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A certain class of integer programming problems, called asymptotic or steady-state, has been shown by Gomory to be cost equivalent to a group-optimization problem. This paper extends the algebraic characterization by demonstrating that there are cost-equivalent group problems for all integer programming problems. Finally, the result is interpreted from the viewpoint of dynamic programming, and this provides the turnpike theorem.
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Jeremy F. Shapiro (1970) studied this question.
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