Application of fuzzy linear programming method to examine routing of passenger trains

Abstract

Abstract. 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.Keywords: fuzzy linear programming, passenger flows, routing, passenger trains capacity utilization coefficient. IntroductionThe development of an optimal transport plan of passenger trains on the railway network is related to a preliminary study of passenger flow, utilization of the train capacity and transport demand. Passenger flows are characterized by irregularity regarding hours, days of the week, months, and seasons. In many cases, passenger flows cannot be determined accurately, we cannot get enough real sample data to calculate the parameters by statistical ways. To deal with the problem in a mathematical way, these parameters can be treated as fuzzy variables. Fuzziness appears when the information is vague or is not clearly defined. The Fuzzy set theory allows for the description of real situations, taking into account the uncertainty of the processes. The fuzzy linear programming approach (FLP) is an extension of the linear programming (LP) approach that allows for the incorporation of the uncertainty factor in the construction of a mathematical model to increase the adequacy of the optimization. Fuzzy programming is more flexible and makes it possible to find solutions, which are more satisfactory for the real problem. In FLP, the uncertainty can be present in the objective function and/or in the constraints of the problem, and it can be represented by fuzzy sets. Many researchers have considered various types of the FLP problems and proposed several approaches for solving the FLP problems, [1][2][3][4][5][6].In the field of railway transport the fu...

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“…Stoilova used fuzzy linear programming method to solve the connection between intercity trains and examine routing of passenger trains. e approach presented can be used for other types of transport which could contribute to increasing transport sustainability [23,24]. Wang introduced a fuzzy optimization model based on improved symmetric tolerance approach.…”