Abstract
The low-carbon supply chain is one of the predominant topics towards a green economy and it establishes the opportunity to reduce carbon emissions across the product value chain. This paper focuses on recycling and optimized sourcing in the paper industry as a case company. The main objective is to engage the case company with their supplier networks to diminish the greenhouse gases (GHG) emissions and cost in their production process. It proposes a model to support the selection of the best green supplier and an allocation of order among the potential suppliers. The proposed model contains a two-phase hybrid approach. The first phase presents the rating and selection of potential suppliers by considering economics (cost), operational factors (quality and delivery), and environmental criteria (recycle capability and GHG emission control) using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) methodology. The second phase presents the order allocation process using multi-objective linear programming in order to minimize cost, material rejection, late delivery, recycle waste and \(\mathrm{CO}_{2}\) emissions in the production process. A case study from a paper manufacturing industry is presented to elucidate the effectiveness of the proposed model. The results demonstrate a 26.2 % reduction of carbon emission by using recycle products in the production process. The firm benefits by forming a systematic methodology for green supplier evaluation and order allocation. Finally, a conclusion and a suggested direction of future research are introduced.
Similar content being viewed by others
References
Aissaoui, N., Haouari, M., & Hassini, E. (2007). Supplier selection and order lot sizing modeling: A review. Computers & Operations Research, 34(12), 3516–3540.
Alyanak, G., & Armaneri, O. (2009). An integrated supplier selection and order allocation approach in a battery company. Makine Mühendisleri Odasi, 19(4), 2–19.
Alzaman, C. (2014). Green supply chain modelling: Literature review. International Journal of Business Performance and Supply Chain Modelling, 6(1), 16–39.
Amid, A., Ghodsypour, S. H., & O’brien, C. (2006). Fuzzy multi objective linear model for supplier selection in a supply chain. International Journal of Production Economics, 104(2), 394–407.
Amid, A., Ghodsypour, S. H., & O’Brien, C. (2011). A weighted max-min model for fuzzy multi-objective supplier selection in a supply chain. International Journal of Production Economics, 131(1), 139–145.
Bai, C., & Sarkis, J. (2010). Green supplier development: Analytical evaluation using rough set theory. Journal of Cleaner Production, 18(12), 1200–1210.
Bansal, A. (2011). Trapezoidal fuzzy numbers (a, b, c, d): Arithmetic behavior. International Journal of Physical and Mathematical Sciences, 2(1), 39–44.
Bhattacharya, A., Mohapatra, P., Kumar, V., Dey, P. K., Brady, M., Tiwari, M. K., et al. (2014). Green supply chain performance measurement using fuzzy ANP-based balanced scorecard: A collaborative decision-making approach. Production Planning & Control, 25(8), 698–714.
Büyüközkan, G., & Çifçi, G. (2012). A novel hybrid MCDM approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy TOPSIS to evaluate green suppliers. Expert Systems with Applications, 39(3), 3000–3011.
Chai, J., Liu, J. N., & Ngai, E. W. (2013). Application of decision-making techniques in supplier selection: A systematic review of literature. Expert Systems with Applications, 40(10), 3872–3885.
Chen, S. H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems, 17, 113–129.
Chen, T. Y., Ku, T. C., & Tsui, C. W. (2008). Determining attribute importance based on triangular and trapezoidal fuzzy numbers in (z) fuzzy measures. In The 19th international conference on multiple criteria decision making, pp. 75–76.
Chou, S. Y., Chang, Y. H., & Shen, C. Y. (2008). A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes. European Journal of Operational Research, 189(1), 132–145.
Choy, K. L., Fan, K. K. H., & Lo, V. (2003a). Development of an intelligent customer supplier relationship management system: The application of case-based reasoning. Industrial Management and Data Systems, 103(4), 263–274.
Choy, K. L., Lee, W. B., & Lo, V. (2003b). Design of an intelligent supplier relationship management system: A hybrid case based neural network approach. Expert Systems with Applications, 24, 225–237.
De Boer, L., Labro, E., & Morlacchi, P. (2001). A review of methods supporting supplier selection. European Journal of Purchasing & Supply Management, 7(2), 75–89.
Demirtas, E. A., & Üstün, Ö. (2008). An integrated multi objective decision making process for supplier selection and order allocation. Omega, 36(1), 76–90.
