Optimizing Green Supplier Selection and Order Allocation: A Fuzzy DNAP-Fuzzy TOPSIS-Bi Objective Mathematical Model Approach with Harmony Search Algorithm

Document Type : Research Paper


1 MSc., Department of Industrial Engineering, Faculty of Engineering, Khatam University, Tehran, Iran.

2 Assistant Prof., Department of Industrial Engineering, Faculty of Engineering, Khatam University, Tehran, Iran.


In the realm of green supply chain management, the pivotal responsibilities of companies involve supplier selection and order allocation. These tasks were treated as independent challenges in prior studies. This issue holds significant importance within the context of green supply chain management, demanding the simultaneous consideration of both quantitative and qualitative criteria. These criteria, at times conflicting, necessitate an in-depth analysis of trade-offs. There is a pressing need for a comprehensive framework capable of concurrently addressing both aspects. In addition to accommodating green criteria, such a framework should enable the determination of order quantities allocated to suppliers.
The utilized approach in the present study included Fuzzy DNP, Fuzzy TOPSIS, and a Bi-objective optimization model. In the first stage, the criteria weights, encompassing both traditional and green criteria, were determined using the fuzzy DNP. Subsequently, the suppliers' scores were computed using the fuzzy TOPSIS. In the second stage, a non-linear bi-objective model was formulated, aiming to minimize the total cost and maximize the purchased value. The first objective function comprised the purchase price, suppliers' variable costs, ordering and setup costs, as well as buyer's and suppliers' inventory holding costs. Additionally, the second objective function ensured a higher allocation of orders to suppliers who had achieved a superior score in the supplier evaluation process. The model's constraints encompassed the suppliers' capacity, buyer's demand, and constraints associated with the suppliers' discounts. Acknowledging the bi-objective nature of the mathematical model, the Global Criterion method was employed to transform the bi-objective problem into a single-objective one. According to this method, the relative deviations of the objectives from their corresponding single-objective optimal values were minimized. Furthermore, due to the non-linearity of the mathematical model, a harmony search algorithm was developed for the problem, and a repair algorithm was proposed to handle constraints in the problem.
The previous studies and expert opinions were utilized to identify the criteria, encompassing both traditional and green criteria. The results of fuzzy DANP indicated that the supplier's credit holds the utmost importance, followed by quality, green purchasing, green design, green transportation, green production, on-time delivery, and distance. Furthermore, all criteria exhibit an effect on the supplier's credit. Subsequently, six suppliers underwent evaluation based on the criteria using fuzzy TOPSIS, and their final scores were employed as the suppliers' weights in the second objective function of the mathematical model. To validate the proposed approach, a case study with real data in the field of the medical equipment supply chain was examined, and the optimal solution to the problem was presented. Subsequently, by adjusting the weights of the objective functions in the single-objective problem, the Pareto solutions were identified. The proposed approach facilitates the optimal allocation to the suppliers by considering the green criteria.
The results showed that a decision maker can choose the best solution according to the Pareto solutions in such a way that there is a correct trade-off between the supply chain costs and purchased value.


