Industries require planning in transporting their products from production centres to the users end with minimal transporting cost to maximize profit. This process is known as Transportation Problem which is used to analyze and minimize transportation cost. This problem is well discussed in operation research for its wide application in various fields, such as scheduling, personnel assignment, product mix problems and many others, so that this problem is really not confined to transportation or distribution only. In the solution procedure of a transportation problem, finding an initial basic feasible solution is the prerequisite to obtain the optimal solution. Again, development is a continuous and endless process to find the best among the bests. The growing complexity of management calls for development of sound methods and techniques for solution of the problems. Considering these factors, this research aims to propose an algorithm “Incessant Allocation Method” to obtain an initial basic feasible solution for the transportation problems. Several numbers of numerical problems are also solved to justify the method. Obtained results show that the proposed algorithm is effective in solving transportation problems.
Panneerselvam, R. (2010) Operation Research. 2nd Edition, PHI Learning Private Ltd., New Delhi, 71.
Hitchcock, F.L. (1941) The Distribution of a Product from Several Sources to Numerous Localities. Journal of Mathematics and Physics, 20, 224-230. http://dx.doi.org/10.1002/sapm1941201224
Dantzig, G.B. (1951) Application of the Simplex Method to a Transportation Problem, Activity Analysis of Production and Allocation. Koopmans, T.C., Ed., John Wiley and Sons, New York, 359-373.
Charnes, A., Cooper, W.W. and Henderson, A. (1953) An Introduction to Linear Programming. John Wiley & Sons, New York.
Rashid, A., Ahmed, S.S. and Uddin, M.S. (2013) Development of a New Heuristic for Improvement of Initial Basic Feasible Solution of a Balanced Transportation Problem. Jahangirnagar University Journal of Mathematics and Mathematical Sciences, 28, 105-112.
Mhlanga, A., Nduna, I.S., Matarise, F. and Machisvo, A. (2014) Innovative Application of Dantzig’s North-West Corner Rule to Solve a Transportation Problem. International Journal of Education and Research, 2, 1-12.
Khan, A.R. (2011) A Re-Solution of the Transportation Problem: An Algorithmic Approach. Jahangirnagar University Journal of Science, 34, 49-62.
Khan, A.R. (2012) Analysis and Re-Solution of the Transportation Problem: A Linear Programming Approach. M.Phil. Thesis, Jahangirnagar University, Savar.
Khan, A.R., Vilcu, A., Sultana, N. and Ahmed, S.S. (2015) Determination of Initial Basic Feasible Solution of a Transportation Problem: A TOCM-SUM Approach. Buletinul Institutului Politehnic Din Iasi, Romania, Sec?ia Automatica si Calculatoare, LXI (LXV), 39-49.
Khan, A.R., Vilcu, A., Uddin, M.S. and Ungureanu, F. (2015) A Competent Algorithm to Find the Initial Basic Feasible Solution of Cost Minimization Transportation Problem. Buletinul Institutului Politehnic Din Iasi, Romania, Sec?ia Automatica si Calculatoare, LXI (LXV), 71-83.
Khan, A.R., Banerjee, A., Sultana, N. and Islam, M.N. (2015) Solution Analysis of a Transportation Problem: A Comparative Study of Different Algorithms. Accepted for Publication in the Bulletin of the Polytechnic Institute of Iasi, Romania, Section Textile.
Deshmukh, N.M. (2012) An Innovative Method for Solving Transportation Problem. International Journal of Physics and Mathematical Sciences, 2, 86-91.
Russell, E.J. (1969) Letters to the Editor—Extension of Dantzig’s Algorithm to Finding an Initial Near-Optimal Basis for the Transportation Problem. Operations Research, 17, 187-191. http://dx.doi.org/10.1287/opre.17.1.187
Kasana, H.S. and Kumar, K.D. (2005) Introductory Operations Research: Theory and Applications. Springer International Edition, New Delhi.
Kirca, O. and Satir, A. (1990) A Heuristic for Obtaining an Initial Solution for the Transportation Problem. Journal of the Operational Research Society, 41, 865-871.
Uddin, M.S., Anam, S., Rashid, A. and Khan, A.R. (2011) Minimization of Transportation Cost by Developing an Efficient Network Model. Jahangirnagar Journal of Mathematics & Mathematical Sciences, 26, 123-130.
Mathirajan, M. and Meenakshi, B. (2004) Experimental Analysis of Some Variants of Vogel’s Approximation Method. Asia-Pacific. Asia-Pacific Journal of Operational Research, 21, 447-462. http://dx.doi.org/10.1142/S0217595904000333
Amirul Islam, M.D., Khan, A.R., Uddin, M.S. and Abdul Malek, M. (2012) Determination of Basic Feasible Solution of Transportation Problem: A New Approach. Jahangirnagar University Journal of Science, 35, 101-108.
