Reduced gradient methods
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RAC
S. I. Gass et.al., (eds.), Encyclopedia of Operations Research and Management Science © Kluwer Academic Publishers 2001
688
Rail freight operations
bution centers. Historically, separate fleets were assigned to movements between each assembly plant and distribution center, so that the empty mileage equaled the loaded mileage. In 1979, the Multilevel Reload Program combined all the fleets serving General Motors assembly plants (later expanded to the other major manufacturers) and created an industry group that used an LP to minimize empty movements. This led to an immediate, significant reduction in empty mileage of multilevel cars. By 1981, more than 9,000 cars were managed under this program and the ratio of empty to loaded miles had dropped from 0.95 at the outset to 0.55 for the GM fleet and 0.84 for the Ford fleet. The program was still in operation at the end of 1993. It is noteworthy that the analytic application in both of these very successful programs was only a small part of major institutional changes. As suggested by the number of articles cited in the Dejax and Crainic (1987) review, there has been a great deal of methodological research on car distribution modeling over the last 20 years. Much of this research focused on achieving a better optimization by considering such things as a longer forecast period, variability in demand, or unreliability in travel times (Turnquist and Jordan, 1983). However, as Turnquist and Markowicz (1989) point out, the methodological gains were possible only by making the unrealistic assumption that all vehicles were either identical or completely substitutable. In implementing a car distribution system for CSX Transportation, they therefore used a less advanced network linear program and devoted more attention to the practical aspects of supply and demand.
North American rail industry to determine yard work loads under alternative operating plans (Van Dyke and Davis, 1990). The operating plan implies a trip plan for cars, where a trip plan is the sequence of train movements required to move the car from its origin, through a series of yards, to its destination. For a typical boxcar movement, the shipment will depart on the first available local train after the car is made available by the shipper. The local train is scheduled to bring the car to a nearby yard. The car is next scheduled to move in a particular block that could move on various outbound trains. The car can be scheduled to the first outbound train whose cut-off is later than the car's scheduled arrival time. This process is repeated until the car has a scheduled arrival time at its destination. The first computerized freight car scheduling system was developed by the Missouri Pacific Railroad (1976). In 1991, the rail industry established a plan to implement inter-line car scheduling as a major element of interline service measurement (Ad Hoc Committee, 1991). Predicting the time required for a train connection is the most difficult portion of car scheduling and it is also a critical problem in est
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