Calculation of throughputs of intermediate centers in three-index transportation problems

Abstract

A transportation problem of linear programming with intermediate centers was considered. For cases where throughputs of intermediate centers are not specified, a problem of calculating rational distribution of the total throughput in order to minimize the average value of total transportation costs has been stated. Several options of constructing the method for solving the problem were proposed. The first option implements the iterative procedure of successive improvement of the initial distribution of throughputs of the centers by the Nelder-Mead method. Increase in speed of this method was achieved using the duality theory. The second option is based on a preliminary solution of the problem of finding optimal routes for all pairs "supplier-consumer" taking into account a possible intermediate center. In this case, the usual two-index transportation problem of delivering products from the system of suppliers to the system of consumers arises. The optimal plan of this task contains necessary data to calculate required throughput for each of the intermediate centers. Advantage of this method consists in the possibility of its effective propagation for solving problems with a multilayered structure of intermediate centers.Розглянута транспортна задача лінійного програмування з проміжними центрами, коли значення пропускної здатності проміжних центрів не задані. Поставлена задача розрахунку раціонального розподілу сумарної пропускної здатності з метою мінімізації середнього значення транспортних витрат. Запропоновані ефективні методи розв’язання цієї задачі.