FUZZY MULTI-OBJECTIVE NONLINEAR PROGRAMMING PROBLEMS UNDER VARİOUS MEMBERSHIP FUNCTIONS: A COMPARATİVE ANALYSIS

Year 2023, Volume: 11 Issue: 3, 857 - 872, 28.09.2023

Özlem Akarçay , Nimet Yapıcı Pehlivan

https://doi.org/10.21923/jesd.1062118

Abstract

Fuzzy sets have been applied to various decision-making problems when there is uncertainty in real-life problems. In decision-making problems, objective functions and constraints sometimes cannot be expressed linearly. In such cases, the problems discussed are expressed by nonlinear programming models. Fuzzy multi-objective programming models are problems containing multiple objective functions, where objective functions and/or constraints include fuzzy parameters. Membership functions are crucial to obtain optimal solution of fuzzy multi-objective programming model. In this study, a green supply chain network model with fuzzy parameters is proposed. Proposed model with nonlinear constraints is a fuzzy multi-objective nonlinear programming model that minimizes both transportation costs and emissions generated by two vehicle types during transportation. The model is used in Zimmermann's Min-Max approach by considering triangular, hyperbolic and exponential membership functions and optimal solutions are obtained. When optimal solutions are compared, it is seen that optimal solution obtained using the hyperbolic membership function is better than the optimal solutions obtained from triangular and exponential ones. Maximum common satisfaction level calculated using hyperbolic membership function for proposed model is λ=0.97. Sensitivity analysis is also carried out by taking into account distances between suppliers, manufacturers, distribution centers and customers, as well as customer demands.

Keywords

Green Supply Chain, Fuzzy Multi-objective Nonlinear Programming, Fuzzy Multi-objective Programming, Fuzzy Sets, Membership Functions, Zimmermann’s Min-Max Approach

ÇEŞITLI ÜYELIK FONKSIYONLARI ALTINDA BULANIK ÇOK AMAÇLI DOĞRUSAL OLMAYAN PROGRAMLAMA PROBLEMLERİ: KARŞILAŞTIRMALI BIR ANALİZ

Abstract

Bulanık kümeler, gerçek hayat problemlerinde belirsizlik olması durumunda çeşitli karar verme problemlerine uygulanmaktadır. Karar verme problemlerinde amaç fonksiyonları ve kısıtlar bazen doğrusal olarak ifade edilemez. Bu gibi durumlarda, ele alınan problemler doğrusal olmayan programlama modelleri ile ifade edilir. Bulanık çok amaçlı programlama modelleri, amaç fonksiyonları ve/veya kısıtların bulanık terimler içerdiği birden fazla amaç fonksiyonu olan problemlerdir. Bulanık çok amaçlı programlama modellerinin çözümünde kullanılan üyelik fonksiyonları, karar verme aşamasında çok önemlidir. Bu çalışmada, bulanık parametrelere sahip bir yeşil tedarik zinciri ağı modeli önerilmiştir. Doğrusal olmayan kısıtları olan model, hem taşıma maliyetlerini hem de taşıma esnasında iki araç tipi tarafından üretilen emisyonları en aza indiren bulanık çok amaçlı doğrusal olmayan programlama modelidir. Model, üçgensel, hiperbolik ve üstel üyelik fonksiyonları gözönüne alınarak Zimmermann'ın Min-Max yaklaşımında kullanılmış ve optimal çözümler elde edilmiştir. Optimal çözümler karşılaştırıldığında, hiperbolik üyelik fonksiyonu kullanılarak elde edilen optimal çözümün üçgensel ve üstel üyelik fonksiyonlarından elde edilen optimal çözümlerden daha iyi olduğu görülmüştür. Önerilen model için hiperbolik üyelik fonksiyonu kullanılarak hesaplanan maksimum ortak memnuniyet düzeyi λ=0.97’dir. Çalışmada, müşteri taleplerinin yanı sıra tedarikçiler, üreticiler, dağıtım merkezleri ve müşteriler arasındaki mesafeler dikkate alınarak duyarlılık analizi de yapılmıştır.

Keywords

Yeşil Tedarik Zinciri, Bulanık Çok Amaçlı Doğrusal Olmayan Programlama, Bulanık Çok Amaçlı Programlama, Bulanık Kümeler, Üyelik Fonksiyonları, Zimmermann