DIPP (2011). Discussion paper on collection and recycling of waste paper in India. http://dipp.nic.in/english/Discuss_paper/DiscussionPaper_Recycling_WastePaper_21October2011.pdf. Accessed March 15, 2015.
Diabat, A., & Simchi-Levi, D. (2009). A carbon-capped supply chain network problem. In IEEE international conference on IEEM industrial engineering and engineering management, 2009, pp. 523–527.
Ding, H., Benyoucef, L., & Xie, X. (2005). A simulation optimization methodology for supplier selection problem. International Journal Computer Integrated Manufacturing, 18(2–3), 210–224.
Erdem, A. S., & Göçen, E. (2012). Development of a decision support system for supplier evaluation and order allocation. Expert Systems with Applications, 39(5), 4927–4937.
Faez, F., Ghodsypour, S. H., & O’brien, C. (2009). Vendor selection and order allocation using an integrated fuzzy case-based reasoning and mathematical programming model. International Journal of Production Economics, 121(2), 395–408.
Gencer, C., & Gurpinar, D. (2007). Analytic network process in supplier selection: A case study in an electronic firm. Applied Mathematical Modeling, 31(11), 2475–2486.
Gheidar Kheljani, J., Ghodsypour, S. H., & O’Brien, C. (2009). Optimizing whole supply chain benefit versus Buyer’s benefit through supplier selection. International Journal of Production Economics, 121(2), 482–493.
Ghodsypour, S. H., & O’brien, C. (1998). A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming. International Journal of Production Economics, 56, 199–212.
Ghorbani, M., Bahrami, M., & Arabzad, S. M. (2012). An integrated model for supplier selection and order allocation; using Shannon entropy, SWOT and linear programming. Procedia-Social and Behavioral Sciences, 41, 521–527.
Govindan, K., & Jensen, M. B. (2015). ELECTRE: A comprehensive literature review on methodologies and applications. European Journal of Operational Research (in press).
Govindan, K., Diabat, A., & Shankar, K. M. (2015a). Analyzing the drivers of green manufacturing with fuzzy approach. Journal of Cleaner Production, 96, 182–193.
Govindan, K., Rajendran, S., Sarkis, J., & Murugesan, P. (2015b). Multi criteria decision making approaches for green supplier evaluation and selection: A literature review. Journal of Cleaner Production, 98, 66–83.
Govindan, K., Sarkis, J., Chiappetta Jabbour, C. J., Zhu, Q., & Geng, Y. (2014). Eco-efficiency based green supply chain management: Current status and opportunities. European Journal of Operational Research, 233, 293–298.
Gunasekaran, A., Jabbour, C. J. C., & Jabbour, A. B. L. D. S. (2014). Managing organizations for sustainable development in emerging countries: An introduction. International Journal of Sustainable Development & World Ecology, 21(3), 195–197.
Gupta, R., Sachdeva, A., & Bhardwaj, A. (2012). Selection of logistic service provider using fuzzy PROMETHEE for a cement industry. Journal of Manufacturing Technology Management, 23(7), 899–921.
Handfield, R., Walton, S. V., Sroufe, R., & Melnyk, S. A. (2002). Applying environmental criteria to supplier assessment: A study in the application of the Analytical Hierarchy Process. European Journal of Operational Research, 141, 70–87.
Hasanbeigi, A., Price, L., & Kong, L. (2013). Emerging energy-efficiency and CO\(_2\) emissions-reduction technologies for industry: A review of technologies for alternative iron making and pulp and paper industry. In J. Malinowski & R. Naranjo (Eds.), Proceedings from ACEEE Summer Study on Energy Efficiency in Industry: Thinking forward, Leadership in Global Market.
Haq, A. N., & Kannan, G. (2006). Fuzzy analytical hierarchy process for evaluating and selecting a vendor in a supply chain model. International Journal of Advanced Manufacturing Technology, 29, 826–835.
Ho, W., Xu, X., & Dey, P. K. (2010). Multi-criteria decision making approaches for supplier evaluation and selection: A literature review. European Journal of Operational Research, 202(1), 16–24.
Hoffman, A. J. (2005). Climate change strategy: The business logic behind voluntary greenhouse gas reductions. California Management Review, 47(3), 21–46.
