New Procedure of Finding an Initial Basic Feasible Solution of the Time Minimizing Transportation Problems

Author(s)
Mollah Mesbahuddin Ahmed^{1},
Md. Amirul Islam^{1},
Momotaz Katun^{2},
Sabiha Yesmin^{1},
Md. Sharif Uddin^{1}

Affiliation(s)

^{1}
Department of Mathematics, Jahangirnagar University, Savar, Dhaka, Bangladesh.

^{2}
Department of Mathematics, Bangladesh University, Dhaka, Bangladesh.

ABSTRACT

Minimization of transportation time is a great concern of the transportation problems like the cost minimizing transportation problems. In this writing, a transportation algorithm is developed and applied to obtain an Initial Basic Feasible Solution (IBFS) of transportation problems in minimizing transportation time. The developed method has also been illustrated numerically to test the efficiency of the method where it is observed that the proposed method yields a better result.

Minimization of transportation time is a great concern of the transportation problems like the cost minimizing transportation problems. In this writing, a transportation algorithm is developed and applied to obtain an Initial Basic Feasible Solution (IBFS) of transportation problems in minimizing transportation time. The developed method has also been illustrated numerically to test the efficiency of the method where it is observed that the proposed method yields a better result.

Cite this paper

Ahmed, M. , Islam, M. , Katun, M. , Yesmin, S. and Uddin, M. (2015) New Procedure of Finding an Initial Basic Feasible Solution of the Time Minimizing Transportation Problems.*Open Journal of Applied Sciences*, **5**, 634-640. doi: 10.4236/ojapps.2015.510062.

Ahmed, M. , Islam, M. , Katun, M. , Yesmin, S. and Uddin, M. (2015) New Procedure of Finding an Initial Basic Feasible Solution of the Time Minimizing Transportation Problems.

References

[1] Khan, A.R. (2011) A Resolution of the Transportation Problem: An Algorithmic Approach. Jahangirnagar University Journal of Science, 34, 49-62.

[2] Khan, A.R. (2012) Analysis and Resolution of the Transportation Problem: An Algorithmic Approach, M.Phil. Thesis, Department of Mathematics, Jahangirnagar University, Savar.

[3] 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, Sectia Automatica si Calculatoare, LXI (LXV), 1, 39-49.

[4] Khan, A.R., Banerjee, A., Sultana, N. and Islam, M.N. (2015) Solution Analysis of a Transportation Problem: A Comparative Study of Different Algorithms. Bulletin of the Polytechnic Institute of Iasi, Romania, Section Textile, Leathership, in Press.

[5] 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.

[6] Islam, Md.A., Khan, A.R., Uddin, M.S. and Male, M.A. (2012) Determination of Basic Feasible Solution of Transportation Problem: A New Approach. Jahangirnagar University Journal of Science, 35, 101-108.

[7] Islam, Md.A., Haque, Md.M. and Uddin, Md.S. (2012) Extremum Difference Formula on Total Opportunity Cost: A Transportation Cost Minimization Technique. Prime University Journal of Multidisciplinary Quest, 6, 125-130.

[8] Babu, Md.A., Helal, Md.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.

[9] Babu, Md.A., Helal, Md.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.

[10] Babu, Md.A., Das, U.K., Khan, A.R. and Uddin, Md.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.

[11] Uddin, Md.M., Khan, A.R., Roy, S.K. and Uddin, Md.S. (2015) A New Approach For Solving Unbalanced Transportation Problem Due To Additional Supply. Bulletin of the Polytechnic Institute of Iasi, Romania, Section Textile, Leathership, in Press.

[12] Ahmed, M.M., Tanvir, A.S.M., Sultana, S., Mahmud, S. and Uddin, Md.S. (2014) An Effective Modification to Solve Transportation Problems: A Cost Minimization Approach. Annals of Pure and Applied Mathematics, 6, 199-206.

[13] Anam, S., Khan, A.R., Haque, Md.M. and Hadi, R.S. (2012) The Impact of Transportation Cost on Potato Price: A Case Study of Potato Distribution in Bangladesh. The International Journal of Management, 1, 1-12.

[14] Das, U.K., Babu, Md.A., Khan, A.R., Helal, Md.A. and Uddin, Md.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.

[15] Das, U.K., Babu, Md.A., Khan, A.R. and Uddin, Md.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.

[16] Hammer, P.L. (1969) Time Minimizing Transportation Problems. Naval Research Logistics Quarterly, 16, 345-357. Http://Dx.Doi.Org/10.1002/Nav.3800160307

[17] Sharma, J.K. and Swarup, K. (1977) Time Minimizing Transportation Problem. Proceeding of Indian Academy of Sciences, 86, 513-518.

[18] Uddin, M.S. (2012) Transportation Time Minimization: An Algorithm Approach. Journal of Physical Science, 16, 59-64.

[19] Uddin, Md.M., Rahaman, Md.A., Ahmed, F., Uddin, M.S. and Kabir, Md.R. (2013) Minimization of Transportation Cost on the Basis of Time Allocation: An Algorithmic Approach. Jahangirnagar Journal of Mathematics & Mathematical Sciences, 28, 47-53.

