Combining TOPSIS and GRA for supplier selection problem with interval numbers

Abstract

Supplier selection can be regarded as a typical multiple attribute decision-making problem. In real-world situation, the values of the alternative attributes and their weights are always being nondeterministic, and as a result of this, the values are considered interval numbers. In addition, the common approach to measure the similarity between alternatives through their distance suffers from some minor shortcomings. To address these problems, this study develops a novel hybrid decision-making method by combining the technique for order preference by similarity to an ideal solution (TOPSIS) with grey relational analysis (GRA) for supplier selection with interval numbers. By introducing the intervals theory, the extensions of Euclidean distance and grey relational grade are defined. And then a new comprehensive closeness coefficient is constituted for supplier alternatives evaluation based on the interval Euclidean distance and the interval grey relational grade, which could indicate the distance-based similarity and the shape-based similarity simultaneously. A numerical example is taken to validate the flexibility of the proposed method, and result shows that this method can tackle the uncertainty in real-world supplier selection and also help decision makers to effectively select optimal suppliers.

摘要

供应商选择属于典型的多属性决策问题。在实际应用中,备选供应商的属性取值以及属性权重 通常不是确定数值,而是具有一定的不确定性,一般采用区间数进行表达;另外,传统的采用距离测 度度量备选供应商之间相似度的方法存在缺陷。针对这些问题,论文引入区间数理论和灰色系统理论对传统理想解法进行拓展,提出一种基于灰关联分析与理想决策法的区间多属性决策方法,并用于解 决供应商选择问题。该方法构建了基于区间数的欧式距离和基于区间数的灰色关联度,通过对二者进 行有机结合构造了一种新的综合相对贴近度以实现对备选供应商的定量评价。新贴近度同时反映了备选方案与正理想方案和负理想方案之间的位置关系和数据曲线的形状关系,能够更为准确而全面地反 映方案之间的相似或相异程度。最后,通过一个数值算例对所提出的方法进行验证,结果表明该方法 能够有效解决实际不确定条件下的供应商选择问题,为决策者选择最佳供应商提供了一种新的技术途径。