Hongjuan, Y., & Jing, Z. (2011). The strategies of advancing the cooperation satisfaction among enterprises based on low-carbon supply chain management. Energyprocedia, 5, 1225–1229.
Humphreys, P., McIvor, R., & Chan, F. (2003a). Using case-based reasoning to evaluate supplier environmental management performance. Expert Systems with Applications, 25, 141–153.
Humphreys, P. K., Wong, Y. K., & Chan, F. T. S. (2003b). Integrating environmental criteria into the supplier selection process. Journal of Materials Processing Technology, 138(1–3), 349–356.
Hwang, C. L., & Yoon, K. (1981). Multiple attribute decision making. Berlin: Springer.
Igarashi, M., de Boer, L., & Fet, A. M. (2013). What is required for greener supplier selection? A literature review and conceptual model development. Journal of Purchasing and Supply Management, 19(4), 247–263.
IPMA (2015). Recycling of waste paper. http://www.ipma.co.in/recycle.asp. Accessed March 15, 2015.
Jabbour, A. B. L. D. S., Jabbour, C. J. C., Latan, H., Teixeira, A. A., & de Oliveira, J. H. C. (2014a). Quality management, environmental management maturity, green supply chain practices and green performance of Brazilian companies with ISO 14001 certification: Direct and indirect effects. Transportation Research Part E: Logistics and Transportation Review, 67, 39–51.
Jabbour, A. B., Jabbour, C., Govindan, K., Kannan, D., & Arantes, A. F. (2014b). Mixed methodology to analyze the relationship between maturity of environmental management and the adoption of green supply chain management in Brazil. Resources, Conservation and Recycling, 92, 255–267.
Kabassi, K., & Virvou, M. (2004). Personalised adult e-training on computer use based on multiple attribute decision making. Interacting with Computers, 16(1), 115–132.
Kannan, G., Murugesan, P., Senthil, P., & Haq, A. N. (2009). Multi-criteria group decision making for the third party reverse logistics service provider in the supply chain model using Fuzzy TOPSIS for transportation services. International Journal of Services Technology and Management, 11(2), 162–181.
Kannan, G., Devika, K., & NoorulHaq, A. (2010). Analyzing supplier development criteria for an automobile industry. Industrial Management & Data Systems, 110(1), 43–62.
Kannan, G., & Murugesan, P. (2011). Selection of third party reverse logistics provider using Fuzzy extent analysis. Bench Marking: An International Journal, 18(1), 149–167.
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.
Kannan, D., Jabbour, A. B. L. D. S., & Jabbour, C. J. C. (2014a). Selecting green suppliers based on GSCM practices: Using fuzzy TOPSIS applied to a Brazilian electronics company. European Journal of Operational Research, 233(2), 432–447.
Kannan, D., Kannan, G., & Rajendran, S. (2014b). Fuzzy axiomatic design approach based green supplier selection: A case study from Singapore. Journal of Cleaner Production. doi:10.1016/j.jclepro.2013.12.076.
Keufmann, A., & Gupta, M. M. (1991). Introduction to fuzzy arithmetic: Theory and application. New York: Van Nostrand Reinhold.
Kong, L., Price, L., Hasanbeigi, A., Liu, H., & Li, J. (2012). Potential for reducing paper mill energy use and carbon dioxide emissions through plant-wide energy audits: A case study in China. Applied Energy, 102, 1334–1342.
Korhonen, P. (1999). Multiple objective linear programming in supporting forest management. In F. Helles, P. Holten-Andersen & L. Wichmann (Eds.), Multiple use of forests and other natural resources (pp. 85–95). Netherlands: Springer.
Krikke, H. (2011). Impact of closed-loop network configurations on carbon footprints: A case study in copiers. Resources, Conservation and Recycling, 55(12), 1196–1205.
Lee, A. H. I., Kang, H. Y., Hsu, C. F., & Hung, H. C. (2009). A green supplier selection model for high-tech industry. Expert Systems with Applications, 36, 7917–7927.
Lee, K. H. (2011). Integrating carbon footprint into supply chain management: The case of Hyundai Motor Company (HMC) in the automobile industry. Journal of Cleaner Production, 19(11), 1216–1223.
