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We discuss the modeling and reformulation of a resource allocation problem, the assignment of Graduate Teaching Assistants to courses in the University of Nebraska-Lincoln Computer Science Department. We formulate this problem as a non-binary Constraint Satisfaction Problem (CSP) and provide a new convention for consistency checking to deal with the over-constraindness of the problem and the practical requirement of our application. We introduce a new decomposable non-binary constraint, which we call confinement constraint, and describe its relevance in practical requirements of our application. We introduce an new decomposable non-binary constraint, which we call confinement constraint, and describe its relevance in practical settings. We discuss the reformulation of confinement constraints and equality constraints into an equivalent network of binary constraints. Empirical evaluations on three sets of real-world data demonstrate the benefit of such reformulations in reducing the processing time to reach equivalent solution.