Abstract
Fuzzy axial three-dimensional assignment problem is an extension of axial three-dimensional assignment problems. In this situation, when the assignment cost is fuzzied, we cannot use the traditional algorithms for solving axial three-dimensional assignment problems to solve the variant assignment problem. In reviewing the literatures, we find out that the B&B algorithm is a suitable way to find the exact solution of this kind of problem. However, the existing B&B algorithm has low efficiency as the complete enumerational procedure. For this reason, we propose an improved B&B algorithm for solving fuzzy axial three-dimensional assignment problem called the projected B&B algorithm. We first transfer the fuzzy axial three-dimensional assignment into two dimensions, then use the projection method followed by the Hungarian algorithm to obtain the upper bound of the resulting problem. In this way, we maintain the high accuracy and improve the efficiency. In order to demonstrate the procedure of the proposed algorithm, we present a numerical example in this thesis. Besides, computational results show that the performance of the proposed algorithm is superior to the existing algorithm for solving the fuzzy axial three-dimensional assignment problem.