For achieving the minimum cutting cost, it is necessary to find the method for determining the optimum assigned operation for the multi-stage manufacturing system (i. e. a machiningcenter or NC-machine tools combining some operations), and to determine the optimum cutting variables for each operation corresponding to the assignment. In order to find the optimum assignment for the multi-stage manufacturing system, the dynamic programing has been applied to the numerical model for it, which is given by transforming the optimum assignment of operations to the optimum job allocation for each operation, in such a way that the precedence relations are not violated.