Estimating order delivery times and fleet capacity in freight rail networks: part II - analytic approximation

Rail transit is a critical component of intermodal supply chain networks. We consider the problem of providing order delivery time quotations in an unscheduled rail network, where customers place orders requiring movement of freight between specified origins and destinations. Each order is fulfilled as soon as the required rolling stock, e.g., locomotive and rake, can be assembled at the origin. Estimating an order's delivery time is a complex task, depending upon the available fleet capacity, deadhead policy and the level of congestion present in the network. In this paper, we develop an analytic approximation to estimate delivery time quotations for freight movements, along with required fleet capacity to meet a desired service level. The quality of the analytic approximation herein is validated using a real numerical example from the Indian Railway system, one of the largest freight carriers in the world.