On the Progress in Mathematical Programming Software : Computational Experience with FICO Xpress

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 a solution procedure using a mathematical programming software suite (FICO Xpress) with a modeling system, a parallel MIP (Mixed Integer Programming) solver and a tuning tool for the parameters. The aim of this paper is two-fold. One is to illustrate the computational progress of the mathematical programming software and the other is to verify the effectiveness of the solution procedure, through numerical examples of the model applied to an automobile parts manufacturer

On Describing of Model and Solution Procedure in Mathematical Programming Software

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 problem to be solved is twofold. One part is to improve an interface for model solution, as mathematical modeling requires transformations of the model form. The other is to reduce the computational time required, as the mathematical programming model includes many integral variables. The aim of this paper is to discuss the former problem, and specially to illustrate on describing of model and solution procedure in mathematical programming software