Advertisement

OPSEARCH

pp 1–25 | Cite as

A heuristic for obtaining better initial feasible solution to the transportation problem

  • Md. Ashraful Babu
  • M. A. HoqueEmail author
  • Md. Sharif Uddin
Theoretical Article
  • 11 Downloads

Abstract

Vogel’s Approximation Method (VAM) is known as the best algorithm for generating an efficient initial feasible solution to the transportation problem. We demonstrate that VAM has some limitations and computational blunders. To overcome these limitations we develop an Improved Vogel’s Approximation Method (IVAM) by correcting these blunders. It is compared with VAM on obtained initial feasible solutions to a numerical example problem. Reduction in the total transportation cost over VAM by IVAM is found to be 2.27%. Besides, we have compared IVAM with each of twelve previously developed methods including VAM on solutions to numerical problems. IVAM leads to the minimal total cost solutions to seven, better solutions to four and the same better solution to the remaining one. Finally, a statistical analysis has been performed over the results of 1500 randomly generated transportation problems with fifteen distinct dimensions, where each of them has 100 problems instances. This analysis has demonstrated better performance of IVAM over VAM by reducing the total transportation cost in 71.8% of solved problems, especially for large size problems. Thus IVAM outperforms VAM by providing better initial feasible to the transportation problem.

