Solving Multimodal Transport Problems Using Algebraic Approach

Abstract

The paper considers a multicriteria multimodal transport problem, which contains three types of transport and two objective functions. The article investigates the possibility of transforming a multi-criteria multimodal transport problem into a classical transport problem by constructing a system of linear matrix equations and inequalities. It is shown that measurements for the corresponding system of linear matrix equations and inequalities are directly dependent on the number of objective functions of the considered problem. The paper proposes the algorithm for finding the problem reference plans, which is based on finding the reference plans for different types of vehicles. The multicriteria problem is solved using the method of weighted coefficients and the method of sequential concessions according to the relevant criteria. Tools of the computer mathematics system Mathcad were used for the numerical experiment on solving demonstration problems by the methods proposed in the work and for comparing the obtained results. The application of the proposed methods in this paper for solving multicriteria multimodal transport problems allows to reduce the number of iterations in the numerical solution of these problems and to overcome the different measurement problem of the objective functions in their superposition.