Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint

• Authors: KHALIFA Hamiden Abd El-wahed
• Languages of publication: EN

Abstracts

EN

Transportation problem (TP) is a special type of linear programming problem (LPP) where the objective is to minimize the cost of distributing a product from several sources (or origins) to some destinations. This paper addresses a transportation problem in which the costs, supplies, and demands are represented as heptagonal fuzzy numbers. After converting the problem into the corresponding crisp TP using the ranking method, a goal programming (GP) approach is applied for obtaining the optimal solution. The advantage of GP for the decision-maker is easy to explain and implement in real life transportation. The stability set of the first kind corresponding to the optimal solution is determined. A numerical example is given to highlight the solution approach.

Keywords

EN

transportation problem; heptagonal fuzzy numbers; ranking method; goal programming; parametric; study

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2020
• Volume: 30
• Issue: 1
• Pages: 85-96

Contributors

author

KHALIFA Hamiden Abd El-wahed

• Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
• Present address: Mathematics Department, College of Science and Arts, Al- Badaya, Qassim University, Saudi Arabia

References

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• CHHIBBER P., BISHT D.C.S., SRIVASTAVA D.K., Ranking approach based on incenter in triangle of centroids to solve type-1 and type-2 fuzzy transportation problems, AIP Conference Proc., 2019 (1), 2061.
• DUBOIS D., PRADE H., Fuzzy Sets and Systems. Theory and Application, Academic Press, New York 1980.
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• JAIKUMAR K., New approach to solve fully fuzzy transportation problem, Int. J. Math. Appl., 2016, 4 (2-B), 155–162.
• KAUR A., KUMAR A., A new method for solving fuzzy transportation problems using ranking function, Appl. Math. Model., 2011, 35 (12), 5652–5661.
• MAHESWARI P., VIJAYA M., On initial basic feasible solution (IBFS) of fuzzy transportation problem based on ranking of fuzzy numbers using centroid of incenters, Int. J. Appl. Eng. Res., 2019, 14 (4), 155–164.
• MALINI S.U., KENNEDY F.C., An approach for solving fuzzy transportation problem using octagonal fuzzy numbers, Appl. Math. Sci., 2013, 7 (54), 2661–2673.
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• MELITA VINOLIAH E., GANESAN K., Solution of fuzzy transportation problem. A new approach, J. Pure Appl. Math., 2017, 113 (13), 20–29.
• NARAYANAMOORTHY S., SARANYA S., MAHESWARI S., A method for solving fuzzy transportation problem (FTP) using fuzzy Russell’s method, Int. J. Intel. Syst. Appl., 2013 (2), 71–75.
• OSMAN M.S.A., Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints, Appl. Math., 1977 (22), 318–322.
• OSMAN M.S.A., EL- BANNA A.Z.H., Stability of multiobjective nonlinear programming problems with fuzzy parameters, Math. Comp. Sim., 1993 (35), 321–326.
• PATHADE P.A., GHADLE K.P., Optimal solution of balanced and unbalanced fuzzy transportation problem by using octagonal fuzzy numbers, Int. J. Pure Appl. Math., 2018, 119 (4), 617–625.
• RAJARAJESWARI P., SAHAYA SUDHA A., KARTHIKA R., A new operation on hexagonal fuzzy numbers, Int. J. Fuzzy Logic Syst., 2013 (3), 15–26.
• RATHI K., BALAMOHAN S., Representation and ranking of fuzzy numbers with heptagonal membership function value and ambiguity index, Appl. Math. Sci., 2014 (8), 4309–4321.
• RAMESH KUMAR M., SUBRAMANIAN S., Solution of fuzzy transportation problems with trapezoidal fuzzy numbers using robust ranking methodology, Int. J. Pure Appl. Math., 2018, 119 (16), 3763–3775.
• SAHAYA SUDHA A., KARUNAMBIGAI S., Solving a transportation problem using heptagonal fuzzy numbers, Int. J. Adv. Res. Sci., Eng. Techn., 2017, 4 (1), 3118–3125.