Lee, K. H. (2012). Carbon accounting for supply chain management in the automobile industry. Journal of Cleaner Production, 36, 83–93.
Lin, R. H. (2009). An integrated FANP-MOLP for supplier evaluation and order allocation. Applied Mathematical Modelling, 33(6), 2730–2736.
Mafakheri, F., Breton, M., & Ghoniem, A. (2011). Supplier selection-order allocation: A two-stage multiple criteria dynamic programming approach. International Journal of Production Economics, 132(1), 52–57.
Mallidis, I., Dekker, R., & Vlachos, D. (2012). The impact of greening on supply chain design and cost: A case for a developing region. Journal of Transport Geography, 22, 118–128.
Manna, S. K., Lee, C. C., & Chaudhuri, K. S. (2013). An economic order quantity model for deteriorating items with trended demand under inflation, time discounting and a trade credit policy. International Journal of Advanced Operations Management, 5(4), 320–336.
Mudgal, R. K., Shankar, R., Talib, P., & Raj, T. (2009). Greening the supply chain practices: An Indian perspective of enablers’ relationships. International Journal of Advanced Operations Management, 1(2), 151–176.
Muduli, K., Govindan, K., Barve, A., Devika, K., & Yong, G. (2013). Role of behavioural factors in green supply chain management implementation in Indian mining industries. Resources, Conservation and Recycling, 76, 50–60.
Noci, G. (1997). Designing “green” vendor rating systems for the assessment of a suppliers environmental performance. European Journal of Purchasing and Supply Management, 3(2), 103–114.
Özgen, D., Önüt, S., Gülsün, B., Tuzkaya, U. R., & Tuzkaya, G. (2008). A two-phase possibilistic linear programming methodology for multi-objective supplier evaluation and order allocation problems. Information Sciences, 178(2), 485–500.
Plambeck, E. L. (2012). Reducing greenhouse gas emissions through operations and supply chain management. Energy Economics, 34(1), S64–S74.
Rostamzadeh, R., Govindan, K., Esmaeili, A., & Sabaghi M. (2015). Application of fuzzy VIKOR for evaluation of green supply chain management practices. Ecological Indicators, 49, 188–203.
Renukappa, S., Akintoye, A., Egbu, C., & Goulding, J. (2013). Carbon emission reduction strategies in the UK industrial sectors: An empirical study. International Journal of Climate Change Strategies and Management, 5(3), 304–323.
Saaty, T. L. (1980). The analytic hierarchy process. New York: McGraw Hill.
Saen, R. F. (2010). A decision model for selecting appropriate suppliers. International Journal of Advanced Operations Management, 2(1), 46–56.
Saleem, R., Süer, G. A., & Huang, J. (2013). Dual-stage genetic algorithm approach for capacitated lot sizing problem. International Journal of Advanced Operations Management, 5(4), 299–319.
Salimifard, K., & Raeesi, R. (2014). A green routing problem: Optimising \({\rm CO}_2\) emissions and costs from a bi-fuel vehicle fleet. International Journal of Advanced Operations Management, 6(1), 27–57.
Sanayei, A., FaridMousavi, S., Abdi, M. R., & Mohaghar, A. (2008). An integrated group decision-making process for supplier selection and order allocation using multi-attribute utility theory and linear programming. Journal of the Franklin Institute, 345(7), 731–747.
Saremi, M., Mousavi, S. F., & Sanayei, A. (2009). TQM consultant selection in SMEs with TOPSIS under fuzzy environment. Expert Systems with Applications, 36(2), 2742–2749.
Setak, M., Sharifi, S., & Alimohammadian, A. (2012). Supplier selection and order allocation models in supply chain management: A review. World Applied Sciences Journal, 18(1), 55–72.
Shaw, K., Shankar, R., Yadav, S. S., & Thakur, L. S. (2012). Supplier selection using fuzzy AHP and fuzzy multi-objective linear programming for developing low-carbon supply chain. Expert Systems with Applications, 39(9), 8182–8192.
Shen, L., Olfat, L., Govindan, K., Khodaverdi, R., & Diabat, A. (2013). A fuzzy multi criteria approach for evaluating green supplier’s performance in green supply chain with linguistic preferences. Resources, Conservation and Recycling, 74, 170–179.
