When a product is designed, tolerances must be given to the product so that required functions are guaranteed and production costs are minimized. In this research, a model is suggested which allocates tolerances to components optimally according to the STA(Statistical Tolerance Allocation) method. Taking into account the concept that dimensional errors have characteristics of statistical distributions, this model presents the discrete pseudo-boolean approach for the tolerance optimization by minimizing the tolerance cost and the quality loss cost. In this approach, two methods are proposed for the reduction of the problem scale; 1) a method for converting the minimization model for casts into the maximization model for cost savings, and 2) procedures to reduce the number of constraints and variables.