Multiobjective Transportation Problem Using Fuzzy Decision Variable ThroughMulti-Choice Programming

Authors

  • DR.RAJESHWARA REDDY
  • T. Lakshmi

Keywords:

Fuzzy Variable, Goal Programming, Multiobjective Decision-making, Multiple-Choice Programming, Transportation Problem

Abstract

Using fuzzy decision variables, this work examines the examination of the Multi-Objective Transportation Problem (MOTP). When solving a Transportation Problem, the decision variable is usually considered as a real variable. There are a lot of multi-choice fuzzy numbers in this work, but the decision variable in each node is chosen from a collection of those values. Multiobjective Fuzzy Transportation Problems are created when numerous goals are included in a transportation issue with a fuzzy decision variable (MOFTP). We provide a novel mathematical model of MOFTP that incorporates fuzzy goals for each of the objective functions. After that, the multi-choice goal programming methodology is used to define the model's solution method. For further proof of this article's value, a numerical example is provided.

References

Abd El-Wahed Waiel, F. (2001). A multiobjective transportation problem under fuzziness. Fuzzy Sets and Systems, 117(1), 27–33. doi:10.1016/S0165-0114(98)00155-9

Beauchamp, H., Novoa, C., & Ameri, F. (2015). Supplier selection and order allocation based on integer programming. International Journal of Operations Research and Information Systems, 6(3), 60–79.

Chang, C. T. (2007). Multi-choice goal programming. Omega, 35(4), 389–396. doi:10.1016/j.omega.2005.07.009

Chang, C. T. (2008). Revised multi-choice goal programming. Applied Mathematical Modelling, 32(12), 2587–2595. doi:10.1016/j.apm.2007.09.008

Chang, C. T., Ku, C. Y., & Ho, H. P. (2010). Fuzzy multi-choice goal programming for supplier selection.

International Journal of Operations Research and Information Systems, 1(3), 28–52. doi:10.4018/joris.2010070103

Charnes, A., Cooper, W. W., & Ferguson, R. (1955). Optimal estimation of executive compensation by linear programming. Management Science, 1(2), 138–151. doi:10.1287/mnsc.1.2.138

Das, M., Roy, R., Dehuri, S., & Cho, S. B. (2011). A new approach to associative classification based on binary multiobjective particle swarm optimization. International Journal of Applied Metaheuristic Computing, 2(2), 51–73. doi:10.4018/jamc.2011040103

Datta, S., Nandi, G., Bandyopadhyay, A., & Pal, P. K. (2010). Solution of correlated multi-response optimization problem: Case study in submerged arc welding. International Journal of Operations Research and Information Systems, 1(4), 22–46. doi:10.4018/joris.2010100102

Ebrahimnejad, A., Nasseri, S. H., & Mansourzadeh, S. M. (2011). Bounded primal simplex algorithm for bounded linear programming with fuzzy cost coefficients. International Journal of Operations Research and Information Systems, 2(1), 96–120. doi:10.4018/joris.2011010105

Hasan, M. K., & Ban, X. (2013). A link-node nonlinear complementarity model for a multiclass simultaneous transportation dynamic user equilibria. International Journal of Operations Research and Information Systems, 4(1), 27–48. doi:10.4018/joris.2013010102

Hitchcock, F. L. (1941). The distribution of a product from several sources to numerous localities. Journal of Mathematics and Physics, 20(1-4), 224–230. doi:10.1002/sapm1941201224

Ignizio, J. P. (1976). Goal programming and extensions. Lexington, MA: Lexington Books.

Koopmans, T. C. (1949). Optimum utilization of the transportation System. Econometrica, 17, 136–146. doi:10.2307/1907301

Kumar, A., & Kaur, A. (2011). Methods for solving fully fuzzy transportation problems based on classical transportation methods. International Journal of Operations Research and Information Systems, 2(4), 52–71. doi:10.4018/joris.2011100104

Kumar, P. S., & Hussain, R. J. (2016). A simple method for solving fully intuitionistic fuzzy real life assignment problem. International Journal of Operations Research and Information Systems, 7(2), 39–61. doi:10.4018/ IJORIS.2016040103

Lee, S. M. (1972). Goal programming for decision analysis. Philadelphia: Auerbach Publishers.

Liao, C. N. (2009). Formulating the multi-segment goal programming. Computers & Industrial Engineering, 56(1), 138–141. doi:10.1016/j.cie.2008.04.007

Mahapatra, D. R., Roy, S. K., & Biswal, M. P. (2010). Stochastic based on multiobjective transportation problemsinvolving normal randomness. Advanced Modeling and Optimization, 12(2), 205–223.