Srivastava, S. K. (2007). Green supply-chain management: A state-of-the-art literature review. International Journal of Management Reviews, 9(1), 53–80.
Thor, J., Ding, S. H., & Kamaruddin, S. (2013). Comparison of multi criteria decision making methods from the maintenance alternative selection perspective. The International Journal of Engineering and Science, 2(6), 27–34.
Tiwari, R. N., Dharmar, S., & Rao, J. R. (1987). Fuzzy goal programming—an additive model. Fuzzy Sets and Systems, 24(1), 27–34.
Trucost (2009). Carbon emissions—measuring the risks: An analysis of greenhouse gas emissions and costs. In An S&P 500 NSF international sector report.
Trucost (2012). Supply chain carbon briefing: Supply chain carbon briefing. In GHG Protocol scope 3 standard.
Trudeau, N., Tam, C., Graczyk, D., & Taylor, P. (2011). Energy transition for industry: India and the global context (No. 2011/2). France: OECD Publishing.
Tseng, M. L. (2011). Green supply chain management with linguistic preferences and incomplete information. Applied Soft Computing, 11(8), 4894–4903.
UNFCCC (2014). Report of the conference of the parties on its twentieth session, FCCC/CP/2014/10/Add.1.
Validi, S., Bhattacharya, A., & Byrne, P. J. (2014a). A case analysis of a sustainable food supply chain distribution system—A multi-objective approach. International Journal of Production Economics, 152, 71–87.
Validi, S., Bhattacharya, A., & Byrne, P. J. (2014b). Integrated low-carbon distribution system for the demand side of a product distribution supply chain: a DoE-guided MOPSO optimiser-based solution approach. International Journal of Production Research, 52(10), 3074–3096.
Validi, S., Bhattacharya, A., & Byrne, P. J. (2015). A solution method for a two-layer sustainable supply chain distribution model. Computers & Operations Research, 54, 204–217.
Van der Werf, G. R., Morton, D. C., DeFries, R. S., Olivier, J. G., Kasibhatla, P. S., Jackson, R. B., et al. (2009). \({\rm CO}_2\) emissions from forest loss. Nature Geoscience, 2(11), 737–738.
Victor, D. G., Zhou, D., Ahmed, E. H. M. , Dadhich, P. K., Olivier, J. G. J., Rogner, H-H., Sheikho, K., & Yamaguchi, M. (2014). Introductory chapter. In O. Edenhofer, R. Pichs-Madruga, Y. Sokona, E. Farahani, S. Kadner, K. Seyboth, A. Adler, I. Baum, S. Brunner, P. Eickemeier, B. Kriemann, J. Savolainen, S. Schlömer, C. Von Stechow, T. Zwickel & J. C. Minx (Eds.), Climate change 2014: Mitigation of climate change. Contribution of working group III to the fifth assessment report of the intergovernmental panel on climate. Cambridge: Cambridge University Press.
Virvou, M., & Kabassi, K. (2004). Evaluating an intelligent graphical user interface by comparison with human experts. Knowledge-Based Systems, 17(1), 31–37.
Walton, S. V., Handfield, R. B., & Melnyk, S. A. (1998). The green supply chain: Integrating suppliers into environmental management processes. Journal of Supply Chain Management, 34(2), 2–11.
Wang, G., Huang, S. H., & Dismukes, J. P. (2004). Product-driven supply chain selection using integrated multi-criteria decision-making methodology. International Journal of Production Economics, 91(1), 1–15.
Wang, T. Y., & Yang, Y. H. (2009). A fuzzy model for supplier selection in quantity discount environments. Expert Systems with Applications, 36, 12179–12187.
Wei-guo, F., & Hong, Z. (2007). A multi-attribute group decision-making methodapproaching to group ideal solution. In S. Liu (Ed.), Proceedings of the IEEE international conference on grey systems and intelligent services, pp. 815–819.
Wu, C., & Barnes, D. (2011). A literature review of decision-making models and approaches for partner selection in agile supply chains. Journal of Purchasing and Supply Management, 17(4), 256–274.
Wu, T., Shunk, D., Blackhurst, J., & Appalla, R. (2007). AIDEA: A methodology for supplier evaluation and selection in a supplier-based manufacturing environment. International Journal of Manufacturing Technology and Management, 11(2), 174–192.
