a fuzzy minimum risk model for the railway transportation planning problem

the railway transportation planning under the fuzzy environment is investigated in this paper. as a main result, a new modeling method, called minimum risk chance-constrained model, is presented based on the credibility measure. for the convenience ofs olving the mathematical model, the crisp equivalents ofc hance functions are analyzed under the condition that the involved fuzzy parameters are trapezoidal fuzzy variables. an approximate model is also constructed for the problem based on an improved discretization method for fuzzy variables and the relevant convergence theorems. to obtain an approximate solution, a tabu search algorithm is designed for the presented model. finally, some numerical experiments are performed to show the applications ofthe model and the algorithm.