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transportation problem (ITP) in which the cost-coefficients of the objective function, source and destination parameters are all in the form of interval. In this paper, the single objective interval transportation problem is transformed into an equivalent crisp bi-objective transportation problem where the left-limit and width of the interval are to be minimized. The solution to this bi-objective model is then obtained with the help of fuzzy programming technique. The proposed solution procedure has been demonstrated with the help of a numerical example. A comparative study has also been made between the proposed solution method and the method proposed by Das et al.(1999) .
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- Akilbasha, A., Pandian, P., and Natarajan, G. (2018). An innovative exact method for solving fully interval integer transportation problems. Informatics in Medicine Unlocked, 11:95–99.
- Alefeld, G. and Herzberger, J. (1983). Introduction to interval computations, comput. Sci. Appl. Math., Academic Press, New York.
- Bit, A., Biswal, M., and Alam, S. (1992). Fuzzy programming approach to multicriteria decision making trans- portation problem. Fuzzy sets and systems, 50(2):135–141.
- Bitran, G. R. (1980). Linear multiple objective problems with interval coefﬁcients. Management science, 26(7):694–706.
- Chanas, S. and Kuchta, D. (1996). Multiobjective programming in optimization of interval objective func- tions—a generalized approach. European Journal of Operational Research, 94(3):594–598.
- Das, S., Goswami, A., and Alam, S. (1999). Multiobjective transportation problem with interval cost, source and destination parameters. European Journal of Operational Research, 117(1):100–112.
- Guzel, N., Emiroglu, Y., Tapci, F., Guler, C., and Syvry, M. (2012). A solution proposal to the interval fractional ¨ transportation problem. Applied Mathematics & Information Sciences, 6(3):567–571.
- Habiba, U. and Quddoos, A. (2020). Multiobjective stochastic interval transportation problem involving general form of distributions. Advances in Mathematics: Scientiﬁc Journal, 9(6):3213–3219.
- Henriques, C. O. and Coelho, D. (2017). Multiobjective interval transportation problems: A short review. In Optimization and Decision Support Systems for Supply Chains, pages 99–116. Springer.
- Inuiguchi, M. and Kume, Y. (1991). Goal programming problems with interval coefﬁcients and target intervals. European Journal of Operational Research, 52(3):345–360.
- Ishibuchi, H. and Tanaka, H. (1990). Multiobjective programming in optimization of the interval objective function. European journal of operational research, 48(2):219–225.
- Moore, E. (1979). Methods and applications of interval analysis (siam, philadephia, pa).
- Nagarajan, A., Jeyaraman, K., and Prabha, S. (2014). Multi objective solid transportation problem with interval cost in source and demand parameters. International Journal of Computer & Organization Trends, 8(1):33–41. Natarajan, P. P. G. (2010). A new method for ﬁnding an optimal solution of fully interval integer transportation
- problems. Applied Mathematical Sciences, 4(37):1819–1830.
- Panda, A. and Das, C. B. (2013). Cost varying interval transportation problem under two vehicle. Journal of New Results in Science, 2(3):19–37.
- Pandian, P. and Anuradha, D. (2011). Solving interval transportation problems with additional impurity con- straints. Journal of Physical Sciences, 15:103–112.
- Sengupta, A. and Pal, T. K. (2009). Interval transportation problem with multiple penalty factors. In Fuzzy preference ordering of interval numbers in decision problems, pages 121–137. Springer.
- Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations research, 21(5):1154–1157.
- Tanaka, H. and Asai, K. (1984). Fuzzy linear programming problems with fuzzy numbers. Fuzzy sets and systems, 13(1):1–10.