Main Subjects

Abdullah, L., Chan, W., & Afshari, A. (2019). Application of PROMETHEE method for green supplier selection: a comparative result based on preference functions. Journal of Industrial Engineering International, 15, 271-285.
Afrasiabi, A., Tavana, M. & Di Caprio, D. (2022). An extended hybrid fuzzy multi-criteria decision model for sustainable and resilient supplier selection. Environmental Science and Pollution Research, 29, 37291-37314.
Alaei, S., & Khoshalhan, F. (2015). A Hybrid Cultural-Harmony Algorithm for Multi-Objective Supply Chain Coordination. Scientia Iranica, 22(3), 1227-1241.
Aouadni, S., & Euchi, J. (2022). Using integrated MMD-TOPSIS to solve the supplier selection and fair order allocation problem: a Tunisian case study. Logistics, 6(1), 8.
Babbar, C., & Amin, S. H. (2018). A multi-objective mathematical model integrating environmental concerns for supplier selection and order allocation based on fuzzy QFD in beverages industry. Expert Systems with Applications, 92, 27-38.
Chen, C. T. (2000). Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy sets and systems, 114(1), 1-9.
Chin, T. A., Tat, H. H., & Sulaiman, Z. (2015). Green supply chain management, environmental collaboration and sustainability performance. Procedia Cirp, 26, 695-699.
Dalalah, D., & Bataineh, O. (2009). A fuzzy logic approach to the selection of the best silicon crystal slicing technology. Expert Systems with Applications, 36(2), 3712-3719.
Dinçer, H., Yüksel, S., & Martínez, L. (2019). Interval type 2-based hybrid fuzzy evaluation of financial services in E7 economies with DEMATEL-ANP and MOORA methods. Applied Soft Computing, 79, 186-202.
Durmić, E., Stević, Ž., Chatterjee, P., Vasiljević, M., & Tomašević, M. (2020). Sustainable supplier selection using combined FUCOM–Rough SAW model. Reports in mechanical engineering, 1(1), 34-43.
Ecer, F. (2022). Multi-criteria decision making for green supplier selection using interval type-2 fuzzy AHP: a case study of a home appliance manufacturer. Operational Research, 22(1), 199-233.
Fu, Y. K. (2019). An integrated approach to catering supplier selection using AHP-ARAS-MCGP methodology. Journal of Air Transport Management, 75, 164-169.
Gai, L., Liu, H. C., Wang, Y., & Xing, Y. (2023). Green supplier selection and order allocation using linguistic Z-numbers MULTIMOORA method and bi-objective non-linear programming. Fuzzy Optimization and Decision Making, 22(2), 267-288.
Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: harmony search. Simulation76(2), 60-68.
Ghosh, S. K. (2017). Green supply chain management in production sectors and its impact on firm reputation. Journal of new theory, (18), 53-63.
Govindan, K., Khodaverdi, R., & Vafadarnikjoo, A. (2015). Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain. Expert Systems with Applications, 42(20), 7207-7220.
Güneri, B., & Deveci, M. (2023). Evaluation of supplier selection in the defense industry using q-rung orthopair fuzzy set based EDAS approach. Expert Systems with Applications, 222, 119846.
Hamdan, S., & Cheaitou, A. (2017). Supplier selection and order allocation with green criteria: An MCDM and multi-objective optimization approach. Computers & Operations Research, 81, 282-304.
Hashemzahi, P., Azadnia, A., Galankashi, M. R., Helmi, S. A., & Rafiei, F. M. (2020). Green supplier selection and order allocation: a nonlinear stochastic model. International Journal of Value Chain Management, 11(2), 111-138.
Hosseini, Z. S., Flapper, S. D., & Pirayesh, M. (2022). Sustainable supplier selection and order allocation under demand, supplier availability and supplier grading uncertainties. Computers & industrial engineering, 165, 107811.
Jain, N., Singh, A. R., & Upadhyay, R. K. (2020). Sustainable supplier selection under attractive criteria through FIS and integrated fuzzy MCDM techniques. International Journal of Sustainable Engineering, 13(6), 441-462.
Kamali, A., Ghomi, S. F., & Jolai, F. (2011). A multi-objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain. Computers & Mathematics with Applications, 62(8), 3251-3269.
Kannan, D., Khodaverdi, R., Olfat, L., Jafarian, A., & Diabat, A. (2013). Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain. Journal of Cleaner production, 47, 355-367.
Khalili Nasr, A., 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. Journal of Cleaner Production, 287, 124994.
Kuo, T. C., Hsu, C. W., & Li, J. Y. (2015). Developing a green supplier selection model by using the DANP with VIKOR. Sustainability, 7(2), 1661-1689.
Masoomi, B., Sahebi, I. G., Fathi, M., Yıldırım, F., & Ghorbani, S. (2022). Strategic supplier selection for renewable energy supply chain under green capabilities (fuzzy BWM-WASPAS-COPRAS approach). Energy Strategy Reviews, 40, 100815.
Mohammed, A., Harris, I., & Govindan, K. (2019). A hybrid MCDM-FMOO approach for sustainable supplier selection and order allocation. International Journal of Production Economics, 217, 171-184.
Nazari-Shirkouhi, S., Tavakoli, M., Govindan, K., & Mousakhani, S. (2023). A hybrid approach using Z-number DEA model and Artificial Neural Network for Resilient supplier Selection. Expert Systems with Applications, 222, 119746.
Nguyen, T.-L., Nguyen, P.-H., Pham, H.-A., Nguyen, T.-G., Nguyen, D.-T., Tran, T.-H., Le, H.-C., & Phung, H.-T. (2022). A novel integrating data envelopment analysis and spherical fuzzy MCDM approach for sustainable supplier selection in steel industry. Mathematics, 10, 1897.
Opricovic, S., & Tzeng, G. H. (2003). Defuzzification within a multicriteria decision model. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11(05), 635-652.
Rahman, M. M., Bari, A. M., Ali, S. M., & Taghipour, A. (2022). Sustainable supplier selection in the textile dyeing industry: An integrated multi-criteria decision analytics approach. Resources, Conservation & Recycling Advances, 15, 200117.
Razavi Hajiagha, S. H., Alaei, S., Amoozad Mahdiraji, H., & Yaftiyan, F. (2022). International collaboration formation in entrepreneurial food industry: evidence of an emerging economy. British Food Journal, 124(7), 2012-2038.
Rezaeisaray, M., Ebrahimnejad, S., & Khalili-Damghani, K. (2016). A novel hybrid MCDM approach for outsourcing supplier selection. Journal of Modelling in Management, 11(2), 536-559.
Shang, Z., Yang, X., Barnes, D., & Wu, C. (2022). Supplier selection in sustainable supply chains: Using the integrated BWM, fuzzy Shannon entropy, and fuzzy MULTIMOORA methods. Expert Systems with Applications, 195, 116567.
Shao, Y., Barnes, D., & Wu, C. (2023). Sustainable supplier selection and order allocation for multinational enterprises considering supply disruption in COVID-19 era. Australian Journal of Management, 48(2), 284-322.
Sharma, V. K., Chandna, P., & Bhardwaj, A. (2017). Green supply chain management related performance indicators in agro industry: A review. Journal of Cleaner Production, 141, 1194-1208.
Tong, L. Z., Wang, J., & Pu, Z. (2022). Sustainable supplier selection for SMEs based on an extended PROMETHEE Ⅱ approach. Journal of Cleaner Production, 330, 129830.
Tuzkaya, G. (2013). An intuitionistic fuzzy Choquet integral operator based methodology for environmental criteria integrated supplier evaluation process. International Journal of Environmental Science and Technology, 10, 423-432.
Vanalle, R. M., Ganga, G. M. D., Godinho Filho, M., & Lucato, W. C. (2017). Green supply chain management: An investigation of pressures, practices, and performance within the Brazilian automotive supply chain. Journal of Cleaner Production, 151, 250-259.
Yazdani, M., Torkayesh, A. E., & Chatterjee, P. (2020). An integrated decision-making model for supplier evaluation in public healthcare system: the case study of a Spanish hospital. Journal of Enterprise Information Management, 33(5), 965-989.