Interactive Compromise Programming Approach for Solving Vendor Selection Problems under Fuzziness

Authors

  • Hamiden Abd El-Wahed Khalifa Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia
  • Ramin Goudarzi Karim Department of CIS, Stillman College, Tuscaloosa, Alabama, USA

Keywords:

Optimization, Multi-objective integer programming, Vendor selection problem, Fuzzy parameters, Triangular fuzzy numbers

Abstract

This paper studies a Vendor Selection Problem (VSP) with fuzzy parameters in the price of a unit item, an upper limit of the quantity available, and an aggregate demand for the item. These fuzzy parameters are characterized as fuzzy numbers. An extended efficiency concept called that -efficient solution is introduced using the-level sets of fuzzy numbers. A fuzzy programming approach is applied by defining a membership function after converting the fuzzy VSP into an equivalent deterministic VSP. A linear membership function is being used to obtain optimal compromise solution. An interactive procedure for obtaining -optimal compromise solution is also presented. An illustrative numerical example is given to clarify the obtained results.              

References

‎[1] ‎ Wind, Y., & Robinson, P. J. (1968). The determinants of vendor selection: the evaluation function ‎approach. Journal of purchasing, 4(3), 29–42.‎

‎[2] ‎ Pan, A. C. (1989). Allocation of order quantity among suppliers. Journal of purchasing and materials ‎management, 25(3), 36–39. DOI:10.1111/j.1745-493x.1989.tb00489.x‎

‎[3] ‎ Bender, P. S., Brown, R. W., Isaac, M. H., & Shapiro, J. F. (1985). Improving purchasing productivity at ‎IBM with a normative decision support system. Interfaces, 15(3), 106–115.‎

‎[4] ‎ Weber, C. A., & Current, J. R. (1993). A multiobjective approach to vendor selection. European journal of ‎operational research, 68(2), 173–184. DOI:10.1016/0377-2217(93)90301-3‎

‎[5] ‎ Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.‎

‎[6] ‎ Dubois, D. J., & Prade, H. (1980). Fuzzy sets and systems: theory and applications (Vol. 144). Academic Press.‎

‎[7] ‎ Tanaka, H., & Asai, K. (1984). Fuzzy linear programming problems with fuzzy numbers. Fuzzy sets and ‎systems, 13(1), 1–10. DOI:10.1016/0165-0114(84)90022-8‎

‎[8] ‎ Rommelfanger, H., Hanuscheck, R., & Wolf, J. (1989). Linear programming with fuzzy objectives. Fuzzy ‎sets and systems, 29(1), 31–48. DOI:10.1016/0165-0114(89)90134-6‎

‎[9] ‎ Zhao, R., Govind, R., & Fan, G. (1992). The complete decision set of the generalized symmetrical fuzzy ‎linear programming problem. Fuzzy sets and systems, 51(1), 53–65. DOI:10.1016/0165-0114(92)90075-F

‎[10] ‎ Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective ‎functions. Fuzzy sets and systems, 1(1), 45–55. DOI:10.1016/0165-0114(78)90031-3‎

‎[11] ‎ Sakawa, M., & Yano, H. (1989). Interactive decision making for multiobjective nonlinear programming ‎problems with fuzzy parameters. Fuzzy sets and systems, 29(3), 315–326. DOI:10.1016/0165-0114(89)90043-‎‎2‎

‎[12] ‎ 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. ‎DOI:10.1016/j.ijpe.2005.01.005‎

‎[13] ‎ Díaz-Madroñero, M., Peidro, D., & Vasant, P. (2010). Fuzzy multi-objective vendor selection problem ‎with modified S-curve membership function. AIP conference proceedings (pp. 278–285). AIP Publishing. ‎DOI:10.1063/1.3459761‎

‎[14] ‎ 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.‎

‎[15] ‎ Kumar, J., & Roy, N. (2010). A hybrid method for vendor selection using neural network. International ‎journal of computer applications, 11(12), 35–40.‎

‎[16] ‎ Mendoza, A., SantiagoE., & Ravindran, A. R. (2008). A three-phase multicriteria method to the supplier ‎selection problem. International journal of industrial engineering : theory applications and practice, 15(2), 195–‎‎210.‎

‎[17] ‎ 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. ‎DOI:10.1007/s10479-008-0367-5‎

‎[18] ‎ Ware, N., Sing, S., & Banwet, D. (2012). Supplier selection problem: A state-of-the-art review. ‎Management science letters, 2(5), 1465–1490.‎

‎[19] ‎ Ekhtiari, M., & Poursafary, S. (2013). Multiobjective stochastic programming for mixed integer vendor ‎selection problem using artificial bee colony algorithm. ISRN artificial intelligence, 2013, 1–13. ‎DOI:10.1155/2013/795752‎

‎[20] ‎ Arikan, F. (2015). An interactive solution approach for multiple objective supplier selection problem ‎with fuzzy parameters. Journal of intelligent manufacturing, 26(5), 989–998. DOI:10.1007/s10845-013-0782-6‎

‎[21] ‎ Lai, Y. J., & Hwang, C. L. (1996). Fuzzy multiple objective decision making. Springer.‎

‎[22] ‎ Sakawa, M. (1993). Fuzzy sets and interactive multiobjective optimization. Springer.‎

‎[23] ‎ Alves, M. J., & Clímaco, J. (2007). A review of interactive methods for multiobjective integer and mixed-‎integer programming. European journal of operational research, 180(1), 99–115. ‎DOI:10.1016/j.ejor.2006.02.033‎

‎[24] ‎ Khalifa, H. A. (2016). An interactive approach for solving fuzzy multi-objective non-linear ‎programming problems. The journal of fuzzy mathematics, 3(24), 535–545.‎

‎[25] ‎ Naqvi, M. A., & Amin, S. H. (2021). Supplier selection and order allocation: a literature review. Journal of ‎data, information and management, 3(2), 125–139.‎

‎[26] ‎ Tronnebati, I., El Yadari, M., & Jawab, F. (2022). A review of green supplier evaluation and selection ‎issues using MCDM, MP and AI models. Sustainability (Switzerland), 14(24), 16714. ‎DOI:10.3390/su142416714‎

‎[27] ‎ Saputro, T. E., Figueira, G., & Almada-Lobo, B. (2022). A comprehensive framework and literature ‎review of supplier selection under different purchasing strategies. Computers & industrial engineering, ‎‎167, 108010.‎

‎[28] ‎ Moore, R. E. (1979). Methods and applications of interval analysis. SIAM.‎

‎[29] ‎ Kaufmann, A., & Gupta, M. M. (1988). Fuzzy mathematical models in engineering and management science. ‎Elsevier Science Inc.‎

‎[30] ‎ Bellman, R, & Zadeh, L. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B--‎‎141. DOI:10.1142/9789812819789_0004‎

‎[31] ‎ Biswal, M. P. (1992). Fuzzy programming technique to solve multi-objective geometric programming ‎problems. Fuzzy sets and systems, 51(1), 67–71. DOI:10.1016/0165-0114(92)90076-G

Published

2024-03-28

How to Cite

Interactive Compromise Programming Approach for Solving Vendor Selection Problems under Fuzziness. (2024). Risk Assessment and Management Decisions, 1(1), 1-11. https://ramd.reapress.com/journal/article/view/20

Similar Articles

You may also start an advanced similarity search for this article.