Integrated freight car routing and train scheduling

Rail freight transportation is involved with highly complex logistical processes and requires a lot of resources such as locomotives or wagons. Thus, cost-efficient strategies for routing freight cars in a cargo network are of great interest for railway companies. When it comes to single wagon load traffic, trains are usually formed by collecting individual freight cars into batches at shunting yards, in order to transport them jointly to their destinations. The problem of finding optimal routes and schedules for single freight cars is typically solved in two steps: (i) determining routes for the freight cars in the railway network by solving the Single-freight car routing problem (SCRP), and (ii) deciding on time schedules for trains by solving the freight train scheduling problem (FTSP). Since train departure and arrival times, as well as freight car routes are highly interdependent, one aims to solve the SCRP and the FTSP simultaneously. For smooth and convenient operational processes many railway companies apply the concept of a routing matrix. This matrix defines unique routes between all shunting yards that are used for all shipments. In this work, we present an integrated mathematical model based on time discretization, that jointly solves the SCRP and FTSP and enforces the routing matrix concept. To the best of our knowledge, this is the first work that combines all three aspects. The approach is tailored for Rail Cargo Austria's (RCA) needs, incorporating train capacities, yard capacities, and restrictions regarding travel times. We perform an extensive computational study based on real-world data provided by RCA. Besides the performance we analyze the utilization of trains, waiting times of freight cars, and the number of shunting processes.