In this paper, we readdress a layout design problem, PTL[3], for determining an optimal 3-class-based dedicated linear storage layout in a class of unit load storage systems. Based on some fundamental properties derived, we provide a converging exact algorithm with O(n[logn]), which is more efficient than that of Yang and Kim [8] and can be applied to PTL[K] with $K{ge}4$ in order to reduce computational execution time. In addition, we prove that the necessary condition suggested by them is also a sufficient condition to PTL[3].