In this paper, we focus on the theoretical study and numerical solution of a capacitated four-index transportation problem. This model is not properly treated before, it is linked to significant practical problems, some theoretical properties have been shown. We constructed an algorithm for solving the problem, the implementation of the algorithm with its description has led to an encouraging finding for the digital outcome. On the other hand, the initialization method we used avoids unnecessary assignment and the detective method addresses adequately the problems of degeneracy by making the algorithm robust.