A THEORY FOR MARSHALLING RALLWAY CARS INTO A TRAIN——An Approach to a Multiple Objective Problem

About twefity years ago, on some marshalling yards in China, an empirical method, alled the Tabulation Method, was used to make feasible and effective plans for marshalling railway cars into a train, especially, into a local train. Theoretical studies of this method developed some mathematical models of the nature of of combinatorial optimization. The main part of this paper is a survey of a mathematical theory, called the Theory of Standard Numeration. When there is one loco (there are two locos) in operation on the marshalling yard (one on each side of the yard), this theory says that every feasible plan for making up a local train can be characterized by a finite sequence of binary(ternary) numbers which are called the characterlshc numbers of the cars. If the minimum value of the number of ordered subsequences in a standard partition of the initial train is n (which can easily be obtained by the Tabulation Method)and 2~(m-2)