Optimal component tolerances can reduce product cost and improve enterprise competitiveness. In order to obtain optimal tolerances accurately and efficiently, analytical methods are applied to solve tolerance optimization model. In this article, both manufacturing cost and quality loss are included in the total cost, and two kinds of constraints, including assembly tolerance constraint and process accuracy constraints, are considered in the tolerance optimization model. In order to allocate the optimal tolerances among the related components, the following procedure is presented. First, the two kinds of constraints are ignored, and analytical method is applied to find the initial values of component tolerances. If the initial component tolerances cannot satisfy assembly tolerance constraint, the Lagrange multiplier method is executed and the Lambert W function is applied to solve the corresponding equations to obtain the new values of component tolerances. Then, process accuracy constraints are satisfied through the adjustment of component tolerances. Finally, an example is used to demonstrate the effectiveness of the method proposed in this article.