Mathematical model of a railroad grain cargo ridesharing service in the form of coalitions in congestion games

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The object of this study is the processes of transportation of grain cargoes based on the principles of ridesharing in railroad systems without observing the traffic schedule for freight trains. In order to study the influence of the model of railroad transportation of grain based on the principles of joint use on the operation of the railroad system, it is proposed to formalize this process under the conditions of the peak load period. It is proposed to formalize the transportation of grain using the ride-sharing service in the form of coalitions in congestion games. It is proposed to turn the game setup into a nonlinear optimization problem. As part of the research, mathematical modeling of the ride-sharing service of railroad transportation of grain cargoes was carried out. Adequacy of the mathematical model was proven. It was established that compliance with the traffic schedule leads to an increase in non-productive downtime of railroad cars after loading, which reduces incentives for the formation of coalitions by shippers. However, according to the results of the simulation, under the conditions of traffic according to the schedule, taking into account the coordination of the shippers and carrier, the transportation indicators are significantly improved. This encourages shippers to form coalitions. It was found that the average duration of shipment transportation decreased by 14.9 % from the indicator according to the scenario of the current transportation model – without observing the schedule. A feature of the results within the framework of the study is that the proposed mathematical model makes it possible to adequately simulate the ride-sharing service of grain transportation in the railroad system. The field of practical application of the results is the railroad industry. The conditions for the practical application of the research results are the importance of implementing digital platforms of aggregators for the coordination of shippers and carriers. Current research will contribute to devising the improvements for grain logistics in railroad transport.