This paper considers a multi-stage, multi-product production, inventory and transportation system and presents a mathematical programming model of a pull type ordering system based on the concept of kanban system. When we apply a mathematical programming approach to ordering systems, the problems to be solved are( 1) to reduce the computational time because the model includes many integral variables, and( 2) to improve an interface for the model solution because mathematical modeling has required transformations of the model form. In order to tackle the problems, this paper presents an approximate solution procedure using a mixed integer programming(MIP) software with parallel MIP solver and a tuning tool for the parameters. Finally, to verify the effectiveness of the solution procedure and to clarify the applicability of the presented modeling approach, a numerical example of the model applied to an automobile parts manufacturer is shown.