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
Highlights
A problem often arises with drawing up a plan for transporting homogeneous productы from production centers to consumption centers using vehicles of various types
It is clear that it is impossible to solve such a problem based on the classical transport theory since in the case under consideration the cost of transporting a unit of product depends on the mutual location of production and consumption centers and on the type of transport
This problem, apparently, was first formulated in [3] as a general transport-type problem it was redefined as a multi-index transportation problem in [4], and it was formulated as a transportation problem with intermediate stations in [5]
Summary
A problem often arises with drawing up a plan for transporting homogeneous productы from production centers to consumption centers using vehicles of various types. Additional restrictions on the quantity of the product transported by vehicles of a given type are added to the usual transport constraints This problem, as shown in [1], is a three-index transport problem and is solved by the known method of potentials [1, 2]. Necessity of taking into account intermediate centers and possible differences in assignment of their throughputs make the task nontrivial In this case, nature of distribution of the overall throughput of the system of intermediate centers significantly affects magnitude of total transportation costs.
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