## Comparison of the results of application of methods for solving the transportation problem of linear programming

DOI 10.51955/2312-1327_2021_2_6

Roxana E. Shipitsyna

Evgeny E. Vitvitsky

Abstract. The article discusses one of the methods of optimizing the transportation planning – a transport linear programming problem. The main methods for finding the reference plan for loaded riders and the optimal plan for solving it are listed. A formal mathematical model and a system of transport problem constraints are presented. A conceptual mathematical model is built on the basis of a formal mathematical model. An example of solving this problem is given: the reference plan of loaded riders was created with the use of the “north-west corner” method, the optimal plan for the return of empty vehicles with the use of the distribution method. Comparison of the results of application of methods for solving the transport problem of linear programming was carried out: comparison of the reference plans obtained with the use of the least-cost and north-west corner methods, comparison of the optimal plans for the return of empty cars obtained with the use of potential and distribution methods. Comparison criteria selected were the number of iterations, labor intensity, the result. Based on this, it was established that the obtained optimal plan for the return of empty cars is the same; according to other comparison criteria, there are a number of differences.

Keywords: linear programming transport problem, mathematical model, baseline plan, optimal plan, solution methods, north-west corner method, minimum-element (least-cost) method, distribution method, potential method.

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