Yeh, W. C., & Chuang, M. C. (2011). Using multi-objective genetic algorithm for partner selection in green supply chain problems. Expert Systems with Applications, 38, 4244–4253.
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.
Zeng, J., An, M., & Smith, N. J. (2007). Application of a fuzzy based decision making methodology to construction project risk assessment. International journal of Project Management, 25(6), 589–600.
Zhang, G., & Lu, J. (2003). An integrated group decision-making method dealing with fuzzy preferences for alternatives and individual judgments for selection criteria. Group Decision and Negotiation, 12, 501–515.
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45–55.
Zouggari, A., & Benyoucef, L. (2012). Simulation based fuzzy TOPSIS approach for group multi-criteria supplier selection problem. Engineering Applications of Artificial Intelligence, 25(3), 507–519.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix 1
Summary of MCDM approaches for supplier selection and order allocation
MCDM approach | Author |
---|---|
Category: supplier selection; single approach | |
Case-based reasoning (CBR) | Choy et al. (2003a) |
Neural networks | Choy et al. (2003b) |
Genetic algorithm (GA) | Ding et al. (2005) |
AHP | Haq and Kannan (2006) |
ANP | |
DEA | Wu et al. (2007) |
Fuzzy TOPSIS | Kannan et al. (2009) |
ISM | Kannan et al. (2010) |
Fuzzy extent analysis | Kannan and Murugesan (2011) |
Category: order allocation; single approach | |
Mathematical programming | Wang et al. (2004) |
Category: order allocation; integrated approach | |
FAHP and MOLP | Shaw et al. (2012) |
Category: supplier selection and order allocation; integrated approach | |
MAUT and LP | Sanayei et al. (2008) |
ANP and MOMILP | Demirtas and Üstün (2008) |
AHP and MO Possibilistic LP | Özgen et al. (2008) |
CBR and MIP | Faez et al. (2009) |
FANP and MOLP | Lin (2009) |
AHP and Dynamic programming | Mafakheri et al. (2011) |
Shannon entropy and LP | Ghorbani et al. (2012) |
FAHP and Fuzzy TOPSIS | Zouggari and Benyoucef (2012) |
AHP and GP | Erdem and Göçen (2012) |
Category: green supplier selection; single approach | |
Knowledge based system | Humphreys et al. (2003b) |
FEAHP | Lee et al. (2009) |
Multi-objective goal programming | Yeh and Chuang (2011) |
Grey theory | Tseng (2011) |
Fuzzy TOPSIS | Kannan et al. (2014a) |
Category: green supplier selection; integrated approach | |
Rough set theory and Grey system | Bai and Sarkis (2010) |
DEMATEL, ANP and TOPSIS | Büyüközkan and Çifçi (2012) |
Category: green supplier selection and order allocation; integrated approach | |
AHP and MODP | Mafakheri et al. (2011) |
FAHP, Fuzzy TOPSIS and MOLP | Kannan et al. (2013) |
Appendix 2
1.1 The proposed FAHP method for group decision making in MCDM
AHP was first developed by Saaty (1980) to determine the comparative importance of events in MCDM problem by examining the pair-wise comparisons of decision criteria. The pair-wise comparison matrix yields weight from the information of DMs and sometimes the information is uncertain and vague. The FAHP was developed to overcome the uncertainties in AHP and FAHP proposed by Zeng et al. (2007) used in this paper; the steps are presented as follows:
By following the initial condition of MCDM problem as described in the Sect. 3.2 (step 1 to 3), the steps of FAHP are
Step 1: The aggregation of the individual DMs TrFN preferences on each alternative with respect to each criterion in to group TrFN is defined by
where \( \tilde{P}_{ij}\) is the aggregated TrFN preference of criteria \(C_j\) on alternative \(A_i \), \(p_{ij}^l\) is the individual TrFN preference of criteria \(C_j\) on alternative \(A_i \) by \(M^{l}\) and \(\alpha ^{l}\) is the crisp weight of DM.
Step 2: The pair-wise comparison matrix of individual DMs TrFN preferences on each criteria is constructed as follows:
where \(\tilde{a}_{ij}^l \) is the TrFN pair-wise comparison of criteria \(C_i^l \) with \(C_j^l \) where \(i=1,2,..,n; j=1,2,\ldots ,n\)
In this study, the following scale is used for pair-wise comparison of linguistic preferences on selected criteria by DMs. For example, if VH preference is compared with H preference, then preference VH is moderately strong over H preference and reciprocal for reverse comparison. Likewise, VH preference is essentially strong over MH preference and H preference is moderately strong over MH preference.
