A general system theory approach to rail freight car fleet sizing

The transportation of goods from shippers to consignees is a railroad's major activity. Rail freight cars are enormously expensive and a rail vehicle fleet represents one of the largest capital resources of most railroads. Resource allocation to rail freight cars is an extraordinary complex managerial problem. This paper describes the determination of an optimal number of rail freight cars so as to satisfy the demand, on one hand, and minimize the total cost, on the other. A new mathematical model relying on optimal control theory is developed. The problem is formulated as the problem of finding an optimal regulator for a linear system, excited by Gaussian white noise, a quadratic performance index, and random initial conditions. The model has been tested on numerical examples.