An intelligent social-based method for rail-car fleet sizing problem

Freight rail transport is already among the safest and sustainable modes to transport goods, however the rail portion of the overall freight transport market as compared with road transport is small. The utilization of rail-car fleet under limited yard capacity to transport goods is a complex managerial problem in the freight rail network. Rail-car fleet is one of the main capital resources in the railroad industry. Hence, rail operators focus to minimize the size of rail-car fleet. We propose a novel approximation queuing model for the non-myopic dynamic rail-car fleet sizing problem with the objective of maximizing social welfare that improves the utilization of rail freight cars. A Markov decision process (MDP) is proposed to determine an optimal trade-off between the number of rail freight cars and the costs of empty rail-car allocation. A connection between an equilibrium-joining threshold and dynamic pricing policy is also studied where effective customers will join the queue based on their willingness to pay. Our simulation results show that the proposed non-myopic rail-car feet sizing policy improves the average social welfare by 27% compared to the myopic case.