A fuzzy random model for rail freight car fleet sizing problem

•Rail freight car fleet size and allocation problem has been analyzed.•Rail freight transport demand is modeled as a fuzzy random variable.•The problem is based on optimal control theory.•The aim is to find an optimal regulator for a fuzzy linear system•System has a fuzzy quadratic performance index and fuzzy random initial conditions.

In the area of freight transport, the railroads of almost all countries face with strong competition and a prominent trend of market reduction. It has become imperative for rail systems to develop better planned instruments for more rational and efficient utilization of freight cars that represent a great amount of total investments. In this paper a new formulation and a solution procedure is proposed for optimizing the fleet size and freight car allocation in the presence of uncertainty. The uncertainty of the rail freight car demand is often tackled from the traditional probability theory. However, various types of uncertainties and fuzziness are inherent in real rail freight transport operating environment. In this paper, the issue of rail freight car fleet sizing and allocation problem will be addressed under such circumstances. Specifically, an approach based on optimal control theory by considering the fuzziness and randomness for rail freight car demand is developed here. The problem is formulated as the problem of finding an optimal fuzzy regulator for a fuzzy linear system with fuzzy quadratic performance index and fuzzy random initial conditions. Numerical example is given to illustrate the model and solution methodology.