Robustness Analysis
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R Chart
Rail Freight Operations
A quality control chart that shows the variations in the ranges of samples.
Carl D. Martland Massachusetts Institute of Technology, Cambridge, MA, USA
See Introduction ▶ Quality Control Chart ▶X
R&D ▶ Research and Development
RAC ▶ Operations Research Office and Research Analysis Corporation
Radon-Nikodym Derivative If measure P is absolutely continuous w.r.t. measure Q, then dP/dQ is called the Radon-Nikodym derivative. For example, if P is a probability measure (distribution) for a continuous random variable and Q is Lebesgue measure, then the Radon-Nikodym derivative corresponds to the probability density function.
In North America, the railroad industry is predominantly privately owned and overwhelmingly oriented toward freight rather than passenger operations. An emphasis on profitability and practical problems has been a characteristic of OR/MS applications in the rail industry. This article focuses on freight car utilization, operations planning and control, and line dispatching, the three rail areas that have had the longest history of successful OR/MS applications.
Freight Car Utilization There are three main issues in freight car utilization: fleet sizing, allocation of equipment to specific services, and distribution of empty equipment. Each of these issues is complicated by the fact that cars are interchanged among the North American railroads. A complex set of rules has been developed for the use of “foreign” cars owned by another railroad or “private” cars owned by a shipper or a car-supply company. The Freight Car Utilization Research/Demonstration Program (1980), jointly established in 1975 by the Association of American Railroads and the Federal Railroad Administration, conducted a series of studies addressing all facets of freight car utilization. Each study was supervised by an
S.I. Gass, M.C. Fu (eds.), Encyclopedia of Operations Research and Management Science, DOI 10.1007/978-1-4419-1153-7, # Springer Science+Business Media New York 2013
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industry task force in order to promote consideration of the most important issues, to provide access to data, and to enhance implementation. Task Force I-2 (1977), for example, developed an integrated set of performance measures for car utilization and showed how these measures could be used in both fleet sizing and fleet allocation decisions. The process of moving cars from an unloading point to a location where they can be reloaded is called empty car distribution. Railroads typically try to hold enough empty cars at each major yard to cover the expected demand in the surrounding region; extra cars can be sent to locations where additional, or more profitable, loads are required. Southern Railway was a leader in the application of linear programming (LP) to car distribution (AAR 1976). They divided the railroad into 37 zones and created monthly supply and demand estimates for each of 13 car types. They then used a linear program to define flow rules that determined where local car distributors should se
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