A branch and bound approach for solving quadratic product design model and its linear programming transformation

被引：0

作者：

Jiang, Dongxiao ^{[1
]}

Shinzato, Takashi ^{[1
]}

Hoshino, Mitsuhiro ^{[1
]}

Zhang, Renqian ^{[2
]}

Kaku, Ikou ^{[3
]}

机构：

[1] Graduate School of Systems Science and Technology, Akita Prefectural University, Japan

[2] School of Management Science and Engineering, Beijing University of Aeronautics and Astronautics, China

[3] School of Environmental and Information Studies, Tokyo City University, Japan

来源：

Journal of Japan Industrial Management Association | 2014年 / 65卷 / 01期

关键词：

Linear transformations - Linear programming - Product design - Combinatorial optimization - Quadratic programming - Quality function deployment;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In past decades, methods such as quality function deployment (QFD) and the design structure matrix (DSM) have been adopted for quantitative evaluation of product design. QFD involves ideal product design that holds the maximum overall impact value of design rules on design requirements, while DSM rearranges clusters of devices based on the functional dependence among devices. However, QFD does not show the relationships among functions, while DSM can represent the functional relationships in an existing product but cannot provide a creative logic design to develop new product architecture. In this paper, a novel product design model, as a new product design approach, is proposed in terms of total revenue using a quadratic combinatorial optimization model. Our model is characterized by two distinct parts. One is single revenue of the interface itself (connects pair of functional devices) as discussed in previous works. The other one is the correlation revenue, which is one of our contributions. Among distinct interfaces, these revenues are obtained as local properties in a given product. Since it is difficult to solve the proposed quadratic model directly, we transfer the quadratic one to a simple linear programming form without changing its identity and propose a branch-and-bound algorithm to resolve the transferred model. Numerical experiments are provided to show the efficiency and utility of the algorithm. As a result, optimal solution of an applicative 16-device case (close to real world) can be obtained in a reasonable number of calculations.

引用

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