The topic of the paper is the application of dual approach in formulation and resolution of goods distribution tasks problems. The gap in previous goods distribution research is the absence of the methodologies and goods transportation calculation methods for manufacturing companies with not too large amount of goods distribution whereby goods distribution is not the core activity. The goal of this paper is to find a solution for transportation in such companies. In such cases it is not rational to procure a specific software for the improvement of goods transportation but rather apply the calculation presented in this paper. The aim of this paper from mathematical aspect is to show the convenience of switching from the basic geometric interpretation of linear programming applied on transportation tasks to dual approach for the companies with too many costs limitations per transport task but not enough available transportation means. Recent research studies that use dual approach in linear programming are generally not applied to transportation tasks although such approach is very convenient. The goal of the paper is also to resolve transportation tasks by both primal and dual approach in order to prove the correctness of the method.
Gill P, et al. Primal - dual methods for linear programming. Mathematical Programming. 1995;70(1): 251-277. DOI: 10.1007/BF01585940
Kutateladze S. Linear programming and Kantorovich spaces. Journal of Applied and Industrial Mathematics. 2007;1: 137-41. DOI: 10.1134/S1990478907020019
Stojanović V, Spalević LJ, Bozinović M. Software application for solving the transportation problem. International Conference ERK, Portoroz, Slovenia; 2014. p. 23-26.
Soonhong M, Zacharia ZG, Smith CD. Defining supply chain management: In the past, present, and future. Journal of Business Logistics. 2019;40(2): 44-55. DOI: 10.1111/jbl.12201
Philip E, et al. Primal - Dual Methods for Linear Programming. University of California, San Diego, USA. Report number: SOL 91-3, 1994.
Hillier S, Lieberman J. Introduction to Operations Research. New York: Mc Grow Hill Education; 2015.
Mehrotra S. On the implementation of a primal - dual interior point method. SIAM Journal on Optimization. 1993;2(4): 575-601. DOI: 10.1137/0802028
Tošić D. Course of Mathematics III. Belgrade: Naučna knjiga; 1993.
Mc Shane KA, Monma CL, Shanno DF. An implementation of a primal - dual interior point method for linear programming. ORSA Journal on Computing. 1989;1: 70-83. DOI: 10.1287/ijoc.1.2.70
Pratelli A. On the Equality between Monge’s infinum and Kantorovich’s minimum in optimal mass transportation. Annals de L’Institut Henri Poincare (B) Probability and Statistics. 2007;43(1): 1-13. DOI: 10.1016/j.anihpb.2005.12.001
Benamou J-D, et al. Iterative Bergman projections for regularized transportation problems. Society for Industrial and Applied Mathematics, Methods and Algorithms for Scientific Computing. 2015;37(2): A1111-A1138. DOI: 10.1137/141000439
Monteiro RDC, Adler I. Interior path following primal - dual algorithms. Linear Programming. Mathematical Programming, Part I. 1989;44(1): 27-44. DOI: 10.1007/BF02191759
Vukadinović S. Transportation problem in Linear Programming. Belgrade: Naučna knjiga; 1988.
Filić M. [Distribution method in linear programming]. In: Kučinić, et al. Iz matematičkog mozaika. Zagreb, Croatia: Školska knjiga; 1975. Croatian.
Kedia RG. A new variant of simplex method. International Journal of Engineering and Management Research. 2013;3(6): 73-75. Available from: http://www.ijemr.net [Accessed Dec. 2013].
Ghazali Z, et al. Optimal solution of transportation problem using linear programming: A case of a Malaysian Trading Company. Journal of Applied Sciences. 2012;12(23): 2430-20435. DOI: 10.3923/jas
Magano M. A linear programming model for integrated baked production and distribution planning with raw material and routing consideration. Proceedings of the International Conference on Industrial Engineering and Operations Management, 2017, Bogota, Colombia; 2017. ID 261A.
Aydinel M, et al. Optimization of production allocation and transportation of customer orders for a leading forest products company. Mathematical and Computer Modeling. 2008;48(7-8): 1158-1169. DOI: 10.1016/j.mcm.2007.12.025
Rushton A, Croucher P, Baker P. The Handbook of Logistics & Distribution Management. London, U.K: The Chartered Institute of Logistics and Transport; 2010.
Krynke M. Application of linear programming in supply chain management in the foundry. Proceedings 29th International Conference on Metallurgy and Materials. 20-22 May 2020, Brno, Czech Republic; 2020. p. 1280-1286. DOI: 10.37904/metal.2020.3648
Bazaraa MS, Jarvis JJ. Linear Programming and Network Flows. Hoboken, New Jersey: John Wiley & Sons, Inc; 2010.
Sharma K. New dual based procedure for the transportation problem. European Journal of Operational Research. 2000;122(3): 611-624. DOI: 10.1016/S0377-2217(99)00081-8
Schwinn J, Werner R. On the effectiveness of primal and dual heuristics for the transportation problem. Journal of Management Mathematics. 2019;30(3): 281-303. DOI: 10.1093/imaman/dpy011
Sandi C. On a Nonbasic Dual Method for the Transportation Problem. Berlin Heidelberg: Springer Verlag; 1986. p. 65-82.
Schrijver A. On the history of the transportation and maximum flow problems. Mathematical Programming. 2002;91(2002): 437-445. DOI: 101007/s101070100259
Jeffrey A, James J. An algorithm for generating minimum cost network flow problems with specific structure and known optimal solutions. Networks. 1994;24(8): 445-454. DOI: 10.1002/net.3230240805
Manisha V. Application of a dual simplex method to transportation problem to minimize the cost. International Journal of Innovations in Engineering and Science. 2017;2(7). Available from: htpp://w.w.w.ijijes.net [Accessed July 2017].
Wawrzonek J, Ignaciuk S. Dual model for classic transportation problem as a tool for dynamyzing management in a logistics company. An International Quarterly Journal on Economics of Technology and Modeling Processes. 2016;5(3): 95-100. Available from: http://yadda.icm.edu.pl/yadaa/element.baztech-2100f2fe-c687-4756-b5e0-c49822c707e9/c/Wawrzosek.pdf [Accessed Mar. 2016].
Kusraev G, Kutateladze S. Boolean Valued Analysis. Dordrecht, Netherlands: Kluwer Academic Publishers; 1999. DOI: 10.1007/978-94-011-4443-8
Marković B. Optimisation Methods in Transport Organization and Material Handling. Belgrade, Serbia: Tehnikum Taurunum, VIŠSS, Beograd – Zemun; 2019.
Ping J, Chu F. A dual-matrix approach to the transportation problem. Asia – Pacific Journal of Operational Research. 2002;19(1): 35-45.
Sarode M. Application of a dual simplex method to transportation problem to minimize the cost. International Journal of Innovations in Engineering and Science. 2017;2(7); Available from: http://w.w.w.ijies.net [Accessed July 2017].
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