Keywords

Transportation problem VAM IVAM Initial feasible solution Minimal cost solution 

Notes

References

  1. 1.
    Hochbaum, D.S., Woeginger, G.J.: A linear-time algorithm for the bottleneck transportation problem with a fixed number of sources. Oper Res Lett 24(1), 25–28 (1999)CrossRefGoogle Scholar
  2. 2.
    Baidya, A.: Stochastic supply chain, transportation models: implementations and benefits. OPSEARCH (2019).  https://doi.org/10.1007/s12597-019-00370-7 CrossRefGoogle Scholar
  3. 3.
    Sharma, R.R.K., Sharma, K.D.: A new dual based procedure for the transportation problem. Eur. J. Oper. Res. 122(3), 611–624 (2000)CrossRefGoogle Scholar
  4. 4.
    Sabbagh, M.S., Ghafari, H., Mousavi, S.R.: A new hybrid algorithm for the balanced transportation problem. Comput. Ind. Eng. 82, 115–126 (2015)CrossRefGoogle Scholar
  5. 5.
    Dash, S., Mohanty, S.P.: Uncertain transportation model with rough unit cost, demand and supply. OPSEARCH (2018).  https://doi.org/10.1007/s12597-017-0317-6 CrossRefGoogle Scholar
  6. 6.
    Liu, S.: The total cost bounds of the transportation problem with varying demand and supply. Omega 31(4), 247–251 (2003)CrossRefGoogle Scholar
  7. 7.
    Juman, Z.A.M.S., Hoque, M.A.: A heuristic solution technique to attain the minimal total cost bounds of transporting a homogeneous product with varying demands and supplies. Eur. J. Oper. Res. 239(1), 146–156 (2014)CrossRefGoogle Scholar
  8. 8.
    Ahmad, F., Adhami, A.Y.: Total cost measures with probabilistic cost function under varying supply and demand in transportation problem. OPSEARCH (2019).  https://doi.org/10.1007/s12597-019-00364-5 CrossRefGoogle Scholar
  9. 9.
    Khurana, A., Adlakha, V.: On multi-index fixed charge bi-criterion transportation problem. OPSEARCH 52, 733 (2015).  https://doi.org/10.1007/s12597-015-0212-y CrossRefGoogle Scholar
  10. 10.
    Adlakha, V., Kowalski, K., Vemuganti, R.R.: Heuristic algorithms for the fixed-charge transportation problem. OPSEARCH (2006).  https://doi.org/10.1007/BF03398770 CrossRefGoogle Scholar
  11. 11.
    Gupta, S., Ali, I., Ahmed, A.: Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment. OPSEARCH (2018).  https://doi.org/10.1007/s12597-018-0330-4 CrossRefGoogle Scholar
  12. 12.
    Gupta, K., Arora, R.: More for less method to minimize the unit transportation cost of a capacitated transportation problem with bounds on rim conditions. OPSEARCH (2017).  https://doi.org/10.1007/s12597-016-0288-z CrossRefGoogle Scholar
  13. 13.
    Charnes, A., Cooper, W.W., Henderson, A.: An Introduction to Linear programming. Wiley, New Work (1953)Google Scholar
  14. 14.
    Reinfeld, N.V., Vogel, W.R.: Mathematical Programming. Prentice-Hall, Englewood Cliffs (1958)Google Scholar
  15. 15.
    Babu, M.A., Helal, M.A., Hasan, M.S., Das, U.K.: Lowest allocation method (LAM): a new approach to obtain feasible solution of transportation model. Int J Sci Eng Res 4(11), 1344–1348 (2013)Google Scholar
  16. 16.
    Babu, M.A., Helal, M.A., Hasan, M.S., Das, U.K.: Implied cost method (ICM): an alternative approach to find the feasible solution of transportation problem. Glob J Sci Front Res F Math Decis Sci 14(1), 5–13 (2014)Google Scholar
  17. 17.
    Ali, M.A.M., Sik, Y.H.: Transportation problem: a special case for linear programing problems in mining engineering. Int J Min Sci Technol 22(3), 371–377 (2012)CrossRefGoogle Scholar
  18. 18.
    Soomro, A.S., Junaid, M., Tularam, G.A.: Modified Vogel’s approximation method for solving transportation problems. Math Theory Model 5(4), 32–42 (2015)Google Scholar
  19. 19.
    Alkubaisi, M.: Modified VOGEL method to find initial basic feasible solution (IBFS)—introducing a new methodology to find best IBFS. Bus Manag Res 4(2), 22–36 (2015)CrossRefGoogle Scholar
  20. 20.
    Akpan, S., Usen, J., Ajah, O.: A modified Vogel approximation method for solving balanced transportation problems. Am Sci Res J Eng Technol Sci (ASRJETS) 14(3), 289–302 (2015)Google Scholar
  21. 21.
    Kasana, H.S., Kumar, K.D.: Introductory Operations Research: Theory and Applications. Springer, New Delhi (2005)Google Scholar
  22. 22.
    Kirca, O., Satir, A.: A heuristic for obtaining an initial solution for the transportation problem. J. Oper. Res. Soc. 41(9), 865–871 (1990)CrossRefGoogle Scholar
  23. 23.
    Korukoğlu, S., Balli, S.: An improved Vogel’s approximation method for the transportation problem. Math Comput Appl 16(2), 370–381 (2011)Google Scholar
  24. 24.
    Ullah, M.W., Uddin, M.A., Kawser, R.: A modified Vogel’s approximation method for obtaining a good primal solution of transportation problems. Ann Pure Appl Math 11(1), 63–71 (2016)Google Scholar
  25. 25.
    Mathirajan, M., Meenakshi, B.: Experimental analysis of some variants of Vogel’s approximation method. Asia Pac J Oper Res 21, 447–462 (2004)CrossRefGoogle Scholar
  26. 26.
    Shimshak, D.G., Kaslik, J.A., Barclay, T.D.: A modification of Vogel’s approximation method through the use of heuristic. INEOR 19, 259–263 (1981)Google Scholar
  27. 27.
    Goyal, S.K.: Improving VAM for unbalanced transportation problems. J. Oper. Res. Soc. 35(12), 1113–1114 (1984)CrossRefGoogle Scholar
  28. 28.
    Balakrishnan, N.: Modified Vogel’s approximation method for the unbalanced transportation problem. Appl Math Lett 3(2), 9–11 (1990)CrossRefGoogle Scholar
  29. 29.
    Ramakrishnan, C.S.: An improvement to Goyal’s modified VAM for the unbalanced transportation problem. J. Oper. Res. Soc. 39(6), 609–610 (1988)CrossRefGoogle Scholar
  30. 30.
    Brenner, U.: A faster polynomial algorithm for the unbalanced Hitchcock transportation problem. Oper Res Lett 36(4), 408–413 (2008)CrossRefGoogle Scholar
  31. 31.
    Juman, Z.A.M.S., Hoque, M.A.: An efficient heuristic to obtain a better initial feasible solution to the transportation problem. Appl. Soft Comput. 34, 813–826 (2015)CrossRefGoogle Scholar
  32. 32.
    Juman, Z.A.M.S., Hoque, M.A., Buhari, M.I.: A sensitivity analysis and an implementation of the well-known Vogel’s approximation method for solving an unbalanced transportation problem, Malays. J Sci 32(1), 66–72 (2013)Google Scholar
  33. 33.
    Vasko, F.J., Storozhyshina, N.: Balancing a transportation problem: is it really that simple? OR Insight 24(3), 205–214 (2011)CrossRefGoogle Scholar
  34. 34.
    Das, U.K., Babu, M.A., Khan, A.R., Uddin, M.S.: Advanced Vogel’s approximation method (AVAM): a new approach to determine penalty cost for better feasible solution of transportation problem. Int J Eng Res Technol (IJERT) 3(1), 182–187 (2014)CrossRefGoogle Scholar
  35. 35.
    Das, U.K., Babu, M.A., Khan, A.R., Uddin, M.S.: Logical development of Vogel’s approximation method (LD-VAM): an approach to find basic feasible solution of transportation problem. Int J Sci Technol Res 3(2), 42–48 (2014)Google Scholar
  36. 36.
    Babu, M.A., Das, U.K., Khan, A.R., Uddin, M.S.: A simple experimental analysis on transportation problem: a new approach to allocate zero supply or demand for all transportation algorithm. Int J Eng Res Appl (IJERA) 4(1), 418–422 (2014)Google Scholar
  37. 37.
    Das, U.K., Babu, M.A., Uddin, M.S.: OTPA-Optimized Transportation Problem Algorithm, A Web Based Software Tool. http://www.otpa.info. (2014c)
  38. 38.
    Taha, H.A.: TORA-Temporary Ordered Routing AlgorithmGoogle Scholar
  39. 39.
    DasGupta, A.: Normal approximations and the central limit theorem. In: Fundamentals of Probability: A First Course. Springer texts in statistics, Springer, New York (2010).  https://doi.org/10.1007/978-1-4419-5780-1_10 Google Scholar
  40. 40.
    Feller, W.: An Introduction to Probability Theory and Its Applications, vol. I. Wiley, New York (1968)Google Scholar
  41. 41.
    Feller, W.: Introduction to Probability Theory and Its Applications, vol. II. Wiley, New York (1971)Google Scholar
  42. 42.
    Pitman, J.: Probability. Springer, New York (1992)Google Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  • Md. Ashraful Babu
    • 1
  • M. A. Hoque
    • 2
    Email author
  • Md. Sharif Uddin
    • 3
  1. 1.Department of Quantitative Sciences (Mathematics)International University of Business Agriculture and TechnologyDhakaBangladesh
  2. 2.BRAC Business SchoolBRAC UniversityDhakaBangladesh
  3. 3.Department of MathematicsJahangirnagar UniversityDhakaBangladesh

Personalised recommendations