Weight evaluation using range of weight ratio under a structured criteria

This paper proposes a weight sum evaluation method that uses a range of weight ratios under a hierarchical structure of criteria and includes an added Data Envelopment Analysis (DEA) viewpoint. In a multi-criteria selection problem, one of the most popular methods to deal with this selection problem is called weighted sum evaluation. This evaluation means that a decision maker decides the criteria's weight and then calculates the weighted sum. The famous Analytic Hierarchy Process (AHP) method is used to solve this problem, which provides many theorems and cases. However, it is difficult to judge to what extent the result of this weighted sum is valid due to several reasons. One reason is that a decision maker must understand the problem to understand the correct weight. But in many cases, because time and cost are limited, such correct understanding is difficult. In addition, even if the decision maker can decide the weight under the circumstances, the alternative which was chosen by weight sum is not perfect because a little difference of the weight affects the evaluation result. Therefore, a sensitivity analysis is recommended in many cases. However, conducting this sensitivity analysis is still difficult because of the existence of many criteria and their hierarchical structure. This paper proposes a new method and applies an example of plant evaluation using the criteria of the Malcom Baldridge National Quality Award (MBNQA), and shows the advantage of proposing such a method.