Contr. Lett.1(5), 288-294.
Deng, J.L., (1989). The introduction of Grey system. J. Grey Syst. 1, 1–24.
Dorfeshan, Y., Mousavi, S. M., Mohagheghi, V., & Vahdani, B. (2018). Selecting project-critical path by a new interval type-2 fuzzy decision methodology based on MULTIMOORA, MOOSRA and TPOP methods. Computers & Industrial Engineering120, 160-178.
Ebrahimnejad, S., Hashemi, H., Mousavi, S.M., & Vahdani, B. (2015). A NEW INTERVAL-VALUED INTUITIONISTIC FUZZY MODEL TO GROUP DECISION MAKING FOR THE SELECTION OF OUTSOURCING PROVIDERS. Economic Computation & Economic Cybernetics Studies & Research, 49(2).
Ebrahimnejad, S., Mousavi, S.M., & Seyrafianpour, H. (2010). Risk identification and assessment for build–operate–transfer projects: A fuzzy multi attribute decision making model. Expert systems with Applications37(1), 575-586.
Ebrahimnejad, S., Mousavi, S., Tavakkoli-Moghaddam, R., & Heydar, M. (2012). Evaluating high risks in large-scale projects using an extended VIKOR method under a fuzzy environment. International Journal of Industrial Engineering Computations3(3), 463-476.
Gitinavard, H., Mousavi, S.M. and Vahdani, B., (2017). Soft computing based on hierarchical evaluation approach and criteria interdependencies for energy decision-making problems: A case study. Energy, 118, pp.556-577.
Govindan, K., Mina, H., Esmaeili, A., & Gholami-Zanjani, S. M. (2020). An Integrated Hybrid Approach for Circular supplier selection and Closed loop Supply Chain Network Design under Uncertainty. Journal of Cleaner Production242, 118317.
Haeri, S. A. S., & Rezaei, J. (2019). A grey-based green supplier selection model for uncertain environments. Journal of Cleaner Production221, 768-784.
Hamdan, S., & Cheaitou, A. (2017). Supplier selection and order allocation with green criteria: An MCDM and multi-objective optimization approach. Computers & Operations Research81, 282-304.
Jiang, P., Hu, Y. C., Yen, G. F., & Tsao, S. J. (2018). Green supplier selection for sustainable development of the automotive industry using grey decision‐making. Sustainable Development26(6), 890-903.
Kahraman, C., & Karaşan, A. (2018). A Literature Survey on the Usage of Fuzzy MCDM Methods for Digital Marketing. In Intelligent Systems: Concepts, Methodologies, Tools, and Applications (pp. 54-72). IGI Global.
Kellner, F., & Utz, S. (2019). Sustainability in supplier selection and order allocation: combining integer variables with Markowitz portfolio theory. Journal of cleaner production214, 462-474.
Li, G.D., Yamaguchi, D. and Nagai, M., 2007. A grey-based decision-making approach to the supplier selection problem. Mathematical and computer modelling, 46(3), pp.573-581.
Lin, J.L., Wang, K.S., Yan, B.H., Tarang, Y.S., 1998. Optimization of the multi-response process by the Taguchi method with grey relational analysis. The Journal of Grey System 10 (4), 355–370.
Lin, Y. H., Lee, P. C., Chang, T. P., & Ting, H. I. (2008). Multi-attribute group decision making model under the condition of uncertain information. Automation in Construction17(6), 792-797.
Liu, H. C., Quan, M. Y., Li, Z., & Wang, Z. L. (2019). A new integrated MCDM model for sustainable supplier selection under interval-valued intuitionistic uncertain linguistic environment. Information Sciences486, 254-270.
Liu, H. C., Wang, L. E., You, X. Y., & Wu, S. M. (2019). Failure mode and effect analysis with extended grey relational analysis method in cloud setting. Total Quality Management & Business Excellence30(7-8), 745-767.
Liu, P., Gao, H., & Ma, J. (2019). Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment. Information Sciences490, 292-316.
Lu, Z., Sun, X., Wang, Y., & Xu, C. (2019). Green supplier selection in straw biomass industry based on cloud model and possibility degree. Journal of cleaner production209, 995-1005.
Luzon, B., & El-Sayegh, S. M. (2016). Evaluating supplier selection criteria for oil and gas projects in the UAE using AHP and Delphi. International Journal of Construction Management16(2), 175-183.
Martin, D. M., & Mazzotta, M. (2018). Non-monetary valuation using Multi-Criteria Decision Analysis: Sensitivity of additive aggregation methods to scaling and compensation assumptions. Ecosystem services29, 13-22.
