Application of Fuzzy Linear Programming Method to Examine Routing of Passenger Trains

The aim of this study is to develop a methodology for selection of routing of different categories of intercity passenger trains taking into account of the uncertainty of the processes and using the fuzzy linear programming method. The fuzzy theory allows for the presentation of real data with uncertainty due to imprecise measurement. This research studies the fuzzy problems with fuzzy constraints of passengers and with fuzzy triangular numbers as coefficients of the technological matrix that presents how full a train is. As a criterion of the optimization minimum direct operating costs are used. The restrictive conditions of the model include: satisfying the demand for railway transport by sections of the railway network; capacity of the sections; required minimum frequency; available compositions in exploitation; integer and positive decision. The fuzzy linear problem has been reduced to parametric linear programming. Taking into account the parameter, the limits of amendment of the optimal number of trains depending on passenger flows have been defined. The application of the methodology makes it possible to study the impact of the fluctuations in passenger flows on the number of trains. The decision approach proposed in this paper was tested for Bulgarian rail network and proposed an organization of railway passenger transport. The approach presented here can also be used for solving the scheme of transportation for other types of transport.