• SENTHILKUMAR P., VENGATAASALAM S., A note on the solution of fuzzy transportation problem using fuzzy linear system, J. Fuzzy Set Val. Anal., 2013 (2013), article ID jfsva-00138.
• TANAKA H., TCHIHASHI H., ASAL K., A formulation of fuzzy linear programming problem based on comparison of fuzzy number, Control Cyber., 1984, 13 (3), 184–194.
• ZADEH L.A., Fuzzy sets, Inf. Control, 1965, (8), 338–353.
• AHMED M.M., KHAN A.M., AHMED F., SHARIF UDDIN M.D., Incessant allocation method for solving transportation problem, Am. J. Oper. Res., 2016 (6), 236–244.
• BELLMAN R., ZADEH L., Decision making in a fuzzy environment, Manage. Sci., 1970, 17, 141–164.
• CHANDRASEKARAN S., KOKILA G., SAJU J., Fuzzy transportation problem of hexagon number with α-cut and ranking technique, Int. J. Sci. Eng. Appl. Sci., 2015 (1), 530–538.
• CHHIBBER P., BISHT D.C.S., SRIVASTAVA D.K., Ranking approach based on incenter in triangle of centroids to solve type-1 and type-2 fuzzy transportation problems, AIP Conference Proc., 2019 (1), 2061.
• DUBOIS D., PRADE H., Fuzzy Sets and Systems. Theory and Application, Academic Press, New York 1980.
• GANI A.N., ABBAS S., A new method for solving intuitionistic fuzzy transportation problem, Appl. Math. Sci., 2013, 7 (28), 1357–1365.
• JAIKUMAR K., New approach to solve fully fuzzy transportation problem, Int. J. Math. Appl., 2016, 4 (2-B), 155–162.
• KAUR A., KUMAR A., A new method for solving fuzzy transportation problems using ranking function, Appl. Math. Model., 2011, 35 (12), 5652–5661.
• MAHESWARI P., VIJAYA M., On initial basic feasible solution (IBFS) of fuzzy transportation problem based on ranking of fuzzy numbers using centroid of incenters, Int. J. Appl. Eng. Res., 2019, 14 (4), 155–164.
• MALINI S.U., KENNEDY F.C., An approach for solving fuzzy transportation problem using octagonal fuzzy numbers, Appl. Math. Sci., 2013, 7 (54), 2661–2673.
• MATHUR N., SRIVASTAVA P.K., A pioneer optimization approach for hexagonal fuzzy transportation problem, AIP Conference Proc., 2019, (2061), 020030.
• MELITA VINOLIAH E., GANESAN K., Solution of fuzzy transportation problem. A new approach, J. Pure Appl. Math., 2017, 113 (13), 20–29.
• NARAYANAMOORTHY S., SARANYA S., MAHESWARI S., A method for solving fuzzy transportation problem (FTP) using fuzzy Russell’s method, Int. J. Intel. Syst. Appl., 2013 (2), 71–75.
• OSMAN M.S.A., Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints, Appl. Math., 1977 (22), 318–322.
• OSMAN M.S.A., EL- BANNA A.Z.H., Stability of multiobjective nonlinear programming problems with fuzzy parameters, Math. Comp. Sim., 1993 (35), 321–326.
• PATHADE P.A., GHADLE K.P., Optimal solution of balanced and unbalanced fuzzy transportation problem by using octagonal fuzzy numbers, Int. J. Pure Appl. Math., 2018, 119 (4), 617–625.
• RAJARAJESWARI P., SAHAYA SUDHA A., KARTHIKA R., A new operation on hexagonal fuzzy numbers, Int. J. Fuzzy Logic Syst., 2013 (3), 15–26.
• RATHI K., BALAMOHAN S., Representation and ranking of fuzzy numbers with heptagonal membership function value and ambiguity index, Appl. Math. Sci., 2014 (8), 4309–4321.
• RAMESH KUMAR M., SUBRAMANIAN S., Solution of fuzzy transportation problems with trapezoidal fuzzy numbers using robust ranking methodology, Int. J. Pure Appl. Math., 2018, 119 (16), 3763–3775.
• SAHAYA SUDHA A., KARUNAMBIGAI S., Solving a transportation problem using heptagonal fuzzy numbers, Int. J. Adv. Res. Sci., Eng. Techn., 2017, 4 (1), 3118–3125.
• SENTHILKUMAR P., VENGATAASALAM S., A note on the solution of fuzzy transportation problem using fuzzy linear system, J. Fuzzy Set Val. Anal., 2013 (2013), article ID jfsva-00138.
• TANAKA H., TCHIHASHI H., ASAL K., A formulation of fuzzy linear programming problem based on comparison of fuzzy number, Control Cyber., 1984, 13 (3), 184–194.
• ZADEH L.A., Fuzzy sets, Inf. Control, 1965, (8), 338–353.

Identifiers

DOI

10.37190/ord200105