Mathematical models used for determining optimal machining conditions are non-linear functions subject to non-linear constraints. In this paper models for unit production cost and unit production time for multi-pass milling operations are developed, taking cutting speed, depth of cut, feed and number of passes as design variables. The problem is then solved by three non-linear programming methods, namely the generalized reduced gradient (GRG) method, the sequential unconstrained minimization technique (SUMT) and the flexible tolerance method. The efficiency of the methods in obtaining the solution is discussed. It is shown through computational experience that their usefulness differs considerably, some parameters in the computer codes used requiring careful selection for the models in question.