Mahapatra, D. R., Roy, S. K., & Biswal, M. P. (2013). Multi-choice stochastic transportation problem involving extreme value distribution. Applied Mathematical Modelling, 37(4), 2230–2240. doi:10.1016/j.apm.2012.04.024

Maity, G., & Roy, S. K. (2014). Solving multi-choice multiobjective transportation problem: a utility functionapproach. Journal of Uncertainty Analysis and Applications. doi:10.1186/2195-5468-2-11

Maity, G., & Roy, S. K. (2015). (Forthcoming). Solving multiobjective transportation problem with interval goal using utility function approach. International Journal of Operational Research.

Maity, G., & Roy, S. K. (2016). Solving a multiobjective transportation problem with nonlinear cost and multi- choice demand. International Journal of Management Science and Engineering Management, 11(1), 62–70. doi:10.1080/17509653.2014.988768

Mangara, B. K. (2012). Modeling multi- criteria promotional strategy based on fuzzy goal programming. In E-Marketing: Concepts, Methodologies, Tools, and Applications. doi:10.4018/978- 1-4666-1598-4.ch015

Marbini, A. H., Saati, S., & Tavana, M. (2011). Data envelopment analysis with fuzzy parameters: An interactive approach. International Journal of Operations Research and Information Systems, 2(3), 39–53. doi:10.4018/ joris.2011070103

Mariya, A. S., & Suhl, L. (2012). A multi-criteria multi-level group decision method for supplier selectionand order allocation. International Journal of Strategic Decision Sciences, 3(1), 81– 105. doi:10.4018/ IJSDS.2012010103

Midya, S., & Roy, S. K. (2014). Single-sink, fixed-charge, multiobjective, multi-index stochastic transportation problem. American Journal of Mathematical and Management Sciences, 33(4), 300– 314. doi:10.1080/01966 324.2014.942474

Narasimhan, R. (1980). Goal programming in a fuzzy environment. Decision Sciences, 11(2), 325–336. doi:10.1111/j.1540-5915.1980.tb01142.x

Pan, L., Chu, C. K. S., Han, G., & Huang, J. Z. (2011). A heuristic algorithm for the inner-city multi-drop container loading problem. International Journal of Operations Research and Information Systems, 2(3), 1–19. doi:10.4018/joris.2011070101

Pattnaik, M. (2015). Decision-making approach to fuzzy linear programming (FLP) problems with post optimal analysis. International Journal of Operations Research and Information Systems, 6(4), 75– 90. doi:10.4018/ IJORIS.2015100105

Roy, S. K. (2014). Multi-choice stochastic transportation problem involving weibull distribution. InternationalJournal of Operational Research, 21(1), 38–58. doi:10.1504/IJOR.2014.064021

Roy, S. K., & Mahaparta, D. R. (2014). Solving solid transportation problem with multi-choice cost and stochastic supply and demand. International Journal of Strategic Decision Sciences, 5(3), 1– 26. doi:10.4018/ ijsds.2014070101

Roy, S. K., Mahaparta, D. R., & Biswal, M. P. (2012). Multi-choice stochastic transportation problem with exponential distribution. Journal of Uncertain Systems, 6(3), 200–213.

Roy, S. K., & Mahapatra, D. R. (2011). Multiobjective interval-valued transportation probabilistic problem involving log-normal. International Journal of Mathematics and Scientific Computing, 1(2), 14–21.

Singh, S. P., Chauhan, M. K., & Singh, P. (2015). Using multi-criteria futuristic fuzzy decision hierarchy in SWOT analysis: An application in tourism industry. International Journal of Operations Research and InformationSystems, 6(4), 38–56. doi:10.4018/IJORIS.2015100103

Tabrizi, B. B., Shahanaghi, K., & Jabalameli, M. S. (2012). Fuzzy multi-choice goal programming. Applied Mathematical Modelling, 36(4), 1415–1420. doi:10.1016/j.apm.2011.08.040

Tamiz, M., Jones, D. F., & Romero, C. (1998). Goal programming for decision-making: An overview of the current state-of-the-art. European Journal of Operational Research, 111(3), 569– 581. doi:10.1016/S0377- 2217(97)00317-2

Verma, R., Biswal, M. P., & Biswas, A. (1997). Fuzzy programming technique to solve multiobjective transportation problems with some non-linear membership functions. Fuzzy Sets and Systems, 91(1), 37–43. doi:10.1016/S0165-0114(96)00148-0

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

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Published

2020-08-30

How to Cite

REDDY, D. ., & Lakshmi, . T. (2020). Multiobjective Transportation Problem Using Fuzzy Decision Variable ThroughMulti-Choice Programming. The Journal of Contemporary Issues in Business and Government, 26(2), 2218–2233. Retrieved from https://cibgp.com/au/index.php/1323-6903/article/view/494