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The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems

Author

Listed:
  • A. Charnes

    (Carnegie Institute of Technology)

  • W. W. Cooper

    (Carnegie Institute of Technology)

Abstract

Recent scientific research has made available a variety of tools which can be brought to bear on managerial problems. One of these tools, which has already proved its worth in practical applications, is linear programming. It is not the purpose of this article to explore the full ramifications of these research developments or even to explore the general field of linear programming. Only transportation-type problems and models will be discussed in any detail.

Suggested Citation

  • A. Charnes & W. W. Cooper, 1954. "The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems," Management Science, INFORMS, vol. 1(1), pages 49-69, October.
    • Handle: RePEc:inm:ormnsc:v:1:y:1954:i:1:p:49-69
    DOI: 10.1287/mnsc.1.1.49
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    Cited by:

    1. Mie Augier & Michael Prietula, 2007. "Perspective---Historical Roots of the A Behavioral Theory of the Firm Model at GSIA," Organization Science, INFORMS, vol. 18(3), pages 507-522, June.
    2. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    3. P. Senthil Kumar, 2018. "Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 9(2), pages 73-100, April.
    4. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    5. M. Mathirajan & Sujan Reddy & M. Vimala Rani, 2022. "An experimental study of newly proposed initial basic feasible solution methods for a transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 102-145, March.
    6. S. K. Bharati & S. R. Singh, 2018. "A New Interval-Valued Intuitionistic Fuzzy Numbers: Ranking Methodology and Application," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 363-381, November.
    7. Sumati Mahajan & S. K. Gupta, 2021. "On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions," Annals of Operations Research, Springer, vol. 296(1), pages 211-241, January.
    8. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    9. P. Senthil Kumar, 2018. "A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 9(3), pages 90-122, July.
    10. Muwafaq Mohammed Alkubaisi, 2015. "Modified VOGEL Method to Find Initial Basic Feasible Solution (IBFS) Introducing a New Methodology to Find Best IBFS," Business and Management Research, Business and Management Research, Sciedu Press, vol. 4(2), pages 22-36, June.
    11. Hammond, David Harold, 1968. "Analysis of labor supply by skill and spatial location in NIAD: a functional economic area of Iowa," ISU General Staff Papers 196801010800004670, Iowa State University, Department of Economics.
    12. P. Senthil Kumar, 2020. "Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 37(3), pages 418-451.
    13. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    14. William Lee Croft & Wei Shi & Jörg-Rüdiger Sack & Jean-Pierre Corriveau, 2017. "Comparison of approaches of geographic partitioning for data anonymization," Journal of Geographical Systems, Springer, vol. 19(3), pages 221-248, July.
    15. P. Senthil Kumar, 2016. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 5(4), pages 121-146, October.
    16. Richard L. Church, 2018. "Tobler’s Law and Spatial Optimization," International Regional Science Review, , vol. 41(3), pages 287-310, May.
    17. D’Ambrosio, C. & Gentili, M. & Cerulli, R., 2020. "The optimal value range problem for the Interval (immune) Transportation Problem," Omega, Elsevier, vol. 95(C).
    18. Xie, Fanrong & Butt, Muhammad Munir & Li, Zuoan & Zhu, Linzhi, 2017. "An upper bound on the minimal total cost of the transportation problem with varying demands and supplies," Omega, Elsevier, vol. 68(C), pages 105-118.
    19. Charles, V. & Udhayakumar, A. & Rhymend Uthariaraj, V., 2010. "An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems," European Journal of Operational Research, Elsevier, vol. 201(2), pages 390-398, March.
    20. Christian Ackermann & Felix Hahne & Julia Rieck, 2022. "Matching and Scheduling of Student-Company-Talks for a University IT-Speed Dating Event," SN Operations Research Forum, Springer, vol. 3(3), pages 1-29, September.
    21. Juman, Z.A.M.S. & Hoque, M.A., 2014. "A heuristic solution technique to attain the minimal total cost bounds of transporting a homogeneous product with varying demands and supplies," European Journal of Operational Research, Elsevier, vol. 239(1), pages 146-156.
    22. P. Senthil Kumar, 2018. "A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 29(1), pages 102-129.
    23. Zoltan Lakner & Anna Kiss & Bela Vizvari & Jozsef Popp, 2021. "Trade Liberalisation and Sustainability: A Case Study of Agro-Food Transport Optimisation," European Research Studies Journal, European Research Studies Journal, vol. 0(1), pages 822-839.

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