Uncertain models on railway transportation planning problem

This paper investigates the frequency service network design problem in a railway freight transportation system, in which the fixed charge and transportation costs are both nondeterministic. In order to deal with nondeterministic system, uncertain variables are introduced. Here we propose two uncertain programming models, namely, budget-constrained model and possibility-constrained model, to design the fright transportation system. It is proved that the possibility-constrained model can be transformed to an equivalent deterministic transportation model using inverse uncertainty distribution. Based on this equivalence relation, the possibility-constrained optimal transportation plan can be obtained and then the solution of the budget-constrained model can be approximated. Finally, the idea of uncertain models is illustrated by a numerical experiment.