[20] Ahmed, M.M. (2014) Algorithmic Approach to Solve Transportation Problems: Minimization of Cost and Time. M. Phil. Thesis, Department Of Mathematics, Jahangirnagar University, Savar.

[21] Garfinkel, R.S. and Rao, M.R. (1971) The Bottleneck Transportation Problem. Naval Research Logistics Quarterly, 18, 465-472. Http://Dx.Doi.Org/10.1002/Nav.3800180404

[22] Szwarc, W. (1971) Some Remarks on the Transportation Problem. Naval Research Logistics Quarterly, 18, 473-485. Http://Dx.Doi.Org/10.1002/Nav.3800180405

[23] Nikolic, I. (2007) Total Time Minimizing Transportation Problem. Yugoslav Journal of Operations Research, 17, 125-133. Http://Dx.Doi.Org/10.2298/YJOR0701125N

[1] Khan, A.R. (2011) A Resolution of the Transportation Problem: An Algorithmic Approach. Jahangirnagar University Journal of Science, 34, 49-62.

[2] Khan, A.R. (2012) Analysis and Resolution of the Transportation Problem: An Algorithmic Approach, M.Phil. Thesis, Department of Mathematics, Jahangirnagar University, Savar.

[3] 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, Sectia Automatica si Calculatoare, LXI (LXV), 1, 39-49.

[4] Khan, A.R., Banerjee, A., Sultana, N. and Islam, M.N. (2015) Solution Analysis of a Transportation Problem: A Comparative Study of Different Algorithms. Bulletin of the Polytechnic Institute of Iasi, Romania, Section Textile, Leathership, in Press.

[5] 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.

[6] Islam, Md.A., Khan, A.R., Uddin, M.S. and Male, M.A. (2012) Determination of Basic Feasible Solution of Transportation Problem: A New Approach. Jahangirnagar University Journal of Science, 35, 101-108.

[7] Islam, Md.A., Haque, Md.M. and Uddin, Md.S. (2012) Extremum Difference Formula on Total Opportunity Cost: A Transportation Cost Minimization Technique. Prime University Journal of Multidisciplinary Quest, 6, 125-130.

[8] Babu, Md.A., Helal, Md.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.

[9] Babu, Md.A., Helal, Md.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.

[10] Babu, Md.A., Das, U.K., Khan, A.R. and Uddin, Md.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.

[11] Uddin, Md.M., Khan, A.R., Roy, S.K. and Uddin, Md.S. (2015) A New Approach For Solving Unbalanced Transportation Problem Due To Additional Supply. Bulletin of the Polytechnic Institute of Iasi, Romania, Section Textile, Leathership, in Press.

[12] Ahmed, M.M., Tanvir, A.S.M., Sultana, S., Mahmud, S. and Uddin, Md.S. (2014) An Effective Modification to Solve Transportation Problems: A Cost Minimization Approach. Annals of Pure and Applied Mathematics, 6, 199-206.

[13] Anam, S., Khan, A.R., Haque, Md.M. and Hadi, R.S. (2012) The Impact of Transportation Cost on Potato Price: A Case Study of Potato Distribution in Bangladesh. The International Journal of Management, 1, 1-12.

[14] Das, U.K., Babu, Md.A., Khan, A.R., Helal, Md.A. and Uddin, Md.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.

[15] Das, U.K., Babu, Md.A., Khan, A.R. and Uddin, Md.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.

[16] Hammer, P.L. (1969) Time Minimizing Transportation Problems. Naval Research Logistics Quarterly, 16, 345-357. Http://Dx.Doi.Org/10.1002/Nav.3800160307

[17] Sharma, J.K. and Swarup, K. (1977) Time Minimizing Transportation Problem. Proceeding of Indian Academy of Sciences, 86, 513-518.

[18] Uddin, M.S. (2012) Transportation Time Minimization: An Algorithm Approach. Journal of Physical Science, 16, 59-64.

[19] Uddin, Md.M., Rahaman, Md.A., Ahmed, F., Uddin, M.S. and Kabir, Md.R. (2013) Minimization of Transportation Cost on the Basis of Time Allocation: An Algorithmic Approach. Jahangirnagar Journal of Mathematics & Mathematical Sciences, 28, 47-53.

[20] Ahmed, M.M. (2014) Algorithmic Approach to Solve Transportation Problems: Minimization of Cost and Time. M. Phil. Thesis, Department Of Mathematics, Jahangirnagar University, Savar.

[21] Garfinkel, R.S. and Rao, M.R. (1971) The Bottleneck Transportation Problem. Naval Research Logistics Quarterly, 18, 465-472. Http://Dx.Doi.Org/10.1002/Nav.3800180404

[22] Szwarc, W. (1971) Some Remarks on the Transportation Problem. Naval Research Logistics Quarterly, 18, 473-485. Http://Dx.Doi.Org/10.1002/Nav.3800180405

[23] Nikolic, I. (2007) Total Time Minimizing Transportation Problem. Yugoslav Journal of Operations Research, 17, 125-133. Http://Dx.Doi.Org/10.2298/YJOR0701125N