Solving Vendor Selection Problem by Interval Approximation of Piecewise Quadratic Fuzzy Number
Keywords:
Close interval approximation, Fuzzy optimal solution, Piecewise quadratic fuzzy numbers, Vendor selectionAbstract
In this paper, a Vendor Selection Problem (VSP) with fuzzy parameter uncertainty is introduced. The buyer gives a quantity order for a commodity among a set of suppliers. Buyer’s objective is to obtain the requirements of lead time, service level and aggregate quality at the minimum cost. Some of the problem parameters are characterized by the piecewise quadratic fuzzy numbers. In addition, an interval approximation for piecewise quadratic fuzzy numbers is proposed for solving the VSP. The VSP with close interval approximation is approached by taking the minimum and maximum values inequalities with the constraints transformed it to two classical Linear Programming Problems (LPPs). The optimal solution for these LPPs is obtained. A numerical example is provided for illustration of the suggested approach.
References
Dickson, G. W. (1966). An analysis of vendor selection systems and decisions. Journal of purchasing, 2(1), 5–17.
https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1745-493X.1966.tb00818.x
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.
https://www.sciencedirect.com/science/article/pii/S001999586590241X
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions.
Fuzzy sets and systems, 1(1), 45–55. https://www.sciencedirect.com/science/article/pii/0165011478900313
Dubois, D. J. (1980). Fuzzy sets and systems: theory and applications. Elsevier science.
https://books.google.com/books?id=JmjfHUUtMkMC
Kaufmann, A., & Gupta, M. M. (1988). Fuzzy mathematical models in engineering and management science. Elsevier
science. https://dl.acm.org/doi/abs/10.5555/576010
Maleki, H. R., Tata, M., & Mashinchi, M. (2000). Linear programming with fuzzy variables. Fuzzy sets and
systems, 109(1), 21–33. https://www.sciencedirect.com/science/article/pii/S0165011498000669
Buckley, J. J. (1988). Possibilistic linear programming with triangular fuzzy numbers. Fuzzy sets and systems, 26(1), 135–138. https://www.sciencedirect.com/science/article/pii/0165011488900139
Buckley, J. J. (1989). Solving possibilistic linear programming problems. Fuzzy sets and systems, 31(3), 329–341. https://www.sciencedirect.com/science/article/pii/0165011489902042
Lai, Y. J., & Hwang, C. L. (1992). A new approach to some possibilistic linear programming problems. Fuzzy sets and systems, 49(2), 121–133. https://www.sciencedirect.com/science/article/pii/016501149290318X
Lai, Y. J., & Hwang, C. L. (1992). Fuzzy mathematical programming. In Fuzzy mathematical programming: methods and applications (pp. 74–186). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-48753-8_3
Weber, C. A., & Current, J. R. (1993). A multiobjective approach to vendor selection. European journal of operational research, 68(2), 173–184. https://www.sciencedirect.com/science/article/pii/0377221793903013
Amid, A., Ghodsypour, S. H., & O’Brien, C. (2006). Fuzzy multiobjective linear model for supplier selection in a supply chain. International journal of production economics, 104(2), 394–407. https://www.sciencedirect.com/science/article/pii/S0925527305001532
Kumar, M., Vrat, P., & Shankar, R. (2006). A fuzzy programming approach for vendor selection problem in a supply chain. International journal of production economics, 101(2), 273–285. https://www.sciencedirect.com/science/article/pii/S0925527305000423
Mukherjee, S., & Kar, S. (2013). A three phase supplier selection method based on fuzzy preference degree.
Journal of king saud university-computer and information sciences, 25(2), 173–185. https://www.sciencedirect.com/science/article/pii/S1319157812000419
Choi, J., Bai, S. X., Geunes, J., & Edwin Romeijn, H. (2007). Manufacturing delivery performance for supply chain management. Mathematical and computer modelling, 45(1), 11–20. https://www.sciencedirect.com/science/article/pii/S0895717705005327
de Carvalho, R. A., & Costa, H. G. (2007). Application of an integrated decision support process for supplier selection. Enterprise information systems, 1(2), 197–216. https://doi.org/10.1080/17517570701356208
Vasant, P. M. (2005). Solving fuzzy linear programming problems with modified s-curve membership function. International journal of uncertainty, fuzziness and knowledge-based systems, 13(01), 97–109. https://doi.org/10.1142/S0218488505003321
Díaz-Madroñero, M., Peidro, D., & Vasant, P. (2010). Vendor selection problem by using an interactive fuzzy multi-objective approach with modified S-curve membership functions. Computers & mathematics with applications, 60(4), 1038–1048. https://www.sciencedirect.com/science/article/pii/S0898122110002506
Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective
supply chain master planning. Fuzzy sets and systems, 159(2), 193–214. https://www.sciencedirect.com/science/article/pii/S0165011407003739
Selim, H., & Ozkarahan, I. (2008). A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach. The international journal of advanced manufacturing technology, 36(3), 401–418. https://doi.org/10.1007/s00170-006-0842-6
He, S., Chaudhry, S. S., Lei, Z., & Baohua, W. (2009). Stochastic vendor selection problem: chance-constrained model and genetic algorithms. Annals of operations research, 168(1), 169–179. https://doi.org/10.1007/s10479-008-0367-5
Luthra, S., Govindan, K., Kannan, D., Mangla, S. K., & Garg, C. P. (2017). An integrated framework for sustainable supplier selection and evaluation in supply chains. Journal of cleaner production, 140, 1686–1698. https://www.sciencedirect.com/science/article/pii/S0959652616314196
Ishibuchi, H., & Tanaka, H. (1990). Multiobjective programming in optimization of the interval objective
function. European journal of operational research, 48(2), 219–225. https://www.sciencedirect.com/science/article/pii/037722179090375L
Karsak, E. E., & Dursun, M. (2015). An integrated fuzzy MCDM approach for supplier evaluation and selection. Computers & industrial engineering, 82, 82–93. https://www.sciencedirect.com/science/article/pii/S0360835215000388
Jain, V., Kumar, S., Kumar, A., & Chandra, C. (2016). An integrated buyer initiated decision-making process for green supplier selection. Journal of manufacturing systems, 41, 256–265. https://www.sciencedirect.com/science/article/pii/S0278612516300619
Chen, W., & Zou, Y. (2017). An integrated method for supplier selection from the perspective of risk aversion. Applied soft computing, 54, 449455. https://www.sciencedirect.com/science/article/pii/S1568494616305609
Ghaniabadi, M., & Mazinani, A. (2017). Dynamic lot sizing with multiple suppliers, backlogging and quantity discounts. Computers & industrial engineering, 110, 67–74. https://www.sciencedirect.com/science/article/pii/S0360835217302358
Türk, S., Özcan, E., & John, R. (2017). Multi-objective optimisation in inventory planning with supplier selection. Expert systems with applications, 78, 51–63. https://www.sciencedirect.com/science/article/pii/S0957417417300969
Aouadni, S., Aouadni, I., & Rebaï, A. (2019). A systematic review on supplier selection and order allocation problems. Journal of industrial engineering international, 15(1), 267–289. https://doi.org/10.1007/s40092-019-00334
Jain, S. (2010). Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program. Iranian journal of operations research, 2(1), 77–88.
Tanaka, H. (1984). A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers. Control and cybernetics, 13,185–194. https://cir.nii.ac.jp/crid/1570009750311320960
Metrics
