Solution of a Transportation Problem using Bipartite Graph
transportation problem, bipartite graph, balanced and unbalanced, VAM and MODI methods
Abstract
The transportation problem is also one of the important problems in the field of optimization in which the goal is to minimize the total transportation cost of distributing to a specific number of sources to a specific number of destinations. Different techniques have been developed in the literature for solving the transportation problem. Specific methodologies concentrated on finding an initial basic feasible solution and the other to find the optimal solution. This manuscript analyses method of the optimal solution for the transportation problem utilizing a Bipartite graph. This procedure contains topological spaces, graphs, and transportation problems. Initially, it converts the transportation problem into a graphical demonstration then transforms into a new graphical image. Afterward using the proposed algorithmic rule we've obtained the optimal cost of transporting quantities from providing vertices to supply vertices.
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P Adhikari, G Thapa (2000) A Note on Feasibility and Optimality of Transportation Problem. 10(1), 59-68.
S Akpana, T Ugbeb, J Usenc, O Ajahd (2015) A Modified Vogel Approximation Method for Solving Balanced Transportation Problems. 14(3), 289-302.
M Ahmed, A Khan, S Uddin, F Ahme (2016) A New Approach to Solve Transportation Problems. 5, 22-30.
Mollah Ahmed, Aminur Khan, Faruque Ahmed, Md. Uddin (2016) Incessant Allocation Method for Solving Transportation Problems. 06(03), 236-244.
D Atkinson, P Vaidya (1995) Using geometry to solve the transportation problem in the plane. 13(5), 442-461.
A Charnes, W Cooper, A Henderson (1953) An introduction to linear programming. By A. Charnes, W. W. Cooper, and A. Henderson, John Wiley & Sons, Inc., 1953, 74 pp. 1(2), 169-169.
G Dantzig (1963) Linear programming and extensions.
N Deshmukh (2012) An Effective Methodology for Solving Transportation Problem. 5(10), 86-91.
L Ford, D Fulkerson (1956) Solving the Transportation Problem. 3(1), 24-32.
S Goyal (1984) Improving VAM for unbalanced transportation problems. 35, 1113-1114.
A Hamdy (2007) Operations Research: An Introduction.
Frank Hitchcock (1941) The Distribution of a Product from Several Sources to Numerous Localities. 20(1-4), 224-230.
Eghbal Hosseini (2017) Three new methods to find initial basic feasible solution of transportation problems. 11(37), 1803-1814.
T Imam, G Elsharawy, M Gomah, I Samy (2009) Solving Haplotype Assembly Problem Using Harmony Search. 1(2013), 353-361.
Kenan Karagul, Yusuf Sahin (2020) A novel approximation method to obtain initial basic feasible solution of transportation problem. 32(3), 211-218.
A Kaufmann (1973) Introduction a la Theorie des sons-ensembles flous. 1, 41-189.
T Koopmans (1949) Optimum Utiliztion of Transportation System. 17.
Serdar Korukoğlu, Serkan Ballı (2011) An Improved Vogel's Approximation Method for the Transportation Problem. 16(2), 370-381.
S Kulkarni, H Datar (2010) On Solution To Modified Unbalanced Transportation Problem. 11(2), 20-26.
V Manisha, M Sarode (2017) Application of a Dual Simplex method to Transportation Problem to minimize the cost. 2(7).
J Phillips, P Agarwal (2006) On bipartite matching under the rms distance.
N Reinfeld, W Vogel (1958) Mathematical Programming.
Santhi (2019) Topological solution of a Transportation problem using Topologized Graph. VI, 30-38.
Hesham Alhumade, Hiba Nauman, Erij Elkamel, Aiping Yu, Ali Elkamel (2005) CORROSION PROTECTION OF STAINLESS STEEL TYPE 304 USING GRAPHENE COMPOSITES. 1(2), 57-72.
K Varadarajan, P Agarwal (1999) Approximation algorithms for bipartite and non-bipartite matching in the plane. 805-814.
S Vimala, S Kalpana (2017) Topologized Bipartite Graph. 4(1), 1-10.
S Vimala, S Kalpana (2017) Final Report on the Safety Assessment of Ceteareth-2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17 -18, -20, -22, -23, -24, -25, -27, -28, -29, -30, -33, -34 -40, -50, -55, -60, -80, and -100. 18(5), 41-49.
G Monge (1781) Mémoire sur la théorie des déblaiset des remblais. 666-704.
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2021-02-12
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