Islam, M.A., Haque, M.H. and Uddin, M.S. (2012) Extremum Difference Formula on Total Opportunity Cost: A Transportation Cost Minimization Technique. Prime University Journal of Multidisciplinary Quest, 6, 125-130.
Babu, M.A., Helal, M.A., Hasan, M.S. and Das, U.K. (2013) Lowest Allocation Method (LAM): A New Approach to Obtain Feasible Solution of Transportation Model. International Journal of Scientific and Engineering Research, 4, 1344-1348.
Babu, M.A., Das, U.K., Khan, A.R. and Uddin, M.S. (2014) A Simple Experimental Analysis on Transportation Problem: A New Approach to Allocate Zero Supply or Demand for All Transportation Algorithm. International Journal of Engineering Research & Applications (IJERA), 4, 418-422.
Babu, M.A., Helal, M.A., Hasan, M.S. and Das, U.K. (2014) Implied Cost Method (ICM): An Alternative Approach to Find the Feasible Solution of Transportation Problem. Global Journal of Science Frontier Research-F: Mathematics and Decision Sciences, 14, 5-13.
Uddin, M.M., Khan, A.R., Roy, S.K. and Uddin, M.S. (2015) A New Approach for Solving Unbalanced Transportation Problem due to Additional Supply. Accepted for Publication in the Bulletin of the Polytechnic Institute of Iasi, Section Textile, Leather Ship, Romania.
Hasan, M.K. (2012) Direct Methods for Finding Optimal Solution of a Transportation Problem are Not Always Reliable. International Refereed Journal of Engineering and Science (IRJES), 1, 46-52.
Ahmed, M.M., Tanvir, A.S.M., Sultana, S., Mahmud, S. and Uddin, M.S. (2014) An Effective Modification to Solve Transportation Problems: A Cost Minimization Approach. Annals of Pure and Applied Mathematics, 6, 199-206.
Ahmed, M.M. (2014) Algorithmic Approach to Solve Transportation Problems: Minimization of Cost and Time. M. Phil. Thesis, Department of Mathematics, Jahangirnagar University, Savar, Dhaka, Bangladesh.
Ahmed, M.M., Khan, A.R., Uddin, M.S. and Ahmed, F. (2016) A New Approach to Solve Transportation Problems. Open Journal of Optimization, 5, 22-30. http://dx.doi.org/10.4236/ojop.2016.51003
Pandian, P. and Natarajan, G. (2010) A New Approach for Solving Transportation Problems with Mixed Constraints. Journal of Physical Sciences, 14, 53-61.
Wagener, U.A. (1965) A New Method of Solving the Transportation Problem. Journal of the Operational Research Society, 16, 453-469. http://dx.doi.org/10.1057/jors.1965.80
Das, U.K., Babu, M.A., Khan, A.R., Helal, M.A. and Uddin, M.S. (2014) Logical Development of Vogel’s Approximation Method (LD-VAM): An Approach to Find Basic Feasible Solution of Transportation Problem. International Journal of Scientific & Technology Research (IJSTR), 3, 42-48.
Das, U.K., Babu, M.A., Khan, A.R. and Uddin, M.S. (2014) Advanced Vogel’s Approximation Method (AVAM): A New Approach to Determine Penalty Cost for Better Feasible Solution of Transportation Problem. International Journal of Engineering Research & Technology (IJERT), 3, 182-187.
Rashid, A., Uddin, M.S., Ahmed, F. and Kabir, M.R. (2012) An Effective Approach for Profit Maximization in a Transportation Problem. Jahangirnagar University Journal of Science, 35, 37-43.
Rashid, A., Ahmed, S.S. and Uddin, M.S. (2014) A New Approach for Profit Maximization in an Assignment Problem. Jahangirnagar University Journal of Science, 37, 107-117.
Islam, M.A., Uddin, M.S., Hasan, S.M.M., Rashid, F. and Malek, M.A. (2013) Profit Maximization of a Manufacturing Company: An Algorithmic Approach, Jahangirnagar Journal of Mathematics & Mathematical Sciences, 28, 29-37.
Islam M.A., Ahmed, M.M., Uddin, M.S. and Malek, M.A. (2013) Application of a New Transportation Algorithm on Profit Maximization Problem. MIST Journal of Science and Technology, 2, 67-71.
Uddin, M.S. (2012) Transportation Time Minimization: An Algorithmic Approach. Journal of Physical Sciences, 16, 59-64.
Uddin, M.M., Rahaman, M.A., Ahmed, F., Uddin, M.S. and Kabir, M.R. (2013) Minimization of Transportation Cost on the Basis of Time Allocation: An Algorithmic Approach. Jahangirnagar Journal of Mathematics & Mathematical Sciences, 28, 47-53.
Ahmed, M.M., Islam, M.A., Katun, M., Yesmin, S. and Uddin, M.S. (2015) New Procedure of Finding an Initial Basic Feasible Solution of the Time Minimizing Transportation Problems. Open Journal of Applied Sciences, 5, 634-640. http://dx.doi.org/10.4236/ojapps.2015.510062