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Dual model for classic transportation problem as a tool for dynamizing management in a logistics company

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Abstrakty
EN
Each primary model of the linear programming problem has a corresponding dual model. It is widely accepted that the simplex method, in addition to determining the optimal solution for the original problem, also allows specifying a solution to the dual problem. So far, the dual problem solution has mainly served the post-optimization procedure, i.e. the analysis of modification of the primary model [20, 21, 27, 28]. However, the dual model itself is not generally subject to a deeper study and no conclusions are drawn from its full analysis. The lasting and prominent place that the classic transportation model takes, requires also to be complemented through the full development of its dual problem interpretation, including post-optimization problems. This paper presents and, for the first time, widely interprets the dual model for the classic model of the transportation problem. Moreover, potential possibilities connected with the use of ambiguities of the obtained solutions to the dual problem have been shown. It has been pointed out how these capabilities can be applied to a flexible financial policy of a logistics company.
Twórcy
autor
  • Department of Applied Mathematics and Computer Science, Faculty of Production Engineering, University of Life Sciences in Lublin, Poland Głęboka 28, PL 20 612 Lublin, Poland
autor
  • Department of Applied Mathematics and Computer Science, Faculty of Production Engineering, University of Life Sciences in Lublin, Poland Głęboka 28, PL 20 612 Lublin, Poland
Bibliografia
  • 1. Busłowski A. 2000. Stability of optimal solution of linear programming problem. Published by the University of Białystok, (in Polish).
  • 2. Dantzig, G.B. 1949. Programming in a Linear Structure, Report of the September 9, 1948 meeting in Madison, Econometrica 17, 73–74.
  • 3. Dantzig, G.B. 1951. Application of the Simplex Method to the Transportation Problem, in T.C. Koopmans (ed.), Activity Analysis of Production and Allocation, John Wiley & Sons, New York, 359–373.
  • 4. Dantzig G.B., Thapa M.N. 1997. Linear programming. 1. Introduction. Springer. New York, Berlin, Heidelberg.
  • 5. Dantzig G.B., Thapa M.N. 2003. Linear programming. 2. Theory and extensions. Springer. New York, Berlin, Heidelberg.
  • 6. Glaeser E. L., Shapiro J. M. 2002. Cities And Warfare: The Impact Of Terrorism On Urban Form. Journal of Urban Economics, v51(2,Mar), 205-224.
  • 7. Goryl A., Walkosz A. 2016. Elements of the Operational Research. Linear programming. Cracow University of Economics https.//e-uczelnia.uek.krakow.pl/pluginfile.php/96978/mod_folder/content/0/ProgLin.pdf?forcedownload = 1 (in Polish).
  • 8. Guzik B. 2009. Introduction to Operational Research, published by the University of Economy, Poznań (in Polish).
  • 9. Hitchcock F.L. 1941. The distribution of a product from several sources to numerous localities, Journal of Mathematics and Physics 20, 224–230.
  • 10. Ignaciuk Sz., Wawrzosek J. 2013. Economic aspects of functioning of a biomass distribution network. Logistyka (Pozn.) nr 6 dodatek CD ROM nr 1, 62-68.
  • 11. Julien P-A., Andriambeloson E., Ramangalahy C. 2004. Networks, weak signals and technological innovations among SMEs in the land-based transportation equipment sector. Entrepreneurship & Regional Development: An International Journal, Volume 16, Issue 4.
  • 12. Karmarkar N. 1984. A new polynomial-time algorithm for linear programming. Combinatorica, 4, 373 - 395.
  • 13. Kolman B., Beck R. E. 1995. Elementary Linear Programming with Applications, Computer science and scientific computing, Gulf Professional Publishing, Academic Press.
  • 14. Kukuła K. (ed.) 2007. Operational research in the examples and tasks, collective work, 5th edition, revised and expanded, PWN, Warsaw (in Polish).
  • 15. Liu S.-T. 2003. The total cost bounds of the transportation problem with varying demand and supply, Omega-International Journal of Management Science 31, 247 – 251.
  • 16. MacKenzie C. A., Barker K., Santos J. R. 2014. Modeling a severe supply chain disruption and post-disaster decision making with application to the Japanese earthquake and tsunami, IIE Transactions, Vol. 46, Iss. 12, http.//www.tandfonline.com/doi/full/10.1080/0740817X.2013.876241
  • 17. Reeb J. E., Leavengood S. 2000. Operations Research. Using Duality and Sensitivity Analysis to Interpret Linear Programming Solutions, Oregon State University, https.//catalog.extension.oregonstate.edu/em8744.
  • 18. Sab R. 2014. Economic Impact of Selected Conflicts in the Middle East: What Can We Learn from the Past?. International Monetary Fund, Working Paper No. 14/100.
  • 19. Schrijver A. 2016. On the history of the transportation and maximum flow problems. The Netherlands, and Department of Mathematics, University of Amsterdam http.//homepages.cwi.nl/~lex/files/histtrpclean.pdf
  • 20. Sikora W. 2005. Post-optimization analysis in a closed transport task, Scientific Journals, Poznań University of Economics, 62, 199-214 (in Polish).
  • 21. Sikora W. (ed.) 2008. Operational research, collective work, PWE, Warsaw 2008 (in Polish).
  • 22. Smoluk A. 2008. About the perspective, duality and equilibrium, Statistical Review, Volume 55, no. 2, 5-14 (in Polish).
  • 23. Smoluk A. 2009. About the principle of duality in linear programming, Econometrics, 26, 160-169 (in Polish).
  • 24. Stigler G. 1945. The Cost of Subsistence. Journal of Farm Economics, 27(2), 303-314. http.//www.jstor.org/stable/1231810 .
  • 25. Wawrzosek J., Ignaciuk Sz. 2013. Optimum balancing of the transportation problem as a postoptimization problem regulating the structure of the supply and demand parameters, Episteme (Krak.) Nr 21 t. 1, 539-550, (in Polish).
  • 26. Wawrzosek J., Ignaciuk Sz. 2014. Characteristics of the functioning of agricultural products transportation networks. Teka Komis. Mot. Energ. Rol._Pol. Akad. Nauk., Oddz. Lubl. 2014 T. 14 No 3, 135-140.
  • 27. Wawrzosek J., Ignaciuk Sz. 2015. Use f of extended sensitivity reports of linear programming in emergency medicinal services issues. Logistyka (Pozn.) 2015 nr 4 dodatek CD ROM nr 2 - część 5, 8473-8481 (in Polish) .
  • 28. Wawrzosek J., Ignaciuk Sz. 2016. Optimization and postoptimization at linear dependence of constraints. Part 3 Matrix of dual prices in a balanced transportation problem. (The dissertation under way).
  • 29. Woźniak A. 2011. Operational Research in Logistics and Production Management part. I. Ed. P.W.S.Z. Nowy Sącz (in Polish).
  • 30. Ye X, Han SP, Lin A. 2010. A note on the connection between the primal-dual and the A* algorithm. Int. J. Operations Research and Information Systems, 1(1), 73–85.
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Bibliografia
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