The purpose of this study is using methods of CA(Conjoint Analysis) to build the utility function to find the most optimal location of a public service facilities. To that end, this study proposed the Orthogonal design method, through which the process of apply the CA(Conjoint Analysis) methods was effectively and simplify for applying to the actual. The utility function coefficients were extracted by using the linear multiple regression analysis of the SPSS. In this study, Even though this study was limited to the library, one of the public service facilities, the methodology employed by this study is expected to be effectively and significantly applied to other types of pubic service facilities.