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 time-space 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% of the best of the two lower bounds developed.
OPERATIONS RESEARCH AND RAIL TRANSPORTATION
REVIEW OF RAIL MODELING PROGRESS DESCRIPTION OF RAIL, UNDER DEVELOPMENT IN COOPERATION WITH THE WORLD BANK
A MINI-NETWORK COMPUTER SIMULATION MODEL FOR RAILROAD PLANNING
Operating management of a large railroad must frequently deal with problems which effect major segments of the railroad or possibly even the entire railway system. These types of problems include train scheduling, routing, major track and signal improvements, as well as changes in operating policies. The Chessie System has developed the Mini-Network Model as a tool for aiding management in evaluating the impact of these types of problems and the effect of proposed solutions on operations. The Mini-Network Model is a computer simulation model which has the ability to duplicate over-the-road train operations on single and multiple track territories. The modifier, Mini, is used because, unlike other network models, simulation is performed at the train rather than the car level. When required for the specific application, yard and terminal functions can also be simulated. On single track territory, the model will arrange meets and passes with due consideration given to train priorities, track occupancy and trackwork configurations. The major application of the model has been in preparing for the federal (USA) 12-hours of service law. Under this rule, train crews cannot exceed 12 hours on continuous duty between call and relieve times, which represents a change from the 14 hours previously permitted. The model was used on certain regions of the Chessie System to project what will happen under the new law if schedules and facilities remain unchanged. The effect of proposed additional main tracks, yard improvements, and schedule changes to relieve the operating difficulties imposed by the constraint on crew service hours were also simulated. The end product was a recommendation for train schedule revisions providing satisfactory operations under the new law. The model has also been used to aid in the scheduling of a new train service over an already busy territory and it is currently proposed to use the model in studying the effects of single tracking of a multiple main track territory.