Locomotive Scheduling Under Uncertain Demand

Each day, railroads face the problem of allocating power to trains. Often, power requirements for each train are not known with certainty, and the fleet of locomotives may not be homogeneous. To deal with both of these complications, we formulate a multicommodity flow problem with convex objective function on a timespace network. The convex objective allows us to minimize expected cost under uncertainty by penalizing trip arcs likely to have too little power. Our solution heuristic sends locomotives down the shortest paths (based on marginal arc costs) in the time-space network and then attempts to improve interchanges of locomotives around cycles. Two lower bounds are also developed by relaxing the multicommodity aspect of the problem. In 19 test problems, ranging in size from 15 to 404 arcs, the heuristic performed well, with short running times and costs averaging within 3 percent of the best of the two lower bounds developed.