References

• Akarçay, Ö., 2019. Bulanık çok amaçlı doğrusal olmayan programlama problemlerinin çeşitli üyelik fonksiyonları altında incelenmesi, Selçuk Üniversitesi Fen Bilimleri Enstitüsü İstatistik Anabilim Dalı ,Yüksek Lisans Tezi.
• Bellman RE, Zadeh LA., 1970. Decision-Making in a Fuzzy Environment. Management Science, 17(4), 141-164.
• Bit A, Biswal M, Alam S., 1993. Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets and Systems, 57(2), 183-194.
• Bit AK., 2004. Fuzzy programming with hyperbolic membership functions for multiobjective capacitated transportation problem. Opsearch, 41(2), 106-120.
• Bodkhe S, Bajaj VH, Dhaigude RM., 2010. Fuzzy programming technique to solve bi-objective transportation problem. International Journal of Machine Intelligence, 2(1), 46-52.
• Chin TA, Tat HH, Sulaiman Z., 2015. Green supply chain management, environmental collaboration and sustainability performance. Procedia CIRP, 26, 695-699.
• Chunguang Q, Xiaojuan C, Kexi W, Pan P., 2008. Research on Green Logistics and Sustainable Development. 2008 International Conference on Information Management, Innovation Management and Industrial Engineering, Taiwan, 19-21 December.
• Das, S. K., 2022. A fuzzy multi objective inventory model of demand dependent deterioration including lead time. Journal of Fuzzy Extensions and Applicarions, 3(1), 1-18.
• Fares M, Kaminska B., 1995. FPAD: A fuzzy nonlinear programming approach to analog circuit design. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14(7), 785-793.
• Hu KJ., 2017. Fuzzy goal programming technique for solving flexible assignment problem in PCB assembly line. Journal of Information and Optimization Sciences, 38(3-4), 423-442.
• Kuwano H., 1996. On the fuzzy multi-objective linear programming problem: Goal programming approach. Fuzzy Sets and Systems, 82(1), 57-64.
• Liang TF., 2006. Distribution planning decisions using interactive fuzzy multi-objective linear programming. Fuzzy Sets and Systems, 157(10), 301-1316.
• Liang TF., 2007. Applying fuzzy goal programming to production/transportation planning decisions in a supply chain. International Journal of Systems Science, 38(4), 293-304.
• Liang TF, Cheng HW., 2009. Application of fuzzy sets to manufacturing/distribution planning decisions with multi-product and multi-time period in supply chains. Expert Systems with Applications, 36(2), 3367-3377.
• Li, M., Fu, Q., Singh, V. P., Liu, D., Li, T., Zhou, Y., 2020. Managing agricultural water and land resources with tradeoff between economic, environmental, and social considerations: A multi-objective non-linear optimization model under uncertainty. Agricultural systems, 178, 102685.
• 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.
• Kara, N., Kocken, H. G., 2021. A Fuzzy Approach to Multi-Objective Solid Transportation Problem with Mixed Constraints Using Hyperbolic Membership Function. Cybernetics and Information Technologies, 21(4), 158-167.
• Medina-González SA, Rojas-Torres MG, Ponce-Ortega JM, Espuña A, Guillén-Gosálbez G., 2018. Use of nonlinear membership functions and the water stress index for the environmentally conscious management of urban water systems: Application to the city of Morelia. ACS Sustainable Chemistry & Engineering, 6(6), 7752-7760.
• Miah, M. M., Rashid, A., Khan, A. R., Uddin, M. S., 2022. Goal programming approach for multi-objective optimization to the transportation problem in uncertain environment using fuzzy non-linear membership functions. Journal of Bangladesh Academy of Sciences, 46(1), 101-115.
• Mohammed A, Wang Q., 2017. The fuzzy multi-objective distribution planner for a green meat supply chain. International Journal of Production Economics, 184, 47-58.
• Orlovski S, Rinaldi S, Soncini Sessa R., 1984. A min‐max approach to reservoir management. Water Resources Research, 20(11), 1506-1514.
• Peidro D, Vasant P., 2011. Transportation planning with modified S-curve membership functions using an interactive fuzzy multi-objective approach. Applied Soft Computing, 11(2), 2656-2663.
• Sakawa M, Yano H., 1985. Interactive fuzzy decision-making for multi-objective nonlinear programming using reference membership intervals. International Journal of Man-Machine Studies, 23(4), 407-421.
• Shaw K, Shankar R, Yadav SS, Thakur LS., 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.
• Shuwang W, Lei Z, Zhifeng L, Guangfu L, Zhang HC., 2005. Study on the performance assessment of green supply chain, IEEE International Conference on Systems, Man and Cybernetics, Waikoloa, HI, USA,12-12 October.
• Singh SK, Yadav SP., 2018. Intuitionistic fuzzy multi-objective linear programming problem with various membership functions. Annals of Operations Research, 269, 693-707.
• Torabi SA, Hassini E., 2008. An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets and Systems, 159(2), 193-214.
• Verma R, Biswal M, Biswas A., 1997. Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions. Fuzzy Sets and Systems, 91(1), 37-43.
• Wang RC, Liang TF.,2004. Application of fuzzy multi-objective linear programming to aggregate production planning. Computers & Industrial Engineering, 46(1), 17-41.
• Zadeh LA., 1965. Fuzzy sets. Information and Control, 8(3), 338-353.
• Zangiabadi M, Maleki H., 2007. Fuzzy goal programming for multiobjective transportation problems. Journal of Applied Mathematics and Computing, 24(1), 449-460.
• Zangiabadi M, Maleki HR., 2013. Fuzzy goal programming technique to solve multiobjective transportation problems with some non-linear membership functions. Iranian Journal of Fuzzy Systems,10(1), 61-74.
• Zeng X, Kang S, Li F, Zhang L, Guo P., 2010. Fuzzy multi-objective linear programming applying to crop area planning. Agricultural Water Management, 98(1), 134-142.
• Zhao J, Bose BK., 2004. Evaluation of membership functions for fuzzy logic controlled induction motor drive. IEEE 2002 28th Annual Conference of the Industrial Electronics Society, IECON 02(1):229-234, Seville, Spain, 5-8 November 2002.
• Zimmermann, H. J., 1978. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55.