Linguistic scale for fuzzy pair-wise comparisons
Comparison variable | Trapezoidal fuzzy scale | Trapezoidal fuzzy reciprocal scale |
---|---|---|
Equally strong | (1, 1, 1, 1) | (1, 1, 1, 1) |
Moderately strong | (2, 2.5, 3.5, 4) | (0.25, 0.29, 0.4, 0.5) |
Essentially strong | (4, 4.5, 5.5, 6) | (0.17, 0.18, 0.22, 0.25) |
Very strong | (6, 6.5, 7.5, 8) | (0.13, 0.13, 0.15, 0.17) |
Extremely strong | (8, 8.5, 9, 9) | (0.11, 0.11, 0.12, 0.13) |
Step 3: The aggregation of pair-wise comparison of criteria can be calculated by:
Step 4: In order to convert the aggregated TrFN of criteria into matching crisp values that can adequately represent the group preferences, a proper defuzzification is needed. After defuzzification, the crisp pair-wise comparison matrix between \(C_i^l \) and \(C_j^l\) is constructed as follows:
Calculate the consistency ratio (CR) of the pair-wise comparison to check the consistency of the judgment made by the DMs. Saaty (1980) indicates that if the CR value equal to 0 then the judgments are perfectly consistent, and if it is more than 0.1 then the judgments may be inconsistent.
Step 5: The priority weights of criteria in the matrix A can be calculated by using the arithmetic averaging method.
where \( w_j\) is the relative weight of criteria \(C_j \)
Step 6: The final group priority weight of each alternative \(\left( {\tilde{F}S} \right) _i \) is calculated by
Step 7: The matching crisp value \(\left( {FS} \right) _i \) of group priority weight can be calculated and the best alternative are those that have higher value of \(\left( {FS} \right) _i \).
1.2 The proposed FSAW method for group decision-making in MCDM
FSAW is simple in application and is used for solving MADM problems (Hwang and Yoon 1981; Virvou and Kabassi 2004). It consists of two basic steps (Hwang and Yoon 1981; Kabassi and Virvou 2004; Chou et al. 2008): (1) Compare the values of all attributes by proper scale. (2) Sum up the values of all the attributes for each alternative. The procedural steps of FSAW develop by adopting the initial condition given in Sect. 3.2 (step 1–3), and it is described as follows:
Step 1: The individual preference weight of each criterion by each DM is converted to a group preference weight for each criterion by
Step 2: The fuzzy group preference weight of each criteria is converted in to matching crisp value by proper defuzzification, and the normalized group weight of each criterion \(C_j\) can be calculated by
Step 3: The aggregated fuzzy decision matrix of DMs’ preferences on each alternative with respect to j criteria can be constructed as
Step 4: The normalization decision matrix for alternative evaluation based on benefit and cost criteria is constructed by:
where \(\max \left\{ {d_{ij} } \right\} \ >\ 0,\ \tilde{S}_{ij} \) denotes the transformed fuzzy rating of fuzzy benefit \(p_{ij} \)
where \(\min \left\{ {a_{ij} } \right\} \ >\ 0,\ \tilde{S}_{ij} \) denotes the transformed fuzzy rating of fuzzy cost \(p_{ij} \)
Step 5: The total fuzzy scores of individual alternatives are determined by multiplying the normalized decision matrix with the weight vector of each criteria as given by:
where \( \tilde{f}_i =\left( {r_i ,s_i ,t_i ,u_i } \right) ,i=1,2,..,m\)
Step 6: The matching crisp value \(f_i \) of each alternative weight can be calculated and the best alternatives are those that have a higher value of \(f_i \).
Rights and permissions
About this article
Cite this article
Govindan, K., Sivakumar, R. Green supplier selection and order allocation in a low-carbon paper industry: integrated multi-criteria heterogeneous decision-making and multi-objective linear programming approaches. Ann Oper Res 238, 243–276 (2016). https://doi.org/10.1007/s10479-015-2004-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-015-2004-4