Analysis and development of compromise solutions in multicriteria transport tasks

Abstract

The object of research is the multicriteria transport problem of linear programming. Simultaneous consideration of several criteria is a problematic problem, since the optimal solutions for different criteria do not coincide. The possible solution of the problem is investigated – finding a way to obtain a compromise solution. Based on the results of the analysis of known methods for solving multicriteria problems (Pareto-set formation, scalarization of the vector criterion, concessions method), the last is justified. To implement the method, an iterative procedure is suggested, in which the initial plan is optimal according to the main criterion. At subsequent iterations, an assignment is made to the main criterion in order to improve the values of the additional criteria. The solution of the problem is continued until a compromise solution is obtained, ensuring the best value for the main criterion, provided that the values for the remaining criteria are no worse than those given. Important advantages of the proposed method: the simplicity of the computational procedure, the grounded technology of forming a new solution at each iteration, realizing the concept of assignment, quality control of the solution obtained at each step. The application of the proposed method opens the prospect of its generalization to the case when the initial data for the solution of the problem contain uncertainty.

Розглянуто метод розв’язання багатокритеріальних транспортних завдань. Запропонована ітераційна процедура, в якій початковий план завдання є оптимальним за основним з критеріїв. На наступних ітераціях реалізується уступка за основним з критеріїв з метою поліпшення значення додаткових. Процедура триває до отримання компромісного рішення. Розглянуто приклади розв’язання задачі.