Fuzzy model of nonlinear multi-index transportation problem

Abstract

Traditional problems of transport logistics are formulated in terms of linear programming. In this case, the assumption is that the cost of product transportation at any route is proportional to its volume. In practice, this assumption often is not fulfilled. The objective of the problem then becomes nonlinear. The problem becomes more complicated if it is necessary to take into account that the cost of transportation depends not only on supplier-consumer, but also on the type of cargo, type of vehicles used, etc. The problems that arise in this case become multi-index ones. The article includes a theorem, on which the technology for solving such problems is based. We suggested a method for solving nonlinear fuzzy transportation problems, which is based on a multi-stage decomposition procedure, at each stage of which the problems of smaller dimension are solved. The peculiarities of the procedure are illustrated on two-index problem when the suggested method becomes a two-step procedure. Thus, the blurring of parameters of the objective of the problem is taken into account at the first stage of the decomposition procedure