Memon, M. S., Lee, Y. H., & Mari, S. I. (2015). Group multi-criteria supplier selection using combined grey systems theory and uncertainty theory. Expert Systems with Applications42(21), 7951-7959.
Mohagheghi, V., Mousavi, S.M. and Vahdani, B., (2017). Analyzing project cash flow by a new interval type-2 fuzzy model with an application to construction industry. Neural Computing and Applications, 28(11), pp.3393-3411.
Mousavi, S.M., Jolai, F., & Tavakkoli-Moghaddam, R. (2013). A fuzzy stochastic multi-attribute group decision-making approach for selection problems. Group Decision and Negotiation22(2), 207-233.
Mousavi, S.M., Torabi, S. A., & Tavakkoli-Moghaddam, R. (2013). A hierarchical group decision-making approach for new product selection in a fuzzy environment. Arabian Journal for Science and Engineering38(11), 3233-3248.
Mousavi, S.M. and Vahdani, B., (2016). Cross-docking location selection in distribution systems: a new intuitionistic fuzzy hierarchical decision model. International Journal of computational intelligence Systems, 9(1), pp.91-109.
Mousavi, S.M., Vahdani, B. and Behzadi, S.S., (2016). Designing a model of intuitionistic fuzzy VIKOR in multi-attribute group decision-making problems. Iranian Journal of Fuzzy Systems, 13(1), pp.45-65.
Opricovic, S., & Tzeng, G. H. (2007). Extended VIKOR method in comparison with outranking methods. European journal of operational research178(2), 514-529.
Pitchipoo, P., Vincent, D. S., Rajini, N., & Rajakarunakaran, S. (2014). COPRAS decision model to optimize blind spot in heavy vehicles: A comparative perspective. Procedia Engineering97, 1049-1059.
Polat, G., & Eray, E. (2015). An integrated approach using AHP-ER to supplier selection in railway projects. Procedia Engineering123, 415-422.
Safa, M., Shahi, A., Haas, C. T., & Hipel, K. W. (2014). Supplier selection process in an integrated construction materials management model. Automation in Construction48, 64-73.
Sahu, A. K., Sahu, A. K., & Sahu, N. K. (2017). Appraisements of material handling system in context of fiscal and environment extent: A comparative grey statistical analysis. International Journal of Logistics Management, 28(1), 2–28.
Stević, Ž., Pamučar, D., Puška, A., & Chatterjee, P. (2020). Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of alternatives and ranking according to COmpromise solution (MARCOS). Computers & Industrial Engineering140, 106231.
Vahdani, B., Mousavi, S. M., Tavakkoli-Moghaddam, R., Ghodratnama, A., & Mohammadi, M. (2014). Robot selection by a multiple criteria complex proportional assessment method under an interval-valued fuzzy environment. International Journal of Advanced Manufacturing Technology73(5-8), 687-697.
Valipour, A., Yahaya, N., Md Noor, N., Antuchevičienė, J., & Tamošaitienė, J. (2017). Hybrid SWARA-COPRAS method for risk assessment in deep foundation excavation project: An Iranian case study. Journal of Civil Engineering and Management23(4), 524-532.
Vilutienė, T., & Zavadskas, E. K. (2003). The application of multi-criteria analysis to decision support for the facility management of a residential district. Journal of Civil Engineering and Management9(4), 241-252.
Wang, L. E., Liu, H. C., & Quan, M. Y. (2016). Evaluating the risk of failure modes with a hybrid MCDM model under interval-valued intuitionistic fuzzy environments. Computers & Industrial Engineering102, 175-185.
Yazdani, M., Chatterjee, P., Zavadskas, E. K., & Zolfani, S. H. (2017). Integrated QFD-MCDM framework for green supplier selection. Journal of Cleaner Production142, 3728-3740.
Yin, S., Li, B., Dong, H., & Xing, Z. (2017). A new dynamic multicriteria decision-making approach for green supplier selection in construction projects under time sequence. Mathematical problems in Engineering2017.
Zavadskas, E. K., Kaklauskas, A., & Sarka, V. (1994). The new method of multicriteria complex proportional assessment of projects. Technological and economic development of economy1(3), 131-139.
Zavadskas, E. K., Turskis, Z., Tamošaitiené, J., & Marina, V. (2008). Multicriteria selection of project managers by applying grey criteria. Technological and Economic Development of Economy14(4), 462-477.
Zolghadri, M., Eckert, C., Zouggar, S., & Girard, P. (2011). Power-based supplier selection in product development projects. Computers in Industry62(5), 487-500.