| Peer-Reviewed

Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP)

Received: 8 March 2015     Accepted: 24 March 2015     Published: 31 March 2015
Views:       Downloads:
Abstract

In this paper, we present a Linear Programming Problem (LPP) to minimize the cost of transportation of NBC, PLC products from three distribution centres to ten depots. Three methods of analysis were considered namely: Integer Programming, simplex method and transportation method via computer packages. The result of the analysis revealed that, the cost of transportation from these distribution centres to all the 10 depots are the same. That is, the optimal cost is N9, 127, 776.

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3)
DOI 10.11648/j.ajtas.20150403.13
Page(s) 85-88
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Constraints, Algorithm, Simplex Methods, Objective Function, Minimizes

References
[1] Aminu, Y.A (1998). Operation Research for Science and Management studies.Ijagbo Best Way Printer, Nigeria.
[2] Aremu, MA (2007). A Linear Programming Approach to Profit Optimization in a Production Mixed System, Nigerian Journal of Science and Technical Research; Vol. 2, No. 1, pp 30 — 39.
[3] Arsham, H (1992). Post optimality analyses of the transportation problem. Journal of the Operational Research Society, Vol. 43, pp. 121-139.
[4] Arsham, H and Khan, A. B (1989). A simplex-type algorithm for general transportation problems. An alternative to stepping-stone. Journal Operational Research Society, Vol. 40(6), pp. 581-590.
[5] Balinski, M.L and Gomory, R. E (1963). A mutual primal-dual simplex method, Recent Advances in Mathematical Programming (Graves and Wolfe, eds), McGraw-Hill, New York.
[6] Ford, L.R and Fulkerson, D.R (1957). A simple algorithm for finding maximal network flows and application to the Hitchcock problem. Canadian Journal of Mathematics, Vol. 9, pp. 210-218.
[7] Fulkerson, D.R (1961). An out-of-kilter method for minimal cost flow problems. Journal of the Society for Industrial and Applied Mathematics, Vol. 9, pp. 18-27
[8] Garvin, W.W (1960). The distribution of a product from a several sources to numerous localities. Journal of Mathematics Physics. Vol. 20, pp. 224-230.
[9] Handy, T (2002). Operations Research- An Introduction (Sixth Edition). Pearson Education Inc.
[10] Henderson, A and Schlaifer, R (1954). Mathematical programming: Better information for better decision-making, Harvard Business Review. Vol. 32, pp.73-100.
[11] Kirca and Stair (1990). A heuristic for obtaining an initial solution for the transportation problem. Journal of Operational Research Society. Vol. 41(9), pp. 865-867.
[12] Kumar, Tapojit (2001). Comparison of Optimization Techniques in large scale Transportations. Journal of undergraduate Research at Minnesota State University, Mankato Vol. 1, Article 10
[13] Lucey,, T (1992). Introduction to Quantitative Techniques. London Publication.
[14] Marower, M.S and Williamson, E(1970). Teach Yourself Operational Research. English University Press.
[15] Poolsap, U. et al (200). Prediction of RNA Secondary Structure with Pseudoknops using integer programming. BMC Bioinformatics, 10 (Suppi. 1), S38.
[16] Sato, K. et al (2011). IPknot: fast and accurate prediction of RNA secondary structures with Pseudoknops using integer programming Bioinformatics, 27; i85 — i93.
[17] Taha, HA (2003). Operational Research: An Introduction. Prentice Hall Inc(Seventh edition), New York, USA.
[18] Winston, W.L (1994). Operation Research; Application and Algorithm (Third Edition). International Thompson Publishing.
Cite This Article
  • APA Style

    Ayansola Olufemi Aderemi, Oyenuga Iyabode Favour, Abimbola Latifat Adebisi. (2015). Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP). American Journal of Theoretical and Applied Statistics, 4(3), 85-88. https://doi.org/10.11648/j.ajtas.20150403.13

    Copy | Download

    ACS Style

    Ayansola Olufemi Aderemi; Oyenuga Iyabode Favour; Abimbola Latifat Adebisi. Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP). Am. J. Theor. Appl. Stat. 2015, 4(3), 85-88. doi: 10.11648/j.ajtas.20150403.13

    Copy | Download

    AMA Style

    Ayansola Olufemi Aderemi, Oyenuga Iyabode Favour, Abimbola Latifat Adebisi. Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP). Am J Theor Appl Stat. 2015;4(3):85-88. doi: 10.11648/j.ajtas.20150403.13

    Copy | Download

  • @article{10.11648/j.ajtas.20150403.13,
      author = {Ayansola Olufemi Aderemi and Oyenuga Iyabode Favour and Abimbola Latifat Adebisi},
      title = {Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP)},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {3},
      pages = {85-88},
      doi = {10.11648/j.ajtas.20150403.13},
      url = {https://doi.org/10.11648/j.ajtas.20150403.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.13},
      abstract = {In this paper, we present a Linear Programming Problem (LPP) to minimize the cost of transportation of NBC, PLC products from three distribution centres to ten depots. Three methods of analysis were considered namely: Integer Programming, simplex method and transportation method via computer packages. The result of the analysis revealed that, the cost of transportation from these distribution centres to all the 10 depots are the same. That is, the optimal cost is N9, 127, 776.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP)
    AU  - Ayansola Olufemi Aderemi
    AU  - Oyenuga Iyabode Favour
    AU  - Abimbola Latifat Adebisi
    Y1  - 2015/03/31
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajtas.20150403.13
    DO  - 10.11648/j.ajtas.20150403.13
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 85
    EP  - 88
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20150403.13
    AB  - In this paper, we present a Linear Programming Problem (LPP) to minimize the cost of transportation of NBC, PLC products from three distribution centres to ten depots. Three methods of analysis were considered namely: Integer Programming, simplex method and transportation method via computer packages. The result of the analysis revealed that, the cost of transportation from these distribution centres to all the 10 depots are the same. That is, the optimal cost is N9, 127, 776.
    VL  - 4
    IS  - 3
    ER  - 

    Copy | Download

Author Information
  • Department of Mathematics and Statistic, The Polytechnic, Ibadan, Oyo State, Nigeria

  • Department of Mathematics and Statistic, The Polytechnic, Ibadan, Oyo State, Nigeria

  • Department of Mathematics and Statistic, The Polytechnic, Ibadan, Oyo State, Nigeria

  • Sections