Decision-making for the best selection of suppliers by using minor ANP

There are many studies on the application examples and the definitions of the super-matrix in the Analytic Network Process (ANP). The ANP applies network structures with the alternatives and the criteria to clarify a complex decision-making. It is important to obtain the consent from both the criteria and the alternatives because the evaluation is relative and reciprocal. In addition, there are very few studies on the interaction between the criteria and the alternatives. There is no realistic interpretation of the maximum eigenvalue in the ANP and the negative elements of the criteria matrix. Based on our study, the evaluation with only the alternatives consists of the missing values or the non-square matrix, it is not easy to make. The ANP that contains these irregular alternatives is defined as Minor ANP. Then, we describe these methods of making the priority of only the alternative's matrix values by using the ANP. This study has proven that the missing values in the alternative matrix can be replaced by zeros such that the criteria matrix can be derived without using the inverse alternative matrix. Then, the priority of alternative selection can be obtained through the calculation of eigenvector. An empirical case of the best selection of supplier illustrates our proposed methods for applying to the manufacturing industry. The result reveals the methods can be well adopted in the real world.