The evaluation of assignment problems for job suppliers is necessary to meet demands; therefore, academics in the operations research field and management factories have paid considerable attention to assignment problems. Notably, because the central point of classical assignment models with parameters assumes that supplier management oversees all inputs and outputs are fixed data, these types of models cannot provide exact and accurate data. Hence, specific inputs and/or outputs can be improper and ambiguous. Consequently, existing studies have explored various approaches to determine an optimal route that corresponds to assignments to suppliers when ambiguous values are involved. However, the computation of multiple routes for each assignment problem has yet to be explored. Thus, the objectives of this paper propose a new hybrid approach that combines the average ranking method (ARM) with triangular ambiguous values and a super-efficient approach in graph theory, called the brute force method (BFM), which can obtain multiple route results. The proposed method is advantageous in identifying supplier rankings and distinguishing between efficient and inefficient suppliers. The numerical results show that different routes to achieve optimality, which affirms the benefit of developing the proposed method in this article.
