Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem
Applied and Computational Mathematics
Volume 5, Issue 2, April 2016, Pages: 78-82
Received: Apr. 14, 2016;
Accepted: Apr. 27, 2016;
Published: May 12, 2016
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Tuncay Can, Department of Econometrics, Faculty of Economics, Marmara University, Istanbul, Turkey
Habip Koçak, Department of Econometrics, Faculty of Economics, Marmara University, Istanbul, Turkey
Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structure of the simplex method used when modelling with linear programming and located in a corner point sometimes at the optimal solution itself but mostly in close proximity to the optimal solution vector. One of the ways to eliminate this degenerated solution is to employ approximation methods. The main aim of this paper is to introduce Tuncay Can’s approximation method, which was developed as an alternative to the approximation methods in the literature for a balanced transport problem. Tuncay Can’s approximation method usually has less iterations than other approximation methods. In this paper, the Tuncay Can approximation method is introduced as an alternative to The North West Corner Rule, Minimum Cost Method, and the RAM and VAM methods.
Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem, Applied and Computational Mathematics.
Vol. 5, No. 2,
2016, pp. 78-82.
T. Can, “Yöneylem Araştırması, Nedensellik Üzerine Diyaloglar I”, Beta Publications, Istanbul, p. 396, 2015.
M., Kırca, A. Satır, “A Heuristic for Obtaining and Initial Solution for the Transportation Problem”, Journal of the Operational Research Society, Vol. 41, No. 9, pp. 865-871, 1990.
K. N., Krishnaswamy, A. I., Sivakumar, M., Mathirajan, Management Research Methodology, Dorling Kindersley Pvt. Ltd., p. 246, 2009.
S. Korukoğlu, S., Ballı, “An Improved Vogel’s Approximation Method for the Transportation Problem”, Mathematical and Computational Applications, Vol. 16, No. 2, pp. 370-381, 2011.
S., Sood, K., Jain, “The Maximum Difference Method to find Initial Basic Feasible Solution For Transportation Problem”, Asian Journal of Management Sciences, 03 (07), pp. 8-11, 2015.
S., Singh, G. C., Dubey, R., Shrivastava, R, “Optimization and Analysis of Some Variants Through Vogel’s Approximation Method (VAM)”, IOSR Journal of Engineering, Vol. 2, Issue 9, pp. 20-30, 2012.
N., Balakrishnan, “Modified Vogel’s Approximation Method for the Unbalanced Transportation Problem”, Applied Mathematics Letters, Vol. 3, Issue. 2, pp. 9-11, 1990.
Z. A. N. S., Juman, M. A., Hoque, “An Efficient Heuristic to Obtain a Better Initial Feasible Solution to the Transportation Problem”, Applied Soft Computing, Vol. 34, pp. 813-826, 2015.
B. G., Dantzig, N. M., Thapa, Linear Programming 1. Introduction, Springer-Verlag New York, p. 214, 1997.
M. Zangiabadi, T. Rabie,” A New Model for Transportation Problem with Qualitative Data”, Iran. Journal of Operations Research, 3 (2), pp. 33–46 (2012).
V. J. Sudhakar, N. Arunsankar, T. Karpagam, “A New Approach for Finding An Optimal Solution for Transportation Problems, Europan Journal of Sciences Research, 68 (2), pp. 254–257, 2012.
V. Srinivasan, G. L. Thompson, “Cost Operator Algorithms for the Transportation Problem”, Mathematical Programming, 12, pp. 372–391, 1977.
N. Sen, T. Som, B. Sinha, “A Study of Transportation Problem for an Essential Item of Southern Part of North Eastern Region of India as an OR Model and Use of Object Oriented Programming”, International Jorunal of Computation Sciences Network Security, 10 (4), pp. 78-86, 2010.
F. Pargar, N. Javadian, A. P. Ganji, “A Heuristic for Obtaining an Initial Solution for the Transportation Problem with Experimental Analysis”, in: The 6th International Industrial Engineering Conference, Sharif University of Technology, Tehran, Iran, 2009.
M. Mathirajan, B. Meenakshi, “Experimental Analysis of Some Variants of Vogel’s Approximation Method”, Asia-Pacian. Journal of Operations Research, 21 (4), p. 447–462, 2004.