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.
Analytical Models In Rail Transportation: An Annotated Bibliography
This research has been supported, in part, by the U.S. Department of Transportation under contract DOT-TSC-1058, Transportation Advanced Research Program (TARP).
Thorium in monazite sand; separation and determination by precipitation from homogeneous solution
A new method is described which consists of three steps: (1) decomposition of the monazite sand with perchloric acid; (2) separation of thorium and the rare earths by hydrolysis of methyl-oxalate in acid solution; and (3) separation of thorium from the rare earths by hydrolysis of urea in the presence of formic acid. The authors consider the